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DAUGAVPILS UNIVERSITY

THE FACULTY OF NATURAL SCIENCES AND MATHEMATICS

THE DEPARTMENT OF MATHEMATICS

The Doctoral study programme “Mathematics”

(code 5146001)Sub-branch "Differential equations"

Director of the programme: Dr.habil.math., prof. Felix Sadyrbaev

ConfirmedAt the meeting of the DU Scientific Council

June 1, 2004

Record No 7

ConfirmedAt the meeting of the

Council of the DU Senate

June 21, 2004

Record No 7

The president of the Council

prof. A. Barshevskis

The president of the Senate

as.prof. V. Shaudina

Daugavpils 2004

Contents

1. General Character of the Study Programme................................................4

2. Doctoral Study Programme............................................................................4

2.1. Requirements for the applicants and entrance examinations....................42.2. Content and Organization..........................................................................5

2.2.1. Content of the programme...................................................................52.2.2. Study organization in the doctoral programme...................................62.2.3. Supervision and working out of the promotion thesis.........................7

3. System of study quality assessment...............................................................8

4. Study Programme Assurance.........................................................................9

4.1. Academic staff............................................................................................94.2. Financing....................................................................................................94.3. Material and technical provision...............................................................9

5. Students..........................................................................................................10

6. Advertising and Information about Study Possibilities.............................10

7. Scientific Research of the University Lecturers and the Doctor’s degree Students..............................................................................................................11

7.1. Participation in Research Projects..........................................................117.2. Participation in Conferences....................................................................11

7.2.1. University lecturers’ participation in Conferences............................117.2.2. Doctor’s degree Students’ participation in Conferences...................13

7.3. Publications..............................................................................................147.3.1. University lecturers’ publications.....................................................147.3.2. Publications of the Doctor’s degree Students....................................18

8. Information about the Cooperation with other DU structure units and other Latvian and foreign Universities during the realization of the programme.........................................................................................................19

9. Comparison of the Programme with the programmes of other universities.........................................................................................................19

9.1. Comparison with the LU doctoral study programme...............................199.2. Comparison with the programme “Doctor of Philosophy” of Utah State University, USA...............................................................................................209.3. Comparison with the Silesian University (Opava, the Czech Republic) doctoral study programme..............................................................................219.3. Comparison with the doctoral study programme of Vilnius University (Lithuania).......................................................................................................21

10. Development of the Programme................................................................22

11. Self-assessment of the Programme............................................................23

12. Annotations of the study programme courses..........................................23Optional specialized courses.......................................................................24

13. List of Appendices.......................................................................................24

Appendix 1. Set of questions for the entrance examination in mathematics...25Appendix 2. Expanded course content............................................................28Appendix 3. Set questions for the final examination in mathematics..............46Appendix 4. Lecturers’ Curriculum Vitae.......................................................48Appendix 5. List of lecturers’ most important publications............................68

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1. General Character of the Study Programme

The doctoral study programme in mathematics is realized in the sub-branch of differential equations during full-time studies.

The study programme is to be acquired in 6 semesters (3 academic years).The study process is organized in conformity with the DU Satversme

(Constitution), the Law on Higher Education and other normative documents valid in the Republic of Latvia, as well as in conformity with DU study by-laws adopted by the DU Senate.

The precondition for the implementation of the programme is the body of researchers and lecturers of the DU Department of Mathematics who in some perspective are able to carry out research in theoretical mathematics, mainly in differential equation theory and branches relating to it, thus approaching the European level.

The aim of the study programme is to prepare highly qualified specialists in mathematics who are able to advance and independently solve the essential problems of contemporary mathematics.

Objectives of the programme: to impart knowledge in the sub-branch of differential equations adequate to

the contemporary level of mathematics; to acquire research methods of contemporary mathematics; to practise the management of research and study work in a higher education

establishment; to create for the Doctor’s degree students optimal conditions for research –

possibilities to use library and contemporary information technologies, to regularly participate in scientific conferences in Latvia and abroad, to have in – service training at other universities and research centres;

to provide conditions for preparing and defending the promotion thesis.The topicality of the study programme is determined by the following

factors: the necessity to prepare highly qualified researchers in mathematics for the

areas of Eastern Latvia; the development of the DU scientific potential will promote knowledge based

development of economy, education and culture of the areas of Eastern Latvia, thus promoting the development of natural sciences in whole Latvia.

2. Doctoral Study Programme

2.1. Requirements for the applicants and entrance examinations

Requirements for the applicants: master’s degree in mathematics.Entrance examinations:

an examination in mathematics (see examination tasks in appendix 1); a report on the theme chosen and a discussion on the report;

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a discussion in a foreign language.

2.2. Content and Organization

2.2.1. Content of the programme

The doctoral study programme is organically linked with bachelor and master study programmes. All programmes together make up an undivided system of DU education in mathematics.

The doctoral study programme comprises lecture courses, seminars and independent research of the Doctor’s degree students.

Course title Credit points

Form of assessment

Responsible teaching staff

The study of theoretical findings (32 KP)

Obligatory courses (28KP)

Differential equations. The main course 8 a credit, an exam

Dr.h.mat., prof. F. SadyrbaevDr.mat., as.prof. V. Starcevs

Computers for mathematics 4 a credit Dr.mat., doc. A. GritsansEnglish for mathematicians 8 3 credits Dr.h.filol., prof. Z. Ikere

Dr.h.mat., prof. F. SadyrbaevApproximative methods of solutions of ordinary differential equations

4 a credit Dr.mat., as.prof. O. Lietuvietis

Selections from the spline theory 4 a credit Dr.mat., as.prof. S. Asmuss

Optional specialized courses (4KP)

Actual problems in the theory of differential equations

4 a credit Dr.h.mat., prof. F. Sadyrbaev

Methods of the theory of boundary value problems for ordinary differential equations


Boundary value problems for ordinary differential equations


Approbation of theoretical findings (88 KP)

Specialized department seminars 12 6 credits Dr.mat., as.prof. V. StarcevsWorking out of the promotion thesis 76 3 credits Dr.h.mat., prof. F. Sadyrbaev

Dr.mat., doc. A. Gritsansfinal examination in mathematics Final examination in EnglishIn total 120 credit point

The expanded content of the courses see in appendix 2.Final examination tasks see in appendix 3.

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2.2.2. Study organization in the doctoral programme

The length of studies in the doctoral programme is 6 semesters (3 academic years). The study of theoretical findings.

In a month’s time after enrolment, the Doctor’s degree student together with his/her scientific supervisor, make up an individual plan for work, in which the dates of examinations in theoretical courses and tests are pointed out (see the study plan below).

Obligatory courses.1st study year. In the course "Computers for Mathematics" the Doctor’s

degree students are to acquire both the use of special computer programmes in mathematic calculations (MathCad, Maple, Mathematica) and the use of TeX systems (MiKTeX) for designing mathematical texts. The course "English for mathematicians" introduces Doctor’s degree students to the terminology used in the differential equation theory and to Contemporary English spelling used in texts on mathematics.. Both the above mentioned courses serve, on the one hand, to enable the student to read the latest scientific literature on differential equation theory without any assistance, make reports at conferences and seminars and, on the other hand, to enable them to prepare their publications and submit them to journal editorial boards in conformity with the requirements. In course "Differential equations. The main course" introduces the students to the fundamentals of the general theory of differential equations.

2nd study year. The Doctor’s degree student continues the course "Differential equations. The main course" and at the end of the year is to take an examination in this course. In the same academic year the student is to acquire numerical methods of the differential equation theory in the course "Approximative methods of solutions of ordinary differential equations". These methods are widely applied in using differential equation theory. At the end of the academic year the student is to take the examination in English.

3rd study year. In the course "Selections from the spline theory" the student of doctoral studies is to acquire methods of spline research and construction and get acquainted with various methods of solving equations based on splines At the end of the study year the student is to take a final examination in mathematics.

Optional specialized courses. During his/her studies in doctoral programme the student has to choose one of the courses: "Actual problems in the theory of differential equations" (1st study year), "Methods of the theory of boundary value problems for ordinary differential equations" (2nd study year), "Boundary value problems for ordinary differential equations" (3rd study year).

Approbation of theoretical findings.In two months’ time after enrolment, the Doctor’s degree student and

his/her scientific supervisor working together, choose the theme of promotion thesis which, then, is confirmed at the department meeting. At the beginning of

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every study year, the tasks which the student has to carry out while working at his/her promotion thesis are confirmed at a department meeting, and the supervisor’s proposals are taken into consideration. At the end of every study year a department meeting is held, and the student is to report on what he/she has done. The scientific supervisor evaluates how the students has coped with his/her tasks during the whole academic year, and the department meeting, taking into account the supervisor’s evaluation, assesses the student’s work by a text.

During all three academic years the Doctor’s degree student should participate in specialized seminars organized by the department, at which the student is to make reports and take part in discussions about both the theme of his/her own promotion thesis and the latest achievements and results in the theory of boundary value problems of ordinary differential equations. The participation of the Doctor’s degree student in such discussions is essential for the improvement of the promotion thesis quality.

Study plan

Course titleForm of assessment Credit

points1. study

year2. study

year3. study

yearExaminations

(semester)Tests

(semester)1.

sem.2.

sem.3.

sem.4.

sem.5.

sem.6.

sem.The study of theoretical findings (32KP)Obligatory courses (28KP)Differential equations. The main course 4 2 8 2 2 2 2Computers for mathematics 2 4 2 2English for mathematicians 1,3,4 8 2 2 2 2Approximative methods of solutions of ordinary differential equations

4 4 2 2

Selections from the spline theory 6 4 2 2Optional specialized courses (4KP)Actual problems in the theory of differential equations

2 4 2 2

Methods of the theory of boundary value problems for ordinary differential equations

4 4 2 2

Boundary value problems for ordinary differential equations

6 4 2 2

Approbation of theoretical findings (112KP)Specialized department seminars 1,2,3,4,5,6 12 2 2 2 2 2 2Working out of the promotion thesis 2,4,6 76 10 10 12 12 16 16Final examination in mathematics 6Final examination in English 4In total 3 17 120

2.2.3. Supervision and working out of the promotion thesis

By the decision of the department, a specialist with a degree of Dr.habil. in mathematics or Dr. in mathematics is appointed as a supervisor of the promotion thesis.

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The promotion thesis is an independent original research on some topical scientific problem that plays an important role in the development of mathematics.

The Doctor’s degree student is to carry out research on the theme of the promotion thesis and publish at least 5 papers in universally-known scientific reviewed journals (editions), which are on the list of scientific editions confirmed by the Latvian Council of Science. The order of the promotion thesis is determined by the "Regulation of the Order and Criteria of Promotion" (Regulation No. 134 of the Cabinet of Ministers, April 6, 1999). The defence of the promotion theses is to take place at the LU Promotion Council of Mathematics.

3. System of study quality assessment

The system of study quality assessment includes both the assessment of the student’s study work and the assessment of his/her research work.

Traditional forms – examinations and tests – are used to assess students’ work and knowledge. The participation of the Doctor’s degree student in seminar discussions on some certain scientific problem has become a vital criterion for the evaluation of his/her study work because it testifies to both the students’ knowledge and their abilities to solve scientific problems. The scientific supervisor and other lecturers play an enormous role in the assessment and improvement of study quality.

The quality and level of the research are determined by the results in examinations and by the reviewers of scientific papers and promotion thesis.

The quality of studies is assessed by: the Department of Mathematics; the DU Centre of study quality assessment (at the end of each academic

year the study programme director is to write a self-assessment report on the results of the current academic year in which he/she analyses the work done and offers his/her proposals; the Centre of study quality assessment, then, analyses the report and, in cooperation with the programme director, works out proposals for the improvement of study quality);

the DU Council of Science; the DU Council of Doctoral Studies; the Promotion Council in Mathematics.

The students of doctoral studies regularly discuss the problems concerning their study process with their scientific advisor and head of the Department of Mathematics. The problems mainly pertain to the racionalization of the study process organization, new acquisitions of scientific literature and some other problems.

Taking into consideration the fact that the implementation of the programme was started only in 2002./2003. study year, it is difficult to speak

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http://www.lzp.lv/latv/Promocija.htm

about the attitude of the employers towards the study programme graduates at the present moment.

4. Study Programme Assurance

4.1. Academic staff

The implementation of the doctoral programme is assured by the following lecturers.

N.p.k. Name, surname Scientific degree Academic position1. Felix Sadyrbaev Dr.habil.mat. Professor2. Zaiga Ikere Dr.habil.fil. Professor3. Svetlana Asmuss Dr.mat. Associated professor4. Ojars Lietuvietis Dr.mat. Associated professor5. Vyacheslavs Starcevs Dr.mat. Associated professor6. Armands Gritsans Dr.mat. Docent7. Anita Sondore Dr.mat. Docent8. Vitolds Gedroics Dr.ped. Docent

Curriculum Vitae of the lecturers see in appendix 4.

The professional perfection of academic staff is a systematic process which takes place in accordance with the annual plan.

The following forms of professional perfection are used: theoretical seminars, participation in conferences, in – service practice abroad, acquainting oneself with the latest achievements in science by using libraries and information technologies, participation in research themes.

4.2. Financing

The principal source of financing the doctoral study programme in mathematics is the state budget resources. Additional resources are obtained from tuition fees - Ls 600 per academic year (in 2002./2003. and 2003./2004. academic years there was one student who studied for the state budget resources).

4.3. Material and technical provision

The implementation of the study programme takes place in technically well equipped classrooms adequate to the specific character of the course.

The Department of Mathematical Analysis has at its disposal:

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6 computers which all are connected to INTERNET and have licenced software;

scanners; printers; xerox.

The computer classrooms of the DU Department of Computer Science, the equipment of the DU Multimedia Centre and Distance Learning Centre as well as material and technical basis of all structure units involved in the implementation of the programme are available for the realization of the study programme.

Teaching and scientific literature of the DU library is at the disposal of the Doctors degree students. Unfortunately, at present the choice of latest foreign textbooks and scientific periodicals is quite limited. Though in recent years certain progress is obvious. However the information available through the Internet, to a certain extent compensates this.

The DU library acquisitions of new books in 2003 see in appendix 5.

5. Students

Doctoral studies are mainly oriented towards the needs of young lecturers and specialists of DU and Eastern Latvia area who use contemporary methods in mathematics in their professional activities.

At present, two women – students acquire the doctoral study programme: I. Yermachenko (2nd study year) – master in mathematics, a lecturer

of the DU Department of Mathematics; S. Ogorodnikova (1st study year) – master in mathematics, a teacher

of mathematics and Computer Science in Daugavpils City gymnasium N 1, a graduate of the DU master study programme “Mathematics” in 2003, a graduate of the bachelor study programme “Mathematics” in 2001.

As it has been mentioned above, the bachelor, master and doctoral study programmes “Mathematics” form an undivided DU system of education in mathematics. Therefore the most capable master students are stimulated to continue their studies in the doctoral study programme (for instance, at present there are two 1st year master students – N. Sergeyeva and T. Garbuza – whose scientific supervisor is prof. F. Sadyrbaev. These two students are now oriented towards beginning their studies in the doctoral programme in 2005).

6. Advertising and Information about Study Possibilities

In mass media a purposeful advertising of the doctoral programme is being carried out: information about enrolment requirements, subjects and

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interviews with the programme designers, informative materials on TV, radio, press..

The most important form of advertising the doctoral programme is active scientific research of the Doctor’s degree students: their papers, reports at conferences and scientific publications. The most important factor in advertising the doctoral programme is the scientific reputation of the department. 7. Scientific Research of the University Lecturers and the Doctor’s degree Students 7.1. Participation in Research Projects

Prof. F. Sadyrbaev is head of the project of the Latvian Academy of Sciences Nr.01.0356 “Non-linear boundary value problems of ordinary differential equations” (the execution time of the project - 01.01.2001.-31.12.2004.).

Prof. F. Sadyrbaev is an editorial board member of the journal “Research Papers of the University of Latvia. Acta Universitatis Latviensis”.

7.2. Participation in Conferences

7.2.1. University lecturers’ participation in Conferences

A. Gricāns, F. Sadirbajevs. Asymptotic behavior of solutions to the Emden - Fowler type equations, Fourth World Congress of Nonlinear Analysts WCNA-2004 June 30 through July 7, 2004, Orlando Florida USA. Coreporter J. Klokovshttp://my.fit.edu/~dkermani/rogovchenko.htm

A. Gricāns, F. Sadirbajevs. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. 9th International Conference “Mathematical Modelling and Analysis”, Jurmala, 2004, May 27 – 29.http://www.mma2004.lv/

S. Asmuss. On positive co-monotone histopolation by combined quartic splines. 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia.http://www.mma2004.lv/

O. Lietuvietis. Small perturbations of free interface dynamics for gas bubble in the magnetic liquid on account of gravitational and magnetic forces. 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia. Coreporter T. Cīrulis.http://www.mma2004.lv/

A. Gricāns, F. Sadirbajevs. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. 5th Latvian Mathematical Conference, Daugavpils, April 6-7.

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http://www.mma2004.lv/



http://my.fit.edu/~dkermani/rogovchenko.htm

http://www.de.dau.lv/matematika/lmb5/

S. Asmuss. On a method for construction of shape preserving histosplines. 5th Latvian Mathematical Conference, Daugavpils, April 6-7.http://www.de.dau.lv/matematika/lmb5/

S. Asmuss. A central algorithm of approximation of linear functionals under fuzzy information. 5th Latvian Mathematical Conference, Daugavpils, April 6-7. Coreporter A. Šostaks.http://www.de.dau.lv/matematika/lmb5/O. Lietuvietis. Application of DM methods for problems in mathematical physics. 5th Latvian Mathematical Conference, Daugavpils, April 6-7. Coreporter T. Cīrulis.http://www.de.dau.lv/matematika/lmb5/

A. Gricāns, F. Sadirbajevs. Par lemniskātiskā sinusa Teilora rindu. LU 62. zinātniska konference, 2004. gada 6. februārī. http://www.lu.lv/petnieciba/konf62.html

F. Sadirbajevs. Sharp conditions for the superlinearity of the secondorder ordinary differential equations. EQUADIFF-2003. International Conference on Differential Equations, Hasselt, Belgium, July 22-26, 2003. Coreporter J. Klokovs.http://www.equadiff.be/

F. Sadirbajevs. Nonlinear boundary value problems of the calculus of variations. The Fourth International Conference on Dynamical Systems and Differential Equations, May 24-27, 2002, Wilmington, USA.http://www.uncw.edu/mathconf/

S. Asmuss. On a central algorithm of the approximation of linear functionals under inexact information. 7th International Conference Mathematical Modelling and Analysis MMA 2002, Kääriku, 2002.http://www.iam.ut.ee/mma2002/main.html

F. Sadirbajevs. Nonlinear Boundary Value Problems of the Calculus of Variations. International Congress of Mathematicians ICM’2002, Beijing, 2002.http://www.icm2002.org.cn/

A. Gricāns. On canonical connection of Killing f-manifold. 4th Latvian Mathematical Conference, Ventspils, 2002.

O. Lietuvietis. Application of DM methods for PDE with nonlocal boundary conditions. 4 th

Latvian Mathematical Conference, Ventspils, 2002. Co reporter T. Cīrulis.

S. Asmuss. On a central algorithm of the approximation under inexact information described by natural splines. 4th Latvian Mathematical Conference, Ventspils, 2002.

F. Sadirbajevs. Nonlinear eigenvalue problems with a condition at infinity. “EQUADIFF-10” Czechoslovak International Conference on Differential Equations and Their Applications. Prāga, Čehija, 2001.http://www.math.cas.cz/~equadiff/

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http://www.math.cas.cz/~equadiff/

http://www.icm2002.org.cn/

http://www.iam.ut.ee/mma2002/main.html

http://www.uncw.edu/mathconf/

http://www.equadiff.be/

http://www.lu.lv/petnieciba/konf62.html





F. Sadirbajevs. Nonlinear eigenvalue problems and multiple solutions of BVP for ODE. The Third World Congress of Nonlinear Analysts – 2000, Catania, Sicily, Italy, 19 – 26 July, 2000.http://www.fit.edu/AcadRes/math/ifna/wcna/wcna2000.htm - scient

O. Lietuvietis. Degenerate matrix method for solving some stiff differential equations. Numerical Mathematics and Advanced Applications. 3rd European Conference, 2000. Coreporter T. Cīrulis.O. Lietuvietis. The numerical study of heating and burning process in glass fabric manufacture. Numerical Mathematics and Advanced Applications. 3rd European Conference, 2000. Coreporter H. Kalis.

F. Sadirbajevs. Par periodisko problēmu. LU 58. zinātniskā konference, 2000.

F. Sadirbajevs. Superlineāras problēmas. 3. Latvijas Matemātikas konference. Jelgava, 2000.

S. Asmuss. On optimal algorithms of approximation under imprecise information. International Congress of Mathematicians ICM’98, Berlin, 1998. http://elib.zib.de/ICM98/info.html

A. Sondore. FB-компактные и CB-компактные пространства. International Conference “Teaching Mathematics: Retrospective and Perspective”, Šiauliai University, 1998.

7.2.2. Doctor’s degree Students’ participation in Conferences

I. Jermačenko. Types of Solutions and Multiplicity Results for Two-Point Nonlinear Boundary Value Problems, Fourth World Congress of Nonlinear Analysts WCNA-2004 June 30 through July 7, 2004, Orlando Florida USA. Coreporter F. Sadirbajevs.http://my.fit.edu/~dkermani/cabada.htm

S. Ogorodņikova. Planar systems with critical points: multiple solutions of two-point nonlinear boundary value problems, Fourth World Congress of Nonlinear Analysts WCNA-2004 June 30 through July 7, 2004, Florida USA. Coreporter F. Sadirbajevs.http://my.fit.edu/~dkermani/gaiko..htm

S. Ogorodņikova. Estimations of the number of solutions of the second order autonomous boundary value problems. 9th International Conference “Mathematical Modelling and Analysis”, May 27 - 29, 2004, Jurmala.http://www.mma2004.lv/

I. Jermačenko. Kvazilinearizācija un otrās kārtas robežproblēmas vairāku atrisinājumu eksistence. 46. Daugavpils Universitātes Jauno zinātnieku konference, Daugavpilī, 2004. gada 21. aprīlī.

S. Ogorodņikova. Bifurcation of solutions for the second order boundary value problem. 46. Daugavpils Universitātes Jauno zinātnieku konference, Daugavpilī, 2004. gada 21. aprīlī.

I. Jermačenko. Multiple solutions of Sturm-Lioville type boundary value problems.

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http://my.fit.edu/~dkermani/gaiko..htm

http://my.fit.edu/~dkermani/cabada.htm

http://elib.zib.de/ICM98/info.html

http://www.fit.edu/AcadRes/math/ifna/wcna/wcna2000.htm#scient

5. Latvijas matemātikas konference, Daugavpilī, 2004. gada 6.-7. aprīlī.http://www.de.dau.lv/matematika/lmb5/

S. Ogorodņikova. The second-order equation of Duffing type. 5. Latvijas matemātikas konference, Daugavpilī, 2004. gada 6.-7. aprīlī.http://www.de.dau.lv/matematika/lmb5/

I. Jermačenko. Nelineāro robežproblēmu atrisinājumu skaita novērtējumi. LU 62. konference, Rīga, 2004. gada 6. februārī. http://www.lu.lv/petnieciba/konf62.html

S. Ogorodņikova. Autonomas sistēmas uz plaknes. Nelineāro robežproblēmu skaita novērtējumi. LU 62. konference, Rīga, 2004. gada 6. februārī.http://www.lu.lv/petnieciba/konf62.html

It should be mentioned that prof. F. Sadyrbaev’s project “Boundary value problems with Sturm-Liouville boundary conditions” has won the DU internal grant of Ls 500. The project will enable two doctor’s degree students – I. Yermachenko and S. Ogorodnikova – to participate in the conference “Seventh Crimean Workshop on the Method of Lyapunov Functions and its Applications”, which will take place on September 11-18, 2004, in Alushta, the Ukraine.

7.3. Publications

7.3.1. University lecturers’ publications

A. Gritsans, F. Sadyrbaev. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. P. 20. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia.http://www.mma2004.lv/

S. Asmuss. On positive co-monotone histopolation by combined quartic splines. P. 71. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia.http://www.mma2004.lv/

O. Lietuvietis. Small perturbations of free interface dynamics for gas bubble in the magnetic liquid on account of gravitational and magnetic forces. P. 40. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia. Coauthor T. Cīrulis.http://www.mma2004.lv/

F. Sadirbajevs. Two-point nonlinear boundary value problems: quasilinearization and types of solutions. P. 54. Acta Societatis Mathematicae Latviensis, Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/

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A. Gricāns, F. Sadirbajevs. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. P. 32. Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/

S. Asmuss. On a method for construction of shape preserving histosplines. P. 10. Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/

S. Asmuss. A central algorithm of approximation of linear functionals under fuzzy information. P. 11. Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. Coauthor A. Šostaks.http://www.de.dau.lv/matematika/lmb5/

O. Lietuvietis. Application of DM methods for problems in mathematical physics. P. 25. Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. Coauthor T. Cīrulis.http://www.de.dau.lv/matematika/lmb5/

A. Gricāns, F. Sadirbajevs. Trigonometry of lemniscatic functions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 22-29.http://www.lumii.lv/sbornik1/contents.htm

F. Sadyrbaev. Nonlinear boundary value problems of the calculus of variations. Discrete and Continuous Dynamical Systems, Additional Volume, 2003, P. 770-779.

A. Gricāns, F. Sadirbajevs. Lemniscatic functions in the theory of the Emden – Fowler differential equation. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 5.-27. http://www.lumii.lv/sbornik/contents.htmhttp://www.mathpreprints.com/math/Preprint/

F. Sadyrbaev. Boundary value problems for -Laplasian equations. Abstracts of the 4th

Latvian Mathematical Conference, Ventspils, 2002, p.26. Coauthors A. Ya. Lepin, L. Lepin.

S. Asmuss. On a central algorithm of the approximation under inexact information described by natural splines. P. 10. Abstracts of the 4th Latvian Mathematical Conference, Ventspils, 2002.

A. Gritsans. On canonical connection of Killing f-manifolds. P. 116. Abstracts of the 4th

Latvian Mathematical Conference, Ventspils, 2002.

O. Lietuvietis. Application of DM methods for PDE with nonlocal boundary conditions. P. 14. Abstracts of the 4th Latvian Mathematical Conference, Ventspils, 2002. Coauthor T. Cīrulis.

O. Lietuvietis. Application of DM methods for problems with partial differential equations. Math. Modelling and Analysis, vol.7, Nr.2 (2002). - 191-200. Coauthor T. Cīrulis.

A. Gricāns, V. Starcevs. Lebega mērs un integrālis. Daugavpils, DU, 2002. - 291 lpp. http://www.de.dau.lv/matematika.html

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http://www.de.dau.lv/matematika.html

http://www.mathpreprints.com/math/Preprint/

http://www.lumii.lv/sbornik/contents.htm

http://www.lumii.lv/sbornik1/contents.htm





F. Sadirbajevs. Ievads optimizācijā. Daugavpils, DU izdevniecība “Saule”, 2002. - 86 lpp.http://www.de.dau.lv/matematika.html

V. Gedroics. Viena argumenta funkciju diferenciālrēķini. – Daugavpils, DPU izdevniecība ”Saule”, 2002. – 100 lpp.http://www.de.dau.lv/matematika.html

V. Gedroics. Ievads matemātiskajā analīzē.http://www.de.dau.lv/matematika.html

V. Gedroics. Viena argumenta funkciju integrālrēķini.http://www.de.dau.lv/matematika.html

V. Gedroics. Vairāku argumentu funkciju diferenciālrēķini.http://www.de.dau.lv/matematika.html

V. Gedroics. Vairāku argumentu funkciju integrālrēķini.http://www.de.dau.lv/matematika.html

F. Sadyrbaev. The upper and lower functions method for second order systems. Zeitschrift für Analysis und ihre Anwendungen (Journal for Analysis and its Applications), 20 (2001), No.3., pp.739–753. Coauthor A.Ya. Lepin.

O. Lietuvietis. Multistep degenerate matrix method for ordinary differential equations. Mathematical Modelling and Analysis, vol. 6, Nr. 1, Vilnius’Technika’ (2001). pp.58-67. Coauthors D. Cīrule, T. Cīrulis.

O. Lietuvietis. Analysis of generalized multistep Adam’s methods by degenerate matrix method for ordinery differential equations. Mathematical Modelling and Analysis, vol. 6, Nr. 2, Vilnius’ Technika’ (2001). pp.192-198. Coauthor T. Cīrulis.

S. Asmuss. Nenoteiktais un noteiktais (Rīmaņa) integrālis. Mācību līdzeklis. Rīga, LU, 2001. - 112 lpp. Coauthor A. Šostaks.

F. Sadyrbaev. On some non-elementary function. LU MII Zinātniskie raksti. Matemātika. 2. sējums, LU MII, 2001. - 57–64lpp. Coauthor L. Maciewska.

A. Gricāns, V. Starcevs. Elementāro pamatfunkciju aksiomātiskā teorija. – Daugavpils, DPU, 2001. – 91 lpp.http://www.de.dau.lv/matematika.html

F. Sadirbajevs. Two-point boundary value problems for even order differential equations. LU MII Zinātniskie raksti. Matemātika. 1. sējums, LU MII, 2000. - 91-107lpp.

O. Lietuvietis. Degenerate matrix method for solving some stiff differential equations. Numerical Mathematics and Advanced Applications, Proceedings of 3rd European Conference, “World Scientific” (2000), pp.456-461. Coauthor T. Cīrulis.

O. Lietuvietis. The numerical study of heating and burning process in glass fabric manufacture. Numerical Mathematics and Advanced Applications, Proceedings of 3rd

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European Conference, “World Scientific” (2000), pp.556-563. Coauthor H. Kalis.

V. Gedroics. Elementārā skaitļu teorija. Algebras profilkursa jautājumi. – DPU, 2000. – 54 lpp.

V. Starcevs. Loka garums un trigonometriskās funkcijas. DPU 8.ikgadējās zinātniskās konferences rakstu krājums A11. – Daugavpils, DPU, 2000. – 98.-99.lpp.

S. Asmuss. On shape preserving interpolation by splines. Acta Societatis Mathematicae Latviensis, N.3, 2000, p.13.

F. Sadyrbaev. Sharp conditions for rapid nonlinear oscillations, Nonlinear Analysis, 39 (2000), N.39, pp.519 – 533. Coauthor Yu. Klokov.

F. Sadyrbaev. Rapid oscillations in sublinear problems, Funkcialaj Ekvacioj (Functional Equations), Tokyo, 42, 1999, pp.339-353. Coauthor Yu. Klokov.

F. Sadirbajevs. Comparison results for fourth order positively homogeneous differential equations. LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi, 616. sējums, LU, 1999. - 17-23lpp.

S. Asmuss. Extremal problems of approximation theory in fuzzy context. Fuzzy Sets and Systems. V.105, 1999, N.2, pp.249–258. Coauthor A. Šostak.

F. Sadirbajevs. Multiplicity results for third order two-point boundary value problems. LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi, 616. sējums, LU, 1999., 5-16lpp.

V. Starcevs. Об измеримых векторно-значных функциях. 6.ikgadējās zin. konferences rakstu krājums A8. Daugavpils, DPU, 1999. - 10.-14.lpp.

V. Starcevs. О некоторых обобщениях интеграла Лебега векторнозначных функций. 6.ikgadējās zināt. konferences rakstu krājums A8.- Daugavpils, DPU, 1999. - 5.-10.lpp.

V. Starcevs. Trigonometriskās funkcijas: dažādi definēšanas paņēmieni un saskaitīšanas teorēmu pierādījumu īpatnības. DPU 7.ikgadējās zinātniskās konferences rakstu krājums A9. – Daugavpils, DPU, 1999. – 128.-129.lpp.

O. Lietuvietis. Degenerate matrix method with Chebyshev nodes for solving nonlinear systems of differential equations. Mathematical modelling and Analysis, V.4, Vilnius’ Technika’ ,1999, pp.51-57. Coauthor T. Cīrulis.

F. Sadyrbaev. Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities, Nonlinear Analysis: TMA, 33 (1998), n 3, 281-302. Coauthor M. Henrard.

S. Asmuss. On optimal algorithms of approximation under imprecise information. Abstracts of the International Congress of Mathematicians ICM’98 (Berlin, 1998). P.289.

S. Asmuss. On the existence of positive co-monotone quadratic histosplines. Reports of the Departments of Mathematics. University of Helsinki. Preprint Nr.195 (1998), 14 p. Coauthor A. Lahtinen.

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A. Sondore. On CB-compact, countably CB-compact and CB-Lindelöf spaces. –“Математички весник”, 50, 1998., – p. 125-133.

A. Sondore. Ar speciāliem vaļējiem pārklājumiem definētās kompaktības tipa topoloģiskās īpašības. Daugavpils Pedagoģiskās universitātes 6.ikgadējās zinātniskās konferences materiāli, 6.sējums. – 1998. - 18.-24.lpp.

A. Sondore. FB-компактные и CB-компактные пространства. – thesis of the International Conference “Teaching Mathematics: Retrospective and Perspective” at the Šiauliai University. – 1998. – p. 38-40.

O. Lietuvietis. Application of DM-method for numerical solving of nonlinear partial differential equation. Mathematical modelling applied problems of mathematical physics. LU zin. raksti, Nr. 612 (1998)., 63.-74. lpp. Coauthor T. Cīrulis.

O. Lietuvietis. Degenerate matrix method for solving nonlinear systems of differential equations. Mathematical Modelling and Analysis, vol. 3, Vilnius’ Technika’ (1998). – 45-56. Coauthor T. Cīrulis.

The list of most important publications of university lecturers see in appendix 5.

7.3.2. Publications of the Doctor’s degree Students

I. Jermačenko, F. Sadirbajevs. Multiple solutions of boundary value problems via Schaudera principle. – LU Zinātniskie raksti (submitted).

I. Jermačenko. On solutions of the Emden-Fowler type equation. P. 68. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis” (May 27-29, 2004, Jurmala, Latvia).http://www.mma2004.lv/

S. Ogorodņikova. Estimations of the number of solutions of the second order autonomous boundary value problems. P. 45. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis” (May 27-29, 2004, Jurmala, Latvia).http://www.mma2004.lv/

I. Jermačenko, F. Sadirbajevs. Types of solutions of the second order Neumann problem: multiple solutions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 5-21.http://www.lumii.lv/sbornik1/contents.htm

I. Jermačenko. Multiple solutions of Sturm-Liouville type boundary value problems. P. 61. Acta Societatis Mathematicae Latviensis, Abstracts of the 5 th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/index.html

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http://www.de.dau.lv/matematika/lmb5/index.html




S. Ogorodņikova. The second-order equation of Duffing type. P. 47. Acta Societatis Mathematicae Latviensis, Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/index.html

I. Jermačenko, J. Azareviča, V. Beinaroviča, A. Kiričuka, S. Radionova. Matemātikas bilingvālās mācīšanas metodika. – Rīga, apgāds “SI”, 2004. – 136 lpp.

8. Information about the Cooperation with other DU structure units and other Latvian and foreign Universities during the realization of the programme

During the realization of the programme the Department of Mathematics cooperates with other DU structure units:

DU Department of Computer Science, DU Multimedia Centre, DU Department of the English Language,

with other higher education establishments an scientific establishments in Latvia:

Faculty of Physics and Mathematics at the University of Latvia, Institute of Mathematics and Computer Science at the University of

Latvia. http://www.lumii.lv/To a certain extent, the cooperation and exchange of information are possible with:

Central European University (Hungary) www.ceu.hu/indexnsie.html Louvain-la-Neuve Catholic University (Belgium); Olomouc University (the Czech Republic); Universidad de Santjago-di-Compostella (Spain); Belarus state University (Minsk); Kiev State University (Kiev).

9. Comparison of the Programme with the programmes of other universities

9.1. Comparison with the LU doctoral study programme

The total workload of doctoral studies in Mathematics is 144 credit points, the length of studies in a full-time study programme is 3 years. The courses of the programme are subdivided into 4 parts.

1. Theoretical courses – 30 credit pints (20,8% of a total study workload).2. Individual research work and working out the promotion thesis – 90

credit points (62,6% of a total study workload).

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http://www.ceu.hu/indexnsie.html

http://www.lumii.lv/

http://www.de.dau.lv/matematika/lmb5/index.html

3. Pedagogical practice at a higher educational establishment or practice in applied mathematics in some scientific establishment – 12 credit points (8,3% of a total study workload).

4. Optional courses or additional courses set individually – 12 credit points (8,3% of a total study workload).

The realization of the doctoral study programme in mathematics is carried out by professors with Dr.habil. degree in mathematics. Besides, some work with the Doctor’s degree students is carried out by doctors in mathematical sciences..

The results of the studies in the doctoral programme are assessed according to the regulations adopted by the University of Latvia: the quantitative index – credit points according to the programme; the qualitative index – a mark according to a 10-grade system or a test according to the study programme.

In September of every academic year an expert commission on Doctor’s degree students in mathematics carries out the annual attestation of students’ work done in the study and research part of the programme. The results of the attestation are confirmed by the Council meeting of the Structure unit, the chairperson of which is a professor of the respective sub-branch. Then the results of attestation are submitted to the Department of Doctoral Studies.

9.2. Comparison with the programme “Doctor of Philosophy” of Utah State University, USA

The doctoral programme is realized in 4 sub-branches. To be awarded the PhD degree, the following requirements should be

fulfilled.1. Competence in analysis, algebra and topology or in mathematical

statistics..2. Master’s degree.3. Examination in the 1st study year and the respective examinations

when finishing the 2nd year.4. Presentation of a dissertation theme.5. Completion of a dissertation.6. Final oral examination and the defence of the dissertation.

A special Supervisory Committee is responsible for the student’s individual programme, supervision of the dissertation and its approval. The committee is elected at the beginning of work. It consists of the supervisor of the dissertation and representatives of the faculty (at least five faculty members of a doctoral rank). The doctoral study course consists of 60 credit hours. It consists of basic courses in modern mathematics and specialized courses.

During the first year the student is to define his/her scope of interests and is to pass the examination in English. During the 2nd study year the student must pass the comprehensive examinations. The content covered by these

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examinations should be related to the area of research of the student’s dissertation.

9.3. Comparison with the Silesian University (Opava, the Czech Republic) doctoral study programme

The doctoral studies at Silesian University (Opava, Czech Republic) are organized in three or four study years, in full-time and part-time study forms. Persons with a master’s degree in mathematics can be enrolled in the study programme. Every student will have his/her supervisor. A scientific advisor will be appointed for every student, who (in cooperation with the student) will draw up a study plan and will follow how it carried out. The student has to attend obligatory study courses and has to choose 4 optional courses. The student is to take examinations in all courses. Full-time students have to teach 4 lessons every week. Besides theoretical courses, which the student has to acquire, he/she is to carry out independent research on chosen topic and participate in some scientific seminar. The study will be finished by a state examination and the oral defence of the thesis in front of the Promotion Council. The defence can be held in Czech, Slovak or English (in agreement with the supervisor possibly also in another language). The promotion thesis must be written in English or, as an exception, in Czech, Slovak or another language.

The comparison with the DU study programme: common features – the study programme consists of a theoretical part (including both obligatory and optional courses) and independent research; features that differ: the thesis at the Silesian University takes place at the University Promotion Council while DU does not have such council; there are fewer obligatory courses in the programme at Silesian University.

9.3. Comparison with the doctoral study programme of Vilnius University (Lithuania)

In Vilnius University (Lithuania) the duration of doctoral studies is four years and consists of theoretical studies and writing of doctoral thesis. A doctoral student must take up at least three courses from the selected area and at least one course from some other area of science. Every course is at least forty-five lecture hours and is completed by an examination. The individual programme and the theme of doctoral dissertation are confirmed by a special committee (doctoral supervisory committee). A doctoral student has to report on the progress of his/her studies and research to this committee. The doctoral dissertation must be written in Lithuanian, however, under the approval of the doctoral supervisory committee, it may be written in a foreign language. The The doctoral student must produce at least two research articles, announcing the main results of his/her research.

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In comparison with the DU study programme: common features - the study programme consists of a theoretical part and independent research; features that differ – the defence of the doctoral dissertation at Vilnius University takes place in front of the promotion Council at the University itself while DU does not have such council; the duration of studies at Vilnius University is four years.

The information about doctoral study programms in mathematics at the University of Latvia, Utah State University (USA), Silesian University (The Czech Republic) and Vilnius University (Lithuania) see in appendix 6.

Summing everything up, we can state that the content and study load the doctoral study programme of DU are similar to those of the above mentioned. There is a certain difference between the time allotted to full-time studies as well as between the amount of credit points, which in different countries is different.

It should be pointed out that in Latvia the training of doctoral students and the implementation of the study programme, traditionally, is not directly linked with the defence of the promotion thesis, because the promotion thesis can be defended only after at lest five articles in reviewed journals have been published. The duration of the DU study programme is shorter – three years, and, normally, the defence of the promotion thesis can take place at the respective Promotion Council only some time after the doctoral study programme has been fulfilled.

10. Development of the Programme

Development directions of the programme: inviting guest lecturers more frequently during the study process; systematic in-service training of students and lecturers at the universities

abroad; creating the necessary conditions for the students’ systematic participation

in scientific conferences abroad; supplying the library with foreign periodicals in the field of mathematical

science; increasing students’ financial possibilities so that they can realize the

programme more effectively.

11. Self-assessment of the Programme

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DU has all the preconditions for a successful implementation and perfection of the programme:

high qualification of the academic staff, their continuous development, active research work;

contacts with universities and academic institutes in Latvia and abroad; adequate material and technical basis.

12. Annotations of the study programme courses

Obligatory coursesDifferential equations. The main course - 8 credit points, a credit, an examThe goals of the course are to get acquainted with basics of the theory of ordinary differential equations and to study the specific items such as special functions, the interpolation, splines.Program designer: prof. F. Sadyrbaev

Computers for mathematics - 4 credit points, a creditThe goals of the course are to learn how to perform the mathematical calculations with the specific programs like MathCad, Maple, Mathematica as well as to improve the TeX (MiKTeX) skills to design and create mathematical texts.Program designer: doc. A. GritsansEnglish for mathematicians - 8 credit points, 3 creditsThe main goal of the course is to get acquainted with the modern terminology used in the theory of ordinary differential equations as well as with main principles of writing of mathematical texts. The main tasks are to improve the student’s language skills so that they will be able to read the special literature, to write mathematical texts and to present the results during conferences and seminars.Program designers: prof. Z. Ikere, prof. F. Sadyrbaev, doc. A. Gritsans

Approximative methods of solution of ordinary differential equations - 4 credit points, a creditThe goals of the course are to get acquainted with the one-step methods (namely: the Euler method, the improved the Euler method, trapezoidal and rectangle methods, the collocation method, Runge – Kutta type methods etc.) as well as with multi-step methods (the Adams’ method, the Gear’ method, the degenerate matrices method).Program designer: as. prof. O. Lietuvietis

Selected problems of the spline theory - 4 credit points, a creditThe goal of the course is to introduce the student to the subject of spline theory. The main tasks are to learn the methods of investigation and construction of splines. The common principles of application of splines in numerical analysis are presented. The following items are discussed, which are based on the spline theory: functions interpolation, the numerical differentiation, the integration procedures, extremal problems, the numerical methods of solution of differential and integral equations. Elements of the finite difference method are given, the spline theory applications in the computer graphics are overviewed.Program designer: as.prof. S. Asmuss

Optional specialized coursesActual problems in the theory of differential equations - 4 credit points, a creditThe main goal of this course is to give an introduction to basics of the differential equations

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and to study the selected items, such as special functions, the interpolation, splines.Program designer: prof. F. Sadyrbaev

Methods of the theory of boundary value problems for ordinary differential equations - 4 credit points, a creditThe goal of the course is to acquire the specific methods of investigation of problems in the theory of differential equations paying attention to the topological methods of qualitative theory and to the numerical methods.Program designer: prof. F. Sadyrbaev

Boundary value problems for ordinary differential equations- 4 credit points, a credit The goal of the course is to get acquainted with the main results in the theory of boundary value problems for ordinary differential equations with emphasis on nonlinear theory.Program designer: prof. F. Sadyrbaev

13. List of Appendices

1. Set of questions for the entrance examination in mathematics.2. Expanded course content.3. Set of questions for the final examination in mathematics.4. Lecturers’ Curriculum Vitae.5. List of the lecturers’ most important publications.6. Information about the doctoral study programme in mathematics in the

University of Latvia, Utah State University (USA), Silesian University (the Czech Republic) and Vilnius University (Lithuania).

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Appendix 1. Set of questions for the entrance examination in mathematics

Set of questions for the entrance examination in mathematicsThe Doctoral study program “Mathematics“

Sub-branch “Differential equations“

I Part of general education (bachelor level in mathematics)

Basics of algebra. Elements of linear algebra: matrices, determinants, vector spaces. Groups, rings, fields, linear operators.

Elements of the set theory. Basic notions. Equivalent sets. The Cantor - Bernshtein theorem. Countable and continuous sets.

Elements of the analysis. Limits of one and multi-variable functions, the continuity, infinitesimal calculus and integrals. Number sequences and series. The power series. Fourier series.

Measure and the theory of integration. The measure. Measurable functions. The Lebesque integral for bounded and non-bounded functions. Summable functions. The spaces L1(E), L2(E), Lp(E).

Foundations of the functional analysis. The scalar product. Norm. Metrics. Topology of a metric space. Convergence in metric spaces. Connectedness, compactness, completeness. Continuous maps. Principles of the contractive maps and applications. Linear operators in normed spaces. The Fourier series in Hilbert spaces.

Complex analysis. Sequences of complex numbers and series. Functions of a complex variable: limits, the continuity, differentiation. Power series. Analytical functions and conformal maps. Integration of functions of a complex variable. The Cauchy theorem. The Taylor and Laurent series.

Basics of topology.

Literature1. Š. Mihelovičs. Grupas. – Daugavpils: DPI, 1979.2. Š. Mihelovičs. Gredzeni. – R: LVU, 1981.3. I. Strazdiņš. Diskrētās matemātikas pamati. – R.: Zvaigzne, 1980.4. T. Cīrulis. Funkcionālanalīze. - Rīga, 2002., 149 lpp.5. Л.А. Калужнин Введение в общую алгебру. – М.: Наука, 1973.6. А.И. Кострикин Введение в алгебру. – М.: Наука, 1977.7. A. Gricāns. Kopu teorijas elementi. – Daugavpils: DPU, izd.”Saule”, 1997.8. T. Cīrulis, Dz. Damberga. Kompleksā mainīgā funkciju teorijas elementi. –

R.: LVU, 1991.

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9. T. Cīrulis, Dz. Damberga. Kompleksā mainīgā funkciju teorijas metodes. – R.: LVU, 1992.

10. V. Kronbergs, P. Rivža, Dz. Bože. Augstākā matemātika. 1., 2. daļa. – R.: Zvaigzne, 1988.

11. V. Starcevs. Matemātiskās analīzes izvēlētie jautājumi (matanalīze metriskā telpā). – Daugavpils, DPI, 1979.

12. V. Starcevs. Attēlojumi metriskajās telpās. – R.: LVU, 1981.13. A. Gricāns, V. Starcevs. Lebega mērs un integrālis.

http://www.de.dau.lv/matematika/lebint.pdf14. Зорич В.А. Математический анализ. Ч. I. – М.: Наука, 1981.

Ч. II. –М.: Наука, 1984. 15. Колмогоров А..Н., Фомин С. В. Элементы теории функций и

функционального анализа. – М.: Наука, 1976.16. Маркушевич А.И., Маркушевич Л.А. Введение в теорию

аналитичес-ких функций. – М.: Просвещение, 1977.17. Натансон И.П. Теория функций вещественной переменной. –

М.: Наука, 1974.18. Старцев В.А. Измеримые множества и

интеграл. Ч. III. – Р.: ЛГУ, 1987.19. Старцев В.А. Основные структуры математического анализа

(метрические пространства). – Р.: ЛГУ, 1988.20. Старцев В.А. Основные структуры математического анализа

(непрерывные отображения). – Р.: ЛГУ, 1989.21. Старцев В.А. Введение в математический анализ I. Теория

пределов. Введение в математический анализ II. Непрерывные функции и отображения. (в двух частях) – Даугавпилс: ДПУ, изд.”Сауле”, 1996.

II Special part (master level in mathematics)

Basic elements of ODE theory. Concept of mathematical modelling. Boundary value problems of the issues chosen. Cauchy problem. Basic principles of functional analysis: Banach-Steinhaus theorem, Banach

theorem about the inverse operator, Hahn-Banach theorem. Hilbert space geometry.

Literature1. S. Čerane. Diferenciālvienādojumi. – 1998.

ftp://ftp.liis.lv/macmat/matemat/dif-mega.zip2. S. Čerane. Diferenciālvienādojumi un modeļi. – 1999.

ftp://ftp.liis.lv/macmat/matemat/difv_mod/3. S. Čerane. Diferenciālvienādojumi. – 2001.

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ftp://ftp.liis.lv/macmat/matemat/difv_mod/

ftp://ftp.liis.lv/macmat/matemat/dif-mega.zip

http://www.de.dau.lv/matematika/lebint.pdf

ftp://ftp.liis.lv/macmat/matemat/div_vdj/4. Эльсгольц Л. Дифференциальные уравнения и вариационное

исчисление. – М., 1970 и др.5. Трикоми Ф. Дифференциальные уравнения. – М., 1962.6. Коддингтон Э.А., Левинсон Н. Теория обыкновенных дифференциаль-

ных уравнений. – М., 1958.7. Красносельский М.А. и др. Векторные поля на плоскости. – М., 1963.8. Васильев Н.И., Клоков Ю.А. Основы теории краевых задач

обыкновенных дифференциальных уравнений. – Рига, 1978.9. Березанский К.И., Ус Г.Ф., Шефтель З.Г. Функциональный анализ. –

Киев: Выша школа, 1990.10. Рудин У. Функциональный анализ. – М.: Mир, 1975.11. Садовничий В.А. Теория операторов. – М.: МГУ, 1986.

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ftp://ftp.liis.lv/macmat/matemat/div_vdj/

Appendix 2. Expanded course content

DAUGAVPILS UNIVERSITYTHE FACULTY OF NATURAL SCIENCES AND MATHEMATICS


1. COURSE DIFFERENTIAL EQUATIONS. THE MAIN COURSE

2. STUDY PROGRAMME

The Doctoral study program “Mathematics”.Sub-branch “Differential equations”

3. COURSE LEVEL An obligatory course

4. CREDIT POINTS 8

5. FORM OF ASSESSMENT

A credit, an exam

6. AUTHORS Dr.habil.math., prof. F. SadirbajevsDr.math., as.prof. V. Starcevs

7. LANGUAGE Latvian

8. THE AIM OF THE COURSE

To get acquainted with basics of the theory of differential equations and related problems

9. COURSE DESCRIPTION

1. Metric spaces. Linear and nonlinear normed spaces. 2. Banach spaces. Linear continuous maps in Banach spaces.

The Hahn – Banach theorem. Conjugate space and conjugate operators. The Banach-Steinhaus theorem.

3. Topology of the linear continuous operator space. 4. Compact sets. Compact sets in functional spaces. Arzela –

Ascoli criterium.5. Hilbert spaces. The orthogonal complement of Hilbert

spaces. Fourir series. Bessel inequality and Parceval equality. Hilbert space as a direct sum of orthogonal subspasec. Riesz’s theorem.

6. Compact operators in Hilberta spaces. The operator spectrum and resolvent. Selfadjoint operators, spectrum. Hilbert – Schmidt theorem. The Fredholm alternative theorems and applications.

7. Maps with fixed points. The contracting maps. The contracting maps in metric spaces. Banach fixed point principles, applications. Non-expansive maps and fixed points. The Bohl – Brower – Schauder principle, applications.

8. Parcial differential equations (PDE) and mathematical modelling. Examples of PDE.

9. Linear transport PDE.

28

10. Laplace equation. Elliptic equations and systems. Well-posed boundary value problems. Classical solutions, the maximum principle. Green’s funcions.

11. Parabolic equations and systems. Well-posed problems. Classical solutions, the maximum principle. Generalized solutions, a priori bounds, regularity properties of generalized solutions Hyperbolic equations and systems. Well-posed problems. Classical solutions, shock front formations.

12. The first order hyperbolic systems. Conservation laws, generalizations of the solution notion.

13. The Cauchy – Kovalevskaja theorem. Fundamental solution. The characteristic surfaces and characteristic directions. PDE classification.

14. Calculus of variations. The classical calculus of variations. The Euler equation. Criteria for the existence of minimizers.

15. The first order nonlinear PDE. 16. Methods for investigation of PDE. Variational methods. 17. Linear equations as the nonlinear phenomena

mathematical model approximations. Conservation laws and variational principles.

18. Mathenatical modelling. Similarity methods, self-similar solutions. The maximum principle and comparison theorems. Bifurcations; dissipative structures in nonlinear media. Strange attractors.

10. LITERATURE 1.M. Schechter. Principles of Functional Analysis: Second Edition. American Mathematical Society, Providence, Rhode Island, 2002, 425 pp.

2.L.C. Evans. Partial Differential Equations. American Mathematical Society, Providence, Rhode Island, 1998, 662 pp.

3.Čerane S. Diferenciālvienādojumi un modeļi. – 1999. http://www.liis.lv/

4.T. Cīrulis. Funkcionālanalīze. - Rīga, 2002., 149 lpp.5.E.A. Coddington, N. Levinson. Theory of Ordinary

Differential Equations. – Mc Graw – Hill, 1955. (Э.А. Коддингтон, Н. Левинсон. Теория обыкновенных дифференциальных уравнений. – М., ИЛ, 1955).

6.A. Givental. Linear Algebra and Differential Equations. - American Mathematical Society, Providence, Rhode Island, 2001, 132 pp.

7.P. Hartman. Ordinary differential equations.- John Wiley, 1964 ( Ф. Хартман. Обыкновенные дифференциальные уравнения. М., Мир, 1970).

8.В.И. Арнольд. Обыкновенные дифференциальные уравнения. - Москва, Мир, 1984.

9.В.И. Арнольд. Дополнительные главы теории обыкновенных дифференциальных уравнений. - Москва, Наука, 1978.

29

http://www.liis.lv/

10. Н. Данфорд, Дж. Шварц. Линейные операторы. Общая теория. - Москва, ИЛ, 1962.

11. Л.В. Канторович, Г.П. Акилов. Функциональный анализ. – Москва, Наука, 1977.

12. А.Н. Колмогоров, С.В. Фомин. Элементы теории функций и функционального анализа. - Москва, Наука, 1981.

13. Р. Курант. Уравнения с частными производными. - Москва, Мир, 1964.

14. А. Куфнер, С. Фучик. Нелинейные дифференциальные уравнения. - М., Наука, 1988.

15. В.П. Михайлов. Дифференциальные уравнения в частных производных. – М., Наука, 1983.

16. Э. Полак. Численные методы оптимизации. - Москва, Мир, 1979.

17. Ф. Трикоми. Дифференциальные уравнения. - М., ИЛ, 1962.

18. М.В. Федорюк. Обыкновенные дифференциаль-ные уравнения. М., Наука, 1980.

19. Л. Хермандер. Линейные дифференциальные операторы с частными производными. - Москва, Мир, 1965.

20. И. Экланд, Р. Темам. Выпуклый анализ и вариационные проблемы. - Москва, Мир, 1979.

30



1. COURSE COMPUTERS FOR MATHEMATICS

2. STUDY PROGRAMME



4. CREDIT POINTS 4


A credit

6. AUTHOR Dr.math., doc. A.Gricāns

7. LANGUAGE Latvian, English

8. THE AIM AND TASKS OF THE COURSE

The main goal of the course is to get acquainted with the practical usage of computers in studying and doing mathematics. The tasks of the course are: 1) to learn how to solve practical problems with Mathcad, Maple and Mathematica; 2) to improve TeX skills using the LaTeX package designing mathematical texts.


1. Mathcad, Maple, Mathematica.Overview of the Mathcad, Maple and Mathematica packages versions. The main window. Mathematical functions. Creating graphics. Analytical calculations. Solution of equations and systems. The mathematical analysis problems with Mathcad, Maple and Mathematica (calculation of limits of functions, differentiation, integration), problems in the theory of differential equations (the Cauchy problem for equations and systems), optimization problems (extremes of functions, linear programming), problems in the theory of functions of complex variables, combinatorial problems and statistics.2. MiKTeX.The text editor WinEdt. Introduction to MiKTeX and installation. LaTeX document structure and classes. The most important LaTeX packages (amsmath, amsfonts, amssymb, hyperref, graphicx, babel). Mathematical symbols. Designing of mathematical texts. LaTeX files convertation to DVI, PS, PDF and HTML formats.

31

10. LITERATURE1. H. Kalis, S. Lācis, O. Lietuvietis, I. Pogodkina.

Programmu paketes Mathematica lietošana mācību procesā. - R.: Mācību grāmata, 1997.

2. H. Kalis, R. Millere. Datorprogrammas Maple lietošana matemātikas mācību procesā. - R., 1999.

3. H. Kalis, R. Millere. Datorprogrammas Maple lietošana vidusskolas algebras un matemātiskās analīzes elementu kursā. - R., 2000.

4. H. Kalis. Skaitliskās metodes (ar datorprogrammu Maple, Mathematica lietošanu). - R., 2001.

5. Johannes Braams. Babel, multilingual package for use with LaTeX's standart document classes. 22.02.2001.

6. Nikos Drakos. The LaTeX2HTML Translator. Computer Based Learning Unit, University of Leeds, March 26, 1999.

7. LaTeX2 . The macro package for TeX by Leslie Lamport et al. Edition 1.6.

8. Tobias Oetiker, Hubert Partl, Irene Hyna, Elisabeth Schlegl. Не очень краткое введение в LaTeX2 . Version 3.2, 21. September, 1998. (Перевод Б. Тоботрас 07.10.98.).

9. Sebastian Rahtz. Hypertext marks in LATEX: the hyperref package. June 1998.

10. Keith Reckdahl. Using Imported Graphics in LaTeX2 . Version 2.0. December 15, 1997.

11. Christian Schenk. MiKTeX Manual. Revision 2.0 (MiKTeX 2.0). December 2000.

12. User's Guide for the amsmath Package (Version 2.0). American Mathematical Society, 13.12.99.

32



1. COURSE ENGLISH FOR MATHEMATICIANS

2. STUDY PROGRAMME



4. CREDIT POINTS 8


3 credits

6. AUTHORS Dr.habil.math., prof. F. SadirbajevsDr.habil.philol., prof. Z. IkereDr.math., doc. A. Gricāns

7. LANGUAGE Latvian, English, Russian


The aim of the course is to get sufficient knowledge of mathematical terminology (especially in the field of ordinary differential equations), as well as to improve reading and writing skills with respect to mathematical texts


1. The widely used mathematical expressions and terms.

2. The widely used mathematical expressions and terms in the field of ordinary differential equations.

3. The structure of mathematical texts.4. Translation English to Latvian (Russian).5. Translation Latvian (Russian) to English.

10. LITERATURE 1. S. Bernfeld S., V. Lakshmikantham. An Introduction to Nonlinear Boundary Value Problems. - New York: Academic Press 1974.

2. C. de Coster and P. Habets. Upper and Lower Solutions in the Theory of ODE Boundary Value Problems: Classical and Recent Results. – In: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations. CISM Courses and Lectures, # 371. Springer, 1997.

3. U. Kaasik, H. Espenberg, E. Etverk, O. Runk, A. Vihman. Matematika oskussonastik, "Valgus", Tallin, 1978.

4. S.G. Krantz. How to Teach Mathematics, Second Edition. - American Mathematical Society,

33

Providence, Rhode Island, 1999, 307 pp.5. S. Katok, A. Sossinsky, S. Tabachnikov, Editors.

MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics. American Mathematical Society, Providence, Rhode Island, 2003, pp. 313.

6. A.J. Lohwater's Russian-English Dictionary of the Mathematical Sciences. Edited by R.P. Boas. American Mathematical Society, Providence, Rhode Island, 1990.

7. Англо-русский словарь математических терминов. Издательство иностранной литературы, Москва, 1962.

8. С.С. Кутателадзе. Russian-English in Writing. Советы эпизодическому переводчику. Издательство Института математики им. С.Л. Соболева СО РАН, Новосибирск, 1997.http :// www . emis . de / monographs / Kutateladze / R - E .4/ index . html

9. А.Б. Сосинский. Как написать математическую статью по-английскию. Издательство "Факториал Пресс", Москва, 2000.http :// ega - math . narod . ru / Quant / ABS . htm

10. Учебный словарь-минимум для студентов математиков. Составитель М.М. Глушко. Издательство МГУ, Москва, 1976.

11. С.А. Шаншиева. Английский язык для математиков. Издательство МУ, Москва, 1991.

12. Žurnālu raksti un Internetā pieejamā matemātiskā literatūra.

34

http://ega-math.narod.ru/Quant/ABS.htm

http://www.emis.de/monographs/Kutateladze/R-E.4/index.html

http://www.emis.de/monographs/Kutateladze/R-E.4/index.html



1. COURSE APPROXIMATIVE METHODS OF SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

2. STUDY PROGRAMME



4. CREDIT POINTS 4


A credit

6. AUTHOR Dr.math., as.prof. O. Lietuvietis

7. LANGUAGE Latvian


The aim of the course is to overview the approximative methods of solution of ordinary differential equations. The specific tasks are to get acquainted with both analytical and numerical methods (the one step and the multi-step ones).


1. The Cauchy problem approximative solution Analytical methods

1.1. The Picard successive approximations1.2. The Taylor series method1.3. The power series method1.4. The Tchaplygin method (the method of upper and lower

approximations) Numerical methods One-step methods

1.5. The Euler, the improved Euler and the Euler – Cauchy methods

1.6. Milne's prediction-correction methods1.7. Runge-Kutta type methods1.8. The degenerate matrices method Linear multi-step methods1.9. Adams' methods1.10. Gear’s (back numerical differentiation) method

2. The approximative solution of boundary value problems2.1. Reduction to the Cauchy problem 2.2. Shooting type methods2.3. The finite difference method

3. Approximative solution of ODE with ‘Mathematica’, ‘Maple’,

35

‘Matlab’ and ‘Matcad’

10. LITERATURE 1. H. Kalis. Diferenciālvienādojumu tuvinātās risināšanas metodes. Rīga, Zvaigzne, 1986.

2. К. Деккер Я. Вервер. Устойчивость методов Рунге Кутты для жестких нелинейны дифференциальных уравнений. Москва, Мир, 1988.

3. E. Hairer, G. Wanner. Solving Ordinary Differential Equation. Springer, 1996.

4. A.A. Cамарский, А.В. Гулин. Численные методы. Москва, Наука, 1989.

36



1. COURSE SELECTIONS FROM THE SPLINE THEORY

2. STUDY PROGRAMME



4. CREDIT POINTS 4


A credit

6. AUTHOR Dr.math., as.prof. S. Asmuss

7. LANGUAGE Latvian


The goal of the course is to introduce the student to the subject of spline theory. The main tasks are to learn the methods of investigation and construction of splines. The common principles of application of splines in numerical analysis are presented. The following items are discussed, which are based on the spline theory: functions interpolation, the numerical differentiation, the integration procedures, extremal problems, the numerical methods of solution of differential and integral equations. Elements of the finite difference method are given, the spline theory applications in the computer graphics are overviewed.


1. Basics of splines.1.1. The historical review. Splines in approximative analysis.1.2. The polynomial splines. The degree and defect of a spline.

Spline space.2. Cubic splines.

2.1. The cubic splines with the I, II, III, IV type boundary conditions.

2.2. Schoenberg and Hermite cubic splines.2.3. Cubic B-splines.2.4. Formulas for local approximation.2.5. The numerical differentiation and integration using the

cubic splines.3. High-degree splines.

3.1. The interpolation problem: posing and solution. 3.2. B-splines, their properties. Spline space base.3.3. Algorithms of the numerical differentiation and integration.3.4. Formulas for local approximation.

4. Natural splines.4.1. Natural interpolation splines.

37

4.2. The extremal property of the interpolation spline. Smoothing natural splines.

4.3. The quadrature formulas, based on natural splines. Formulas and optimality.

5. Multi-variable splines.5.1. Multi-variable splines on the regular grid. 5.2. Multi-variable splines on the chaotic grid. 5.3. The interpolation multi-variable cubic splines. The

construction methods.5.4. Smoothing multi-variable splines.

6. Construction of curves and surfaces with the aid of splines.

6.1. Parametric splines.6.2. Rational splines.6.3. Bezier splines. 6.4. Isogeometrical spline approximation preserving the

monotonicity and convexity of data. 7. Solution of differential and integral equations using splines.

7.1. The collocation method.7.2. The method of subintervals. 7.3. The finite difference method.

10. LITERATURE 1. Alberg J.H., Nilson E.N., Walsh J.L. The theory of splines and their applications. New York, Academic Press, 1967.

2. Laurent P.J. Approximation et optimization. Paris, Hermann, 1972.

3. Стечкин С.Б., Субботин Ю.Н. Сплайны в вычислительной математике. Москва, Наука, 1976

4. De Boor C. A practical guide to splines. New York, Springer, 1978.

5. Завьялов Ю.С., Квасов Б.И., Мирошниченко В.Л. Методы сплайн - функций. Москва, Наука, 1980.

6. Schumaker L.L. Spline functions: basic theory. New York, Wiley, 1981.

7. Василенко В.А. Сплайн - функции: теория, алгоритмы, программы. Новосибирск, Наука, 1983.

8. Завьялов Ю.С., Леус В.А., Скороспелов В.А. Сплайны в инженерной геометрии. Москва, Машиностроение, 1983.

9. Малоземов В.Н., Певный А.Б. Полиномиальные сплайны. Ленинград, ЛГУ, 1986.

10. Вершинин В.В., Завьялов Ю.С., Павлов Н.Н. Экстремальные свойства сплайнов и задача сглаживания. Новосибирск, Наука, 1988.

11. Nurnberg G. Approximation by spline functions. Berlin, Springer, 1989.

12. Kvasov B.I. Methods of shape-preserving spline approximation. Singapore, World Scientific, 2000.

38



1. COURSE ACTUAL PROBLEMS IN THE THEORY OF DIFFERENTIAL EQUATIONS

2. STUDY PROGRAMME


3. COURSE LEVEL An optional specialized course

4. CREDIT POINTS 4


A credit

6. AUTHOR Dr.habil.math., prof. F. Sadirbajevs

7. LANGUAGE Latvian


Present basics of the theory of ordinary differential equations, including problematic and overview of the related methods.


1. Basics of the theory of ordinary differential equations (ODE) 1.1. ODE.1.2. ODE classification

1.2.1. The order of ODE1.2.2. Systems of ODE1.2.3. Linear and nonlinear ODE

2. Existence and uniqueness of solutions 2.1. The fundamental items in the theory of ODE – existence

and uniqueness 2.2. ODE and integral equations2.3. The method of successive approximations2.4. Extendability of solutions2.5. Continuous dependence of solutions on the initial data and

parameters

3. Linear ODE 3.1. Linear homogeneous ODE3.2. Linear nonhomogeneous ODE3.3. Linear systems with constant coefficients3.4. Linear systems with periodic coefficients

4. Oscillation and comparison theorems for the second order ODE.

39

4.1. Sturm theory4.2. Eigenvalues4.3. Sturm – Liouville eigenvalue problems4.4. Periodic problem

5. Special functions 5.1. Introduction5.2. Legendre functions5.3. Bessel functions5.4. Mathieu functions5.5. Elliptic function

6. Orthogonal polynomials 6.1. Introduction 6.2. Legendre polynomials 6.3. Chebyshev polynomials6.4. Laguerre polynomials 6.5. Hermite polynomials

7. Interpolation 7.1. Introduction 7.2. Classical polynomials7.3. Splines7.4. Topics of interest

10. LITERATURE1. E.A. Coddington, N. Levinson. Theory of Ordinary

Differential Equations. – Mc Graw – Hill, 1955. (Э.А. Коддингтон, Н. Левинсон. Теория обыкновенных дифференциальных уравнений. – М., ИЛ, 1955).

2. P. Hartman. Ordinary differential equations.- John Wiley, 1964 ( Ф. Хартман. Обыкновенные дифференциальные уравнения. М., Мир, 1970).

3. S. Bernfeld S., V. Lakshmikantham. An Introduction to Nonlinear Boundary Value Problems. - New York: Academic Press 1974.

4. Дж. Сансоне. Обыкновенные дифференциальные уравнения. М., ИЛ, 1953, т. 1; 1954, т. 2.


6. М.В. Федорюк. Обыкновенные дифференциальные уравнения. М., Наука, 1980.

7. Камке Э. Справочник по обыкновенным дифференциаль-ным уравнениям. – М., 1976 и др.

8. Васильев Н.И., Клоков Ю.А., Шкерстена А.Я. Применение полиномов Чебышева в численном анализе. Рига, «Зинатне», 1984.

9. Мэтьюз Дж., Уокер Р. Математические методы физики. М., Атомиздат, 1972.

10. Справочная математическая библиотека. Высшие трансцендентные функции. М., Наука, 1966.

40

11. Čerāne S. Diferenciālvienādojumi un modeļi. – 1999. ftp://ftp.liis.lv/macmat/matemat/difv_mod/difmod_1.zipftp://ftp.liis.lv/macmat/matemat/difv_mod/difmod_2.zipftp://ftp.liis.lv/macmat/matemat/difv_mod/difmod_3.zipftp://ftp.liis.lv/macmat/matemat/difv_mod/difmod_4.zip

41

ftp://ftp.liis.lv/macmat/matemat/difv_mod/difmod_4.zip






1. COURSE METHODS OF THE THEORY OF BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

2. STUDY PROGRAMME



4. CREDIT POINTS 4


A credit


7. LANGUAGE Latvian


To introduce the student to both qualitative and numerical methods of the theory of boundary value problems for ordinary differential equations.


8. Ordinary differential equations (basics) 8.1. Classification of ODE8.2. The Cauchy problem for systems8.3. The Cauchy problem for equations

9. Boundary value problems (BVP)9.1. BVP for systems9.2. Linear BVP9.3. Quasi-linear BVP9.4. Nonlinear BVP

10. Elements of topology 10.1. Topological spaces10.2. Neighborhoods10.3. Functions10.4. Convergence10.5. Homotopies

11. Functional spaces 11.1. Normed spaces11.2. Banach spaces11.3. C and Cn spaces11.4. Spaces of integrable functions 11.5. Wm

n spaces

42

12. The topological degree theory 12.1. The Leray–Schauder theory12.2. Fixed point theorems

12.3. Examples

13. Numerical methods 13.1. Reduction to the Cauchy problem13.2. Reduction to integral equation13.3. Selected topics

10. LITERATURE 1. S. Bernfeld S., V. Lakshmikantham. An Introduction to Nonlinear Boundary Value Problems. - New York: Academic Press 1974.

2. T. Cīrulis. Funkcionālanalīze. - Rīga, 2002., 149 lpp.3. L.C. Evans. Partial Differential Equations. American

Mathematical Society, Providence, Rhode Island, 1998, 662 pp.

4. N. Lloyd. Topological degree. – Cambridge, Cambridge Univ. Press, 1978.

5. J. Mawhin. Topological degree methods in nonlinear boundary value problems. – Reg. conf. series in math., # 40. AMS publication. 1977.

6. A. Granas, R. Guenther, J. Lee. Nonlinear boundary value problems for ordinary differential equations. – Warszawa, Polish Sci. Publ., 1985.

7. J. Leray et J. Schauder. Topologie et équations fonctionnelles. Annales de École Norm. sup., 13 (1934), 45 –78. Русский перевод: Топология и функциональные уравнения.

8. A. Šostaks, M. Zandare. Topoloģijas elementi. 1.d.- R.: LVU, 1977; 2. d. - R.: LVU, 1978.

9. M. Schechter. Principles of Functional Analysis: Second Edition. American Mathematical Society, Providence, Rhode Island, 2002, 425 pp.


11. Н.И. Васильев, Ю.А. Клоков. Основы теории краевых задач обыкновенных дифференциальных уравнений. Рига, «Зинатне», 1978.

12. C. de Coster and P. Habets. Upper and Lower Solutions in the Theory of ODE Boundary Value Problems: Classical and Recent Results. – In: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations. CISM Courses and Lectures, # 371. Springer, 1997.

43



1. COURSE BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

2. STUDY PROGRAMME



4. CREDIT POINTS 4


A credit


7. LANGUAGE Latvian


The goal of the course is to get acquainted with the main results in the theory of boundary value problems for ordinary differential equations with emphasis on nonlinear theory.


1. Ordinary differential equations (basics) 1.1. Classification of ODE1.2. The Cauchy problem for systems1.3. The Cauchy problem for equations

2. Boundary value problems 2.1. BVP for systems2.2. Linear BVP2.3. Quasi-linear BVP2.4. Nonlinear BVP

3. BVP in mathematical modeling

4. Selected topics .

5. The second order BVP 5.1. Linear BVP 5.2. Classical examples5.3. Homogeneous and nonhomogeneous BVP5.4. Green’s function

6. The second order nonlinear BVP 6.1. Introduction6.2. The Picard theorem6.3. The Bernstein theorem

44

6.4. The method of upper and lower solutions6.4.1. A-type conditions6.4.2. B-type conditions6.4.3. The Nagumo conditions

7. Higher order nonlinear BVP 7.1. The third order BVP7.2. The fourth order BVP

8. The second order BVP for systems 8.1. Introduction8.2. A-type conditions 8.3. B-type conditions

10. LITERATURE 1. E.A. Coddington, N. Levinson. Theory of Ordinary Differential Equations. – Mc Graw – Hill, 1955.

2. (Э.А. Коддингтон, Н. Левинсон. Теория обыкно-венных дифференциальных уравнений. – М., ИЛ, 1955).

3. P. Hartman. Ordinary differential equations.- John Wiley, 1964 (Ф. Хартман. Обыкновенные дифференциальные уравнения. М., Мир, 1970).




7. М.В. Федорюк. Обыкновенные дифференциаль-ные уравнения. М., Наука, 1980.

8. Э. Камке Справочник по обыкновенным дифференциальным уравнениям. – М., 1976 и др.


10. Čerāne S. Diferenciālvienādojumi un modeļi. – 1999. http :// www . liis . lv /

45

http://www.liis.lv/

Appendix 3. Set questions for the final examination in mathematics

Set of questions for the final examination in mathematicsThe Doctoral study program “Mathematics“

Sub-branch “Differential equations“

1. Methods of the theory of boundary value problems for ordinary differential equations (ODE).The spaces of continuous functions C and Cn. The spaces of integrable functions Lp. - spaces. Topological spaces and maps. Convergence in a topological space. Homotopic maps. The theory of a topological degree and applications for ODE. Numerical methods for ODE.2. Actual problems in the theory of differential equations.Classification of ODE. Existence and uniqueness of solutions. ODE and integral equations. The method of successive approximations. Continuous dependence on the initial data and parameters. Linear ODE and systems of ODE. Linear systems with constant coefficients. Linear systems with periodic coefficients. Oscillation and comparison theorems for the second order ODE. Interpolation (classical polynomials, splines). Special functions. Orthogonal polynomials.3. Boundary value problems of ODE.ODE and boundary value problems (BVP). BVP in mathematical modelling. The second order linear and nonlinear BVP. Green’s function, the Picard and Bernstein theorems. The method of upper and lower functions (A-type, B-type and the Nagumo conditions). The third and fourth order nonlinear BVP. The second order BVP for systems.4. Foundations of the functional analysis.Metric spaces. Linear and linear normed spaces. Maps in functional spaces. Compact sets. Compact sets in functional spaces and the Arzela theorem. Banach spaces. Linear continuous maps in Banach spaces. A conjugate space and conjugate operators. The Banach – Steinhouse theorem. Hilbert spaces. The orthogonal complement of a Hilbert space. Fourier series. The Bessel inequality and the Parceval equality. A direct sum of orthogonal subspaces in a Hilbert space. The Riesz’s theorem.

5. Operators.Compact operators. Spectrum and resolvent of an operator. Self-adjoint operators, spectra. The Fredholm alternative theory. Fixed points. Contractive maps in metric spaces. Fixed points theorems.

6. Selected items in the theory of approximation of functions.Interpolation. Splines. Special functions.

7. Partial differential equations. Elements of the theory of generalized solutions. The Cauchy – Kovalevskaja theorem, the Gårding theorem. Fundamental solution. The characteristic surfaces and characteristic directions. The general PDV classification. Elliptic equations and systems. Posing of boundary value problems. Classical solutions, the maximum principle. Green’s function. A generalized solution, a priori estimates, smoothness properties of a generalized solution. Parabolic equations and systems. Posing problems. Classical solutions, the maximum principle. . A generalized solution, a priori estimates, smoothness properties of a generalized solution. Hyperbolic equations and systems. Posing problems. Classical solutions, shock wave fronts. The first order

46

hyperbolic systems. Conservation laws, generalizations of the notion of a solution.

8. Calculus of variations.The classical calculus of variations. The Euler equation. Criteria for the minimum.

9. Numerical methods in the theory of differential equations.The Cauchy problem for ODE. One-step and multi-step methods. Convergence and stability. Methods for solution of stigg systems. BVP for ODE. Grid points and shooting methods. Construction of a difference scheme, principles and methods. BVP for PDE of elliptic type. Ritz-Galerkin and finite element methods.

Literature


2. N. Lloyd. Topological degree. – Cambridge, Cambridge Univ. Press, 1978.3. J. Mawhin. Topological degree methods in nonlinear boundary value problems. –

Reg. conf. series in math., # 40. AMS publication. 1977.4. A. Granas, R. Guenther, J. Lee. Nonlinear boundary value problems for ordinary

differential equations. – Warszawa, Polish Sci. Publ., 1985.5. J. Leray et J. Schauder. Topologie et équations fonctionnelles. Annales de École

Norm. sup., 13 (1934), 45 –78. Русский перевод: Топология и функциональные уравнения.



8. C. de Coster and P. Habets. Upper and Lower Solutions in the Theory of ODE Boundary Value Problems: Classical and Recent Results. – In: Nonlinear Analysis and Boundary. Value Problems for Ordinary Differential Equations. CISM Courses and Lectures, # 371. Springer, 1997.

9. E.A. Coddington, N. Levinson. Theory of Ordinary Differential Equations. – Mc Graw – Hill, 1955. (Э.А. Коддингтон, Н. Левинсон. Теория обыкновенных дифференциальных уравнений. – М., ИЛ, 1955).

10. P. Hartman. Ordinary differential equations.- John Wiley, 1964 (Ф. Хартман. Обыкновенные дифференциальные уравнения. М., Мир, 1970).

11. Ф. Трикоми. Дифференциальные уравнения. - М., ИЛ, 1962.12. М.В. Федорюк. Обыкновенные дифференциальные уравнения. М., Наука,

1980.13. Камке Э. Справочник по обыкновенным дифференциальным уравнениям. –

М., 1976 и др. 14. Васильев Н.И., Клоков Ю.А., Шкерстена А.Я. Применение полиномов

Чебышева в численном анализе. Рига, «Зинатне», 1984.15. Мэтьюз Дж., Уокер Р. Математические методы физики. М., Атомиздат, 1972.16. Справочная математическая библиотека. Высшие трансцендентные функции.

М., Наука, 1966.17. S. Čerane. Diferenciālvienādojumi un modeļi. – 1999.


47


Appendix 4. Lecturers’ Curriculum Vitae

CURRICULUM VITAE

Felix Sadyrbaev

Address: Vejavas iela 10-1, Rīga, Latvija

Phone: 583397

Data of birth: 20.11.1951.

Work experience: 2002 - Daugavpils University, Department of Mathematics, a professor; 2002 - Daugavpils Pedagogical University, the study programme “Doctor

of Mathematics”, a programme director; 1999 - Daugavpils Pedagogical University, Department of Mathematical

Analysis, a professor; 1980-1999 - University of Latvia, a senior scientific researcher; 1975-1980 - University of Latvia, a junior scientific researcher.

Education: 1968-1973 – University of Latvia, student of the Faculty of Physics and

Mathematics.

Qualification: 1995 – Dr.hab.math. 1992 – Dr.math. 1982 - Candidate of Physical and Mathematical Sciences.

Major Publications:1. coauthor A. Gricāns. The Taylor series expansion coefficients of solutions

of the Emden - Fowler type equations. P. 20. 9th International Conference “Mathematical Modelling and Analysis”, Jurmala, 2004, May 27 – 29.http://www.mma2004.lv/

2. Two-point nonlinear boundary value problems: quasilinearization and types of solutions. P. 54. Acta Societatis Mathematicae Latviensis, Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/

3. coauthor A. Gricāns. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. P. 32. Acta Societatis

48



Mathematicae Latviensis, Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.http://www.de.dau.lv/matematika/lmb5/

4. coauthor I. Jermačenko. Types of solutions of the second order Neumann problem: multiple solutions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 5-21.

http://www.lumii.lv/sbornik1/contents.htm5. coauthor A. Gricāns. The Taylor series expansion coefficients of solutions

of the Emden - Fowler type equations. Abstracts of the 9th International Conference “Mathematical Modelling and Analysis” (May 27 - 29, 2004, Jurmala, Latvia).

6. coauthor A. Gricāns. Trigonometry of lemniscatic functions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 22-29.

http://www.lumii.lv/sbornik1/contents.htm7. coauthor I. Jermačenko. Multiple solutions of boundery value problems

via Schaudera principle. – LU Zinātniskie raksti (pieņemts publicēšanai).8. coauthor A. Gricāns. Remarks on lemniscatic functions. – LU Zinātniskie

raksti (pieņemts publicēšanai).9. coauthor Yu.A.Klokov, On exponentially superlinear differential

equations. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 28.-35.

10.coauthor A. Gricans, Lemniscatic functions in the theory of the Emden – Fowler differential equation. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 5.-27.

11. coauthor A.Ya. Lepin, The Upper and Lower Functions Method for Second Order Systems. Zeitschrift für Analysis und ihre Anwendungen (Journal for Analysis and its Applications), 20 (2001), No. 3, 739 –753.

12. coauthor L. Maciewska, On some non-elementary function, Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika.”, 2. sējums, LU MII, 2001. – 57 – 64.

13. Two-point boundary value problems for even order differential equations, Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika.”, 1. sējums, LU MII, 2000. - 91-107.

14. coauthor Yu. Klokov, Sharp conditions for rapid nonlinear oscillations, Nonlinear Analysis, 39 (2000), n.39, pp.519 – 533.

15. Comparison results for fourth order positively homogeneous differential equations, Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 616. sējums, LU, 1999. - 17-23.

16. coauthor Yu. Klokov, Rapid oscillations in sublinear problems, Funkcialaj Ekvacioj, 42 (1999), pp.339-353.

49




17.Multiplicity results for third order two-point boundary value problems, Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādo-jumi", 616. sējums, LU, 1999. - 5-16.

Academic Courses: Calculus Equations, Optimization Basics (best possible solutions), Mathematical Modelling. Differential Equations,

Organisations: A member of the American Mathematical Society, A member of the Latvian Mathematical Society.

Skills: Computer experience; Languages - Latvian - mother tongue, Russian - fluent, English - good.

50

CURRICULUM VITAE

Zaiga Ikere

Address: Ciolkovska Street 5-55, Daugavpils, LV-5410


Work experience: Since 2002 Rector of Daugavpils University 1998-2002 Professor of Daugavpils University, Head of the English

language department 1996-1998 Docent of DPU, Head of the English language department 1985-1996 Docent of DPU 1981-1985 Senior lecturer of DPI 1980-1981 Lecturer of DPI 1975-1977 Lecturer of DPI 1971-1975 The English language teacher at Kuldīga Seconday School

No 2

Education and scientific degrees: 1998 Dr. habil. philol. 1993 Dr.philol. September-December 1993 University of Virginia April-May 1993 Wales University Philosophy Department 1977-1980 University of Latvia, Faculty of Foreign Languages,

postgraduate course 1965-1971 University of Latvia, Faculty of Foreign Languages

Scientific publications (number)Monographs 3Scientific articles 62Theses of conferences 28Textbooks 4Popular science articles, translations 24Publicistic writing 24

Most significant publications:1. Contrastive research of the word semantics and Latvian terminology of

philosophy/ Summary of scientific works for obtaining the degree of habilitated doctor of philology. Daugavpils: Saule. 1998 – 88 pp

51

2. English-Latvian-Russian dictionary of British empirical philosophy terms. Dugavpils: Saule. – 1997 – 136 pp

3. Lexical meaning of a word. Daugavpils, 1991 – 82 pp4. Polysemy within Philosophical Terminology, from the Point of View of

Translation. – In : UTF Series- 4 / International Conference on Terminology Science and Terminology Planning/ Riga, 17 – 19 august 1992. – Vienna: TermNet, 1994. – Pp.168 – 174.

5. Anna-Teresa Tymieniecka’s Philosophy of Life and the Fostering of Ecological Thinking. – A.-T. Tymieniecka (ed.) Analecta Husserliana. – Vol. LII. – Netherlands: Kluwer Academic Publishers, 1998. – Pp. 507 – 516.

6. Translations of the main works of J.Locke, D.Hume, D.Berkley into the Latvian language (Riga: Zvaigzne, 1977, 1986, 1989)

Academic Courses: Introduction to linguistics Introductions to semantics Semantics: theory of the word meaning Latvian scientific terminology History of Latvian lexicography Lexicography in the context of the world culture Latvian phraseology Text interpretation History of linguistics

Activities in professionaland public organizations:

Expert of the LSC branch of linguistic science Expert of the LSC 12th branch (Philosophy. Sociology. Psychology.

Pedagogy). Member of Professors’ board of LU in the branch of linguistics Member of Daugavpils University Senate Member of European Union the English language studies Member of the Latvian association of the English language teachers Member if international Husserl’s and phenomenological research

association Member of the research board of international bibliographical centre

“The American Bibliographical Institute (since 2001) Member of international bibliographical centre “International

Bibliographical Centre “ (since 1999)

Grants: British Royal Academy of Sciences (April – June 1993) The USA Fulbright scholarship (September – December 1993)

52

Swedish Institute (March 1993) Grants of Latvian Scientific Council as the head of LSC projects (1991-

1993; 1993- 1996; 1996-2000; 2001-2003)

Awards: V. Seile award (1991) Diploma of LR Ministry of Education and Science (1996)

Skills and interests: Besides problems of languages and linguistics scientific interests are connected with the following trends in philosophy: the 17th and 18th

century theory of cognition and the 20th century phenomenology

53

CURRICULUM VITAE

Svetlana Asmuss

Address: office:University of Latvia, the Faculty of Physics and Mathematics home: Jūrmalas gatve 93-39, Riga, LV-1029

Phone: 9174053, 2424135

Data of birth: November 19, 1963

Work experience: University of Latvia, the Faculty of Physics and Mathematics

since 2001 – an associate professor1995-2001 – a docent1992-1995 – a university lecturer1986-1987 – an assistent lecturer

the Latvian Academy of Sciences, Institute of Mathematics of the University of Latviasince 1998 – a researcher

the University of Helsinki (Finland), Faculty of Mathematics1998 – a research

Education and scientific degrees: Academic title of a docent

1995 – the University of Latvia LR doctor in mathematical sciences

1992 – by the decision of the Habilitation and Promotion Council of the University of Latvia the candidate degree in Mathematics and Physics was nostrified as a doctor’s degree

Candidate of physics and mathematical sciences1991 – dissertation defended in the Institute of Mathematics at the Ukrainian Academy of Sciences, Kiev

Higher1987-1990 – the University of Latvia, Faculty of Physics and Mathematics, a postgraduate student in mathematical analysis1981-1986 – the University of Latvia, Faculty of Physics and Mathematics, a student of applied mathematics speciality

Research directions: the principal field of research is approximation theory; the most important results have been obtained in the following directions: interpolation and

54

smoothing spline investigation in the case of one and several arguments, isogeometrical approximation and approximation by inexact information; certain research has been done in the problems of functional analysis and topology; has worked also at the theory of fuzzy structures.

Participation in projects: 2001-2004 – project “Research of approximative schemes of topological,

functional and algebraic structures, L-value categories and L-value data” financed by the Latvian Science Council

1996-2000 – project “Research of L-topological and L-algebraic structures and categories; designing of L-approximative schemes ”, financed by the Latvian Science Council

since 1991 – the executer of research projects financed by the Latvian Science Council, last 6 years including

Publications (number): Total number of publications - 31 Teaching aids - 1 Participation in conference - more than 25 conferences

Organisational work:Editorial board member of the LU scientific papers in mathematics. Management of scientific seminars in problems of approximation theory

Scientific work abroad:02-07,1998 – in Helsinki University (Finland) at the Faculty of Mathematics

Activities in Professional organizations:Latvian Association of Mathematics; European women in Mathematics

Academic Courses: since 2001 – Theory of dimensions since 2000 – Research of operations since 1994 – General theory of optimal algorithm since 1991 – Splines and their application 1991-1994 – Functional analysis since 1990 – Mathematical analysis

Supervision of students’ research:supervisor of about 30 course, bachelor, master and diploma papers on issues of approximation theory (mainly about splines and their application). I am a supervisor of one promotion thesis: N. Budkina “Approximation of functions with smoothing splines in the case of approximative data”.

55

Teaching aids:S. Asmuss, A. Shostaks. “Definite and Indefinite (Riemmanian) integral”. – Riga: LU, 2001. – 112 pp.

56

CURRICULUM VITAE

Ojars Lietuvietis

Address: office: the University of Latvia, the Faculty of Physics and Mathematics

home: Kr. Valdemāra iela 93-9, Riga

Phone: 7376695

Data of birth: September 23, 1945

Education and scientific or academic degrees: associate professor

2001 the University of Latvia doctor in mathematics

1992 the University of Latvia docent

1990 the University of Latvia candidate of Physics and Mathematical sciences

1987 Institute of applied mathematics and mechanics at the Ukrainian Academy of Sciences

postgraduate studies1975-1978 the State University of Latvia, differential equations and mathematical physics

higher1963-1968 the State University of Latvia, mathematics

Work experience: 1967-1990 LU Computing Centre junior research associate, engineer-

mathematician programmer, senior engineer-programmer, research associate, senior research associate

1990 docentLU Faculty of Physics and Mathematics, the Department of General Physics

1987 University lecturerthe Faculty of Economies and Mathematics and Physics

1975 junior research assistantthe University of Latvia Computing Centre

Research directions:

57

the numerical methods of solution differential equations the Latvian Science Council Project Nr. 01.0201.The application of no saturated functions and asymptotical approximations for creating numerical methods.

Scientific publications (number): more than 26

58

CURRICULUM VITAE

Vyacheslavs Starcevs

Address: Sporta iela 2-24, Daugavpils, Latvija LV 5400

Phone: 5429291


Work experience: 2002 - Daugavpils University, Chair of Mathematics, an associate

professor; 1998-2002 - Daugavpils Pedagogical University, Chair of Mathematical

Analysis, an associate professor; 1997 - Daugavpils Pedagogical University, the study programme “Master

of Mathematics”, a programme director; 1994-1998 - Daugavpils Pedagogical University, Chair of Mathematical

Analysis, a docent; 1993-1994 - Daugavpils Pedagogical University, head of Chair of

Mathematical Analysis; 1982-1993 - Daugavpils Pedagogical Institute, head of Chair of

Mathematical Analysis; 1972-1982 - Daugavpils Pedagogical Institute, Chair of Mathematical

Analysis, a docent; 1969-1972 - Daugavpils Pedagogical Institute, Chair of Mathematical

Analysis, a lecturer; 1961-1969 – Astrahan Pedagogical Institute, Chair of Mathematical

Analysis, an assistant.

Education: 1966-1969 - Moscow State Pedagogical Institute, Chair of Mathematical

Analysis, a postgraduate; 1965-1966 - Moscow State Pedagogical Institute, Chair of Mathematical

Analysis, a probationer; 1956-1961 – Astrahan Pedagogical Institute, student of the Department of

Physics and Mathematics.

Qualification: 1992 – Dr.math.; 1971 - Candidate of Physical and Mathematical Sciences.

Major Publications:

59

1. Lebega mērs un integrālis, 2002 (coauthor A. Gricāns).2. http://www.de.dau.lv/matematika/lebint.pdf 3. Elementāro pamatfunkciju aksiomātiskā teorija. – Daugavpils, DPU izd.

“Saule”, 2001. – 91 lpp. (coauthor A. Gricāns). http://www.de.dau.lv/matematika/el.pdf4. Loka garums un trigonometriskās funkcijas. // Daugavpils Pedagoģiskās

universitātes 8. ikgadējās zinātniskās konferences rakstu krājums A11 (dabaszinātnes, dabaszinātņu didaktika, matemātika, datorzinātne). - Daugavpils: DPU izd. “Saule”, 2000. - 98.-99.lpp.

5. Trigonometriskās funkcijas: dažādi definēšanas paņēmieni un saskaitīšanas teorēmu pierādījumu īpatnības. // Daugavpils Pedagoģiskās universitātes 7. ikgadējās zinātniskās konferences rakstu krājums A9 (dabaszinātnes, dabaszinātņu didaktika, matemātika, datorzinātne). - Daugavpils: DPU izd. “Saule”, 1999. - 128.-129.lpp.

6. Об измеримых векторно-значных функциях. // 6. ikgadējās DPU zin. konferences rakstu krājums A8. - Daugavpils: izd.”Saule”, 1999. - 10.-14.lpp.

7. О некоторых обобщениях интеграла Лебега векторнозначных функций. // 6. ikgadējās zināt. konferences rakstu krājums A8. - Daugavpils: izd.”Saule”, 1999. - 5.-10. lpp.

Academic Courses: Mathematical Analysis, Functional Analysis, Lebesque Measure and Integral, Theory of Functions of a Complex Variable, Scientific Fundamentals of the Beginnings of Mathematical Analysis and

Algebra, General Topology, Differentiable Mappings.

Skills: Computer experience; Languages: Russian - mother tongue, Latvian - fluent, English - good.

60

http://www.de.dau.lv/matematika/el.pdf


CURRICULUM VITAE

Armands Gritsans

Address: Kastaņu iela 44-28, Ilūkste, Latvija LV 5400

Phone: 5462472


Work experience: 2002 - Daugavpils University, head of the Department of Mathematics; 1997 - Daugavpils Pedagogical University, the study programme

“Bachelor of Mathematics”, a programme director; 1996 - Daugavpils Pedagogical University, head of the Department of

Mathematical Analysis; 1995 - Daugavpils Pedagogical University, the Department of

Mathematical Analysis, a docent; 1991-1993 - Daugavpils Pedagogical Institute, the Department of

Mathematical Analysis, a lecturer.

Education: 1988-1990 - Moscow State Pedagogical University, Postgraduate course:

Topology and Geometry; 1981-1986 - Daugavpils Pedagogical Institute, student of the Faculty of


Qualification: 1992 – Dr.math.; 1991 - Candidate of Physical and Mathematical Sciences.

Qualification Courses: 05.05.1996-19.05.1996. “New Methods in Adult Education” (Sweden).

Major Publications:1. The Taylor series expansion coefficients of solutions of the Emden -

Fowler type equations. P. 20. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia. (coauthor F. Sadirbajevs).http://www.mma2004.lv/

2. Trigonometry of lemniscatic functions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 22-29. (coauthor F. Sadirbajevs).

61


http://www.lumii.lv/sbornik1/contents.htm3. The Taylor series expansion coefficients of solutions of the Emden -

Fowler type equations. P. 32. Acta Societatis Mathematicae Latviensis, Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. (coauthor F. Sadirbajevs).

4. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. Abstracts of the 9th International Conference “Mathematical Modelling and Analysis” (May 27 - 29, 2004, Jurmala, Latvia). (coauthor F. Sadirbajevs).

5. Remarks on lemniscatic functions. – LU Zinātniskie raksti (pieņemts publicēšanai). (coauthor F. Sadirbajevs).

6. Lemniscatic functions in the theory of the Emden – Fowler differential equation. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 5.-27. (coauthor F. Sadirbajevs)

7. On canonical connection of Killing f-manifold. Acta Societatis Mathematicae Latviensis, Abstrakts of the 4th Latvian Mathematical Conference, 26-27 April, 2002, Ventspils, Latvia.

8. Lebega mērs un integrālis (coauthor V.Starcevs).http://www.de.dau.lv/matematika/lebega/lebint.pdf

9. Elementāro pamatfunkciju aksiomātiskā teorija. – Daugavpils, DPU izd. “Saule”, 2001. – 91 lpp. (coauthor V.Starcevs).

10. Kopu teorijas elementi. - Daugavpils: DPU izd. “Saule”, 1997. - 169 lpp.11. Latviešu-krievu matemātisko terminu vārdnīca. - Daugavpils: DPU izd.

“Saule”, 1996.- 66 lpp.12. Krievu-latviešu matemātisko terminu vārdnīca - Daugavpils: DPU izd.

“Saule”, 1996.- 64 lpp.

Academic Courses: Functional Analysis, Lebesque Measure and Integral, Theory of Functions of a Complex Variable, Mathematical Statistics, History of Mathematics, Discrete Mathematics.

Organisations: A member of the Latvian Mathematical Society.

Skills: Computer experience; Languages - Latvian - mother tongue,

62

http://www.de.dau.lv/matematika/lebega/lebint.pdf


Russian - fluent, English - good.

63

CURRICULUM VITAE

Anita Sondore

Address: Sporta iela 8-504, Daugavpils, Latvija LV 5400

Phone: 6495316


Work experience: 2002 - Daugavpils University, the Department of Mathematics, a docent; 2001 - Daugavpils Pedagogical University, the Department of

Mathematical Analysis, a docent; 2000 - Daugavpils Pedagogical Institute, the Department of Mathematical

Analysis, a lecturer. 1995 - Daugavpils Pedagogical Institute, the Department of Mathematical


Education: 1991-1994 - Doctoral Studies at the University of Latvia in mathematics; 1985-1990 - University of Latvia, student of the Faculty of Physics and

Mathematics.

Qualification: 1998 – Dr.math.

Major Publications:1. FB-компактные и CB-компактные пространства. – thesis of the

International Conference “Teaching Mathematics: Retrospective and Perspective” at the Šiauliai University. – 1998. – p. 38-40.

2. Ar speciāliem vaļējiem pārklājumiem definētās kompaktības tipa topoloģiskās īpašības. // Daugavpils Pedagoģiskās universitātes 6.ikgadējās zinātniskās konferences materiāli, 6.sējums. – 1998. - 18.-24.lpp.

3. On CB-compact, countably CB-compact and CB-Lindelöf spaces. –“Математички весник”, 50, 1998., – p. 125-133.

4. CB-kompaktas, sanumurejami CB-kompaktas un CB-Lindelofa telpas. – 2.Latvijas matemātikas konferences tēzes, 1997. – 64.-65.lpp.

5. On kB-compact spaces. - LU, Matemātika. Zinātniskie raksti, 606.sējums, 1997. – 61.-72.lpp.

Academic Courses:

64

Theory of Probability, Mathematical Statistics, Ordinary Differential Equations, Mathematical Logic.

Skills: Computer experience; Languages: Latvian - mother tongue, Russian - fluent, English - good.

65

CURRICULUM VITAE

Vitolds Gedroics

Address: Rīgas iela 76A-14, Daugavpils, Latvija LV 5400

Phone: 5427008


Work experience: 2002 - Daugavpils University, the Department of Mathematics, a docent; 1996 - Daugavpils Pedagogical University, the Department of

Mathematical Analysis, a docent; 1994-1996 - Daugavpils Pedagogical University, head of the Department

of Mathematical Analysis; 1981 - Daugavpils Pedagogical Institute, the Department of Mathematical

Analysis, a lecturer. 1974 - Daugavpils Pedagogical Institute, the Department of Mathematical


Education: 1968-1973 - Daugavpils Pedagogical Institute, student of the Faculty of


Qualification: 1992 - Dr.paed.

Major Publications: 1. Ievads matemātiskajā analīzē. - 2003. http://www.de.dau.lv/matematika/ievmatanavit.pdf2. Viena argumenta funkciju integrālrēķini. - 2002.

http://www.de.dau.lv/matematika/int1ht.pdf 3. Vairāku argumentu funkciju diferenciālrēķini. - 2002. http://www.de.dau.lv/matematika/fun2.pdf4. Viena argumenta funkciju diferenciālrēķini. - DPU: izd.”Saule”, 2002. http://www.de.dau.lv/matematika/fun1.pdf5. Vairāku argumentu funkciju integrālrēķini. - 2004. http://www.de.dau.lv/matematika/int2.pdf6. Elementārā skaitļu teorija. Algebras profilkursa jautājumi. -

DPU: izd.”Saule”, 2000.

66

http://www.de.dau.lv/matematika/int2.pdf

http://www.de.dau.lv/matematika/fun1.pdf


http://www.de.dau.lv/matematika/int1ht.pdf

http://www.de.dau.lv/matematika/ievmatanavit.pdf

7. Matemātikas uzdevumi augstskolu reflektantiem (DPU sadaļa). - R.: Zvaigzne ABC, 1998.

Academic Courses: Mathematical Analysis, Ordinary Differential Equations, Theory of Probability, Mathematical Statistics, Theory of Functions of a Complex Variable.

Skills: Computer experience; Languages: Latvian - mother tongue, Russian - fluent, German - good.

67

Appendix 5. List of lecturers’ most important publications

LIST OF FELIX SADYRBAEV’S PUBLICATIONS

1. О существовании решений системы двух дифференциальных уравненийпервого порядка с линейными краевыми условиями, Латвийский математический ежегодник, 21 (1977), 94-98.

2. Об экстремалях вариационных задач, Латвийский математический ежегодник, 23 (1979), 124-130.

3. О двухточечной краевой задаче для системы обыкновенных дифференциальных уравнений первого порядка, Латвийский математический ежегодник, 23 (1979), 131-136.

4. Периодическая краевая задача, Межвуз. сборник «Проблемы современной теории периодических движений», Ижевск, 1979.

5. Функции Ляпунова и разрешимость первой краевой задачи для обыкновенного дифференциального уравнения второго порядка. Дифференциальные уравнения, 16 (1980), n 4, 629-634.

6. Поверхности уровня функции Ляпунова и разрешимость двухточечной краевой задачи, Латвийский математический ежегодник, 24 (1980 Поверхности уровня функций), 172-177

7. О нелинейных краевых задачах для системы двух обыкновенных дифференциальных уравнений первого порядка, В сб.: «Функциональные методы в уравнениях математической физики».- МГУ, 1980.

8. О разрешимости краевых задач для уравнения Эйлера, Латвийский математический ежегодник, 25 (1981), 81-87.

9. Об экстремалях вапиационных задач в случае медленного роста интегранта. В сб.: "Нелинейные краевые задачи для обыкновенных дифференциальных уравнений", Латв. университет, 1985. - 57-62.

10. соавтор Г. Федорова, О разрешимости краевой задачи для обобщенного уравнения Эмдена - Фаулера, В сб.: "Нелинейные краевые задачи для обыкновенных дифференциальных уравнений", Латв. университет, 1985. - 123-132.

11. О вариационном свойстве решений двухточечной нелинейной краевой задачи, Латвийский математический ежегодник, 29 (1985), 89-92.

12. соавтор Я. Виржбицкий, Об одной двухточечной краевой задаче для обыкновенного дифференциального уравнения второго порядка, Латвийский математический ежегодник, 30 (1986), 39-42.

13. О решениях краевой задачи для обыкновенного дифференциального уравнения второго порядка, Латвийский математический ежегодник, 31 (1987), 87-90.

14. О решениях задачи Неймана. В сб.: "Краевые задачи обыкновенных дифференциальных уравнений", Латв. университет, 1987.- 111-114.

15. Замечание о методе нижних и верхних функций. Acta Mathematica Universita Comeniana (Bratislava), LII-LIII (1987), 229-233.

16. О множествах Тонелли в одномерной задаче вариационного исчисления. В сб.: "Актуальные вопросы краевых задач. Теория и приложения.", Латв. университет, 1988. - 109-114.

17. О числе решений двухточечной краевой задачи, Латвийский математический ежегодник, 32 (1988), 37-41.

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18. О правильных решениях уравнения Эмдена – Фаулера, Доклады расширенных заседаний семинара ИПМ им. И.Н.Векуа, Тбилиси, ТГУ, т. 3, n 3, 1988.

19. О числе стационарных решений скалярного параболического уравнения, Латвийский математический ежегодник, 33 (1989), 76-78.

20. О решениях уравнения типа Эмдена - Фаулера. Дифференциальные уравнения, 25 (1989), n 5, 799-805.

21. Метод Важевского и двухточечная краевая задача для дифференциаль-ной системы четвертого порядка . В сб.: "Топологические пространства и их отображения", Латв. университет, 1989.- 106-111.

22. О правильных решениях уравнения типа Эмдена - Фаулера. В сб.: "Теоретические и численные исследования краевых задач", Латв. университет, 1989.- 19-25.

23. Двухточечная краевая задача для уравнения четвертого порядка, Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 553. sējums, LU, 1990. - 84-97.

24. ar I. Volfson, О сопряженных точках линейных уравнений третьего порядка. Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 570. sējums, LU, 1992. - 102-110.

25. ar A. Cibuli, Единственность и неединственность решений нелинейных эллиптических уравнений, . Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 577. sējums, LU, 1992. - 9-15.

26. Существование нетривиальных решений в периодической краевой задаче для уравнения второго порядка. Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 577. sējums, LU, 1992, - 34-38.

27. coauthor M. Gera, Multiple solutions of a third order boundary value problem, Math.Slovaca, 42 (1992), n 2, 173-180.

28. О регулярности решений в основной задаче классического вариационнгого исчисления, Математические заметки, 52 (1992), n 5, 97-101.

29. Existence theorems for n-th order boundary value problems.In: Proc. Equadiff-91, Intern. Conf. Diff. Eq. (Barcelona, August 19-26, 1991) - World Scientific, 1993, - 873-876.

30. Existence of solutions of even order nonlinear boundary value problems for ordinary differential equations. Proc. Latv. Acad. Sci., Part B. 1993. N 4 (549), 62-66.

31. Об одном свойстве решений уравнений второго порядка, Латвийскийматематический ежегодник, 34 (1993), 30-34.

32. coauthors A. Lepin, V. Ponomarev, Recent progress in investigation of several problems in nonlinear boundary value problems for ordinary differential equations, with Lepin A.Ya., Ponomarev V.D. Proc. Latvian Acad. Sci. Part B, 1993, N 4 (549), 49-55.

33. О числе решений в краевой задаче для системы двух дифференциальных уравнений второго порядка. Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 593. sējums, LU, 1994, - 39-43.

34. A boundary function approach to regularity of solutions inthe problem of the calculus of variations. Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 593. sējums, LU, 1994. - pp.77-81.

35. Нелинейные краевые задачи третьего порядка. Rakstu krājumā: "LU

69

Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 599. sējums, LU, 1995. - 114-130.

36. Nonlinear two-point fourth order boundary value problems. Rocky Mount. Math. J., 25 (1995), n 2, 757-781.

37. Multiplicity of solutions for fourth order nonlinear boundary value problems. Proc. Latv. Acad. Sci., Section B. 1995. N 5/6 (574/575), 115-121.

38. Замечание о методах оценок числа решений нелинейных краевых задач обыкновенных дифференциальных уравнений, Математические заметки, 57 (1995), n 5, 889-895.

39. Multiplicity of solutions for two-point boundary value problems with asymptotically asymmetric nonlinearities, Nonlinear Analysis: TMA, 27 (1997), n 9, 999-1012.

40. Wazewski method and upper and lower solutions for higher order ordinary differential equations. Univ. Jagellonicae Acta Math., 36 (1997), 165 – 170.

41. ar O. Zajakinu, Sturm-Liouville boundary value problem for two-dimensional differential system with asymptotically asymmetric nonlinearities. Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 605. sējums, LU, 1997. - pp.30-47.

42. соавтор Ю. Клоков, О числе решений в двухточечной краевой задаче второго порядка с нелинейной асимптотикой, Дифференциальные уравнения, 34 (1998), n 4, 471-479.

43. coauthor M. Henrard, Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities, Nonlinear Analysis: TMA, 33 (1998), n 3, 281-302.

44. coauthor Yu. Klokov, Sharp conditions for rapid nonlinear oscillations, Nonlinear Analysis, 39 (2000), n.39, pp.519 – 533.

45. coauthor Yu. Klokov, Rapid oscillations in sublinear problems, Funkcialaj Ekvacioj, 42 (1999), pp.339-353.

46. Multiplicity results for third order two-point boundary value problems, Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 616. sējums, LU, 1999. - 5-16.

47. Comparison results for fourth order positively homogeneous differential equations, Rakstu krājumā: "LU Zinātniskie raksti. Matemātika. Diferenciāl-vienādojumi", 616. sējums, LU, 1999. - 17-23.

48. Two-point boundary value problems for even order differential equations, Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika.”, 1. sējums, LU MII, 2000. - 91-107.

49. coauthor L. Maciewska, On some non-elementary function, Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika.”, 2. sējums, LU MII, 2001. – 57 – 64.

50. coauthor A.Ya. Lepin, The Upper and Lower Functions Method for Second Order Systems. Zeitschrift für Analysis und ihre Anwendungen (Journal for Analysis and its Applications), 20 (2001), No. 3, 739 –753.

51. Boundary value problems for -Laplasian equations. Acta Societatis Mathematicae Latviensis, Abstrakts of the 4th Latvian Mathematical Conference, 26-27 April, 2002, Ventspils, Latvia.

52. F. Sadirbajevs. Ievads optimizācijā. – Daugavpils: DU izdevniecība “Saule”, 2003. – 88 lpp.Ievads optimizācijā (2002.)http://www.de.dau.lv/matematika/opt.pdf

53. coauthor A. Gricāns, Lemniscatic functions in the theory of the Emden –

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http://www.de.dau.lv/matematika/opt.pdf

http://www.de.dau.lv/matematika/optfs/index.html

Fowler differential equation. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 5.-27. http://www.lumii.lv/sbornik/contents.htmhttp://www.mathpreprints.com/math/Preprint/

54. coauthor Yu.A.Klokov, On exponentially superlinear differential equations. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 28.-35.

55. Nonlinear boundary value problems of the calculus of variations. Discrete and Continuous Dynamical Systems, Additional Volume, 2003, P. 770-779.

56. Two-point nonlinear boundary value problems: quasilinearization and types of solutions. P. 54. Acta Societatis Mathematicae Latviensis, Abstrakts of the 5th

Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.57. coauthor A. Gricāns. The Taylor series expansion coefficients of solutions of

the Emden - Fowler type equations. P. 32. Acta Societatis Mathematicae Latviensis, Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.

58. coauthor I. Jermačenko. Types of solutions of the second order Neumann problem: multiple solutions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 5-21.http://www.lumii.lv/sbornik1/contents.htm

59. coauthor A. Gricāns. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. P. 20. Book of the abstracts of the 9th International Conference “Mathematical Modelling and Analysis” (May 27 - 29, 2004, Jurmala, Latvia).

60. coauthor A. Gricāns. Trigonometry of lemniscatic functions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 22-29.http://www.lumii.lv/sbornik1/contents.htm

61. coauthor I. Jermačenko. Multiple solutions of boundary value problems via Schauder principle. – LU Zinātniskie raksti (submitted).

62. coauthor A. Gricāns. Remarks on lemniscatic functions. – LU Zinātniskie raksti (submitted).

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LIST OF SVETLANAS ASMUSS’S PUBLICATIONS

1. V. Ponomarev, S. Pavlova (Asmuss). Existence and uniqueness theorems for three point boundary problems for third order non-linear differential equations. Proceedings of the VII School on Theory of Operators in Functional Spaces. Riga, 1983, P. 40-41 (in Russian).

2. M. Goldman, S. Pavlova (Asmuss). A characterisation on collectionwise normal spaces by means of divergent nets. Topological Spaces and Their Mappings. Riga, 1985, P. 55-58 (in Russian).

3. M. Goldman, S. Pavlova (Asmuss). Continuous functions with compact supports in the problem of normal solvability of equations. Continuous Functions on Topological Spaces. Riga, 1986, P. 56-63 (in Russian).

4. S. Asmuss. Error bounds of interpolation by splines. Topological Spaces and Their Mappings. Riga, 1987, P. 15-26 (in Russian).

5. S. Asmuss. On interpolation and smoothing of integral mean values by quadratic splines. Topological Spaces and Their Mappings. Riga, 1989, P. 13-35 (in Russian).

6. S. Asmuss. On interpolation of local mean values by bivariate spline- functions. Abstracts of the Conference on Extremal Problems of Approxi-mation Theory and Applications (Kiev, 1990). P. 10 (in Russian).

7. S. Asmuss. Bivariate spline functions in some interpolation problems. Acta Universitatis Latviensis. Mathematics. V. 552 (1990), P. 7-28 (in Russian).

8. S. Asmuss. Approximation of functions by splines and operator method based on it. Ph.D. Thesis. Kiev, 1991 (in Russian).

9. S. Asmuss. The exact error bounds of bivariate spline functions. Acta Universitatis Latviensis. Mathematics. V. 562 (1991), P. 11-26 (in Russian).

10. S. Asmuss. An operator method based on the transformation of stepwise representations by means of splines for local mean values. Acta Universitatis Latviensis. Mathematics. V. 562 (1991), P. 27-42 (in Russian).

11. S. Asmuss. On the extremal property of bivariate spline-functions. Acta Universitatis Latviensis. Mathematics. V. 576 (1992), P. 111-126 (in Russian).

12. S. Asmuss. Error bounds for bivariate interpolation by splines. Abstracts of the International Congress of Mathematicians ICM’94 (Zürich, 1994). P. 236.

13. S. Asmuss. Error estimates of the approximation by smoothing splines. Acta Universitatis Latviensis. Mathematics. V. 595 (1994), P. 167-178.

14. S. Asmuss, A. Šostak. A fuzzy approach to extremal problems of approximation theory. Problems of Pure and Applied Mathematics. Abstracts of the International Conference (Tallinn, 1995). P. 5.

15. S. Asmuss, A. Šostak. Extremal problems of approximation of fuzzy sets. Acta Societatis Mathematicae Latviensis. N. 1 (1995), P. 2 - 3.

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16. S. Asmuss, A. Šostak. A fuzzy approach to extremal problems of approximation theory. Proceedings of the International World Congress on Fuzzy System Association IFSA’97 (Prague, 1997). Academia, 1997, V. 1, P. 135 – 140.

17. S.Asmuss, N. Budkina, P. Oja. On smoothing problems with weights and obstacles. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics. V. 46 (1997), N. 4, P.262 – 272.

18. S. Asmuss. On optimal methods of approximation under imprecise information. Acta Societatis Mathematicae Latviensis. N. 2 (1997), P.4 - 5.

19. S. Asmuss, A. Šostak. Extremal problems of approximation of fuzzy sets. Acta Universitatis Latviensis. Mathematics. V. 606 (1997), P. 9 – 18.

20. S. Asmuss, A. Lahtinen. On the existence of positive co-monotone quadratic histosplines. Reports of the Departments of Mathematics. University of Helsinki. Preprint Nr.195 (1998), 14 p.

21. S. Asmuss. Shape preserving histopolation by quadratic splines. Approximation methods and orthogonal expansions. Abstracts of the International Conference, (1998). P.6.

22. S. Asmuss. On optimal algorithms of approximation under imprecise information. Abstracts of the International Congress of Mathematicians ICM’98 (Berlin, 1998). P.289.

23. S. Asmuss, A. Šostak. Extremal problems of approximation theory in fuzzy context. Fuzzy Sets and Systems. V. 105 (1999), N. 2, P.249 – 258.

24. S. Asmuss. On shape preserving interpolation by splines. Acta Societatis Mathematicae Latviensis. N.3 (2000), P.13.

25. S. Asmuss, A. Šostak. Nenoteiktais un noteiktais (Rīmaņa) integrālis. Mācību līdzeklis. Rīga, LU, 2001, 112 lpp.

26. S. Asmuss. On a central algorithm of the approximation under inexact information described by natural splines. Abstracts of the 4th Latvian Mathematical Conference (Ventspils, 2002). P. 10.

27. S. Asmuss. On a central algorithm of the approximation of linear functionals under inexact information. Abstracts of the 7th International Conference Mathematical Modelling and Analysis MMA2002 (Kääriku, 2002). (to appear)

28. S. Asmuss, A. Lahtinen. On the existence of positive co-monotone quadratic histosplines. Journal of Computational and Applied Mathematics. (to appear).

29. S. Asmuss. A central algorithm of approximation of linear functionals under fuzzy information. P. 11. Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. Coauthor A. Šostaks. http://www.de.dau.lv/matematika/lmb5/

30. S. Asmuss. On a method for construction of shape preserving histosplines. P. 10. Abstrakts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia.

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31. S. Asmuss. On positive co-monotone histopolation by combined quartic splines. P. 71. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia.


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LIST OF OJARS LIETUVIETIS’ PUBLICATIONS

1. У.Ё. Райтум, О.И. Лиетувиетис. О приближенном решении одного почти линейного уравнения. Латв. матем. ежегодник, № 7 (1970). – с. 161-171.

2. Ю.А. Бирзвалк, О.И. Лиетувиетис. Кондукционный мгд-канал с проводящими стенками. Магнитная гидродинамика, № 3 (1971). – с. 111-117.

3. Г.К. Гринберг, И.Я. Лауманис, О.И. Лиетувиетис. Оптимальная форма сверхпроводящего соленоида. Изв. АН Латв. ССР. Сер.физ. и тех.наук, № 2(1973). – с. 82-85.

4. Г.К. Гринберг, И.Я. Лауманис, О.И. Лиетувиетис. Авторское свидетельство СССР N 450242 на изобретение: Сверхпроводящий соленоид. Открытия, изобретения, промышленные образцы и товарные знаки, № 42 (1974). – с. 117.

5. Г.К. Гринберг, И.Я. Лауманис, О.И. Лиетувиетис. Оптимальная форма пар коаксиальных катушек из сверхпроводящего материала. Изв.АН Латв.ССР. Сер.физ. и тех. наук, № 6 (1976). – с. 51-57.

6. О.И. Лиетувиетис, Г.А. Радзиньш, У.Ё. Райтум. К оптимизации плоскопараллельных магнитных полей. Журнал вычислительной математики и математической физики, № 3 (1977). – с. 780-785.

7. О.И. Лиетувиетис. Уравнение для плотности потенциала простого слоя на кусочно гладком контуре. Латв. матем. ежегодник, № 22 (1978)ю – с. 52-61.

8. О.И. Лиетувиетис. Дифференцируемость по Фреше одного функционала в задачах оптимизации плоскопараллельных магнитных полей. Латв. матем. ежегодник, № 23 (1979). – с. 112-118.

9. О.И. Лиетувиетис. Об аналитичности решения одного операторного уравнения. Латв. матем. ежегодник, № 23 (1979). – с.112-118.

10. О.И. Лиетувиетис. Вопросы оптимизации форм ферромагнитного тела в магнитном поле постоянных токов. В кн.: Уравнения в частных производных и задачи со свободной границей. – Киев: Наукова думка, 1983. – с. 71-72.

11. О.И. Лиетувиетис. Существование решения в некоторых задачах оптимизации магнитного поля. Латв. матем. ежегодник, № 27 (1983). – с. 76-79.

12. О.И. Лиетувиетис. О вариациях угловых точек контура в некоторых задачах оптимального управления формой области. Латв. матем. ежегодник, № 31 (1988). – с. 54-65.

13. О.И. Лиетувиетис. Об одной задаче оптимального управления кусочно-гладкой границей. Автореферат диссертации кандидата физико-математических наук. Академия наук Украинской ССР Институт прикладной математики и механики. – Донецк, 1987.

14. О.И. Лиетувиетис. Об одном методе приближения кусочно гладких в смысле Ляпунова контуров. Прикл. задачи матем. физики, ЛГУ (1988).

15. H. Kalis, S.Lācis, O. Lietuvietis, I. Pagodkina. Programmu paketes MATHEMATICA lietošana mācību procesā. Mācību līdzeklis. – Rīga: Mācību grāmata, 1977. – 72 lpp.

16. T. Cīrulis, O. Lietuvietis. Application of DM-method for numerical solving of nonlinear partial differential equation. Mathematical modelling applied problems of mathematical physics. LU zin. raksti, Nr. 612 (1998). – 63.-74. lpp.

17. T. Cīrulis, O. Lietuvietis. Degenerate matrix method for solving nonlinear systems of differential equations. Mathematical Modelling and Analysis, vol. 3, Vilnius’ Technika’ (1998). – 45-56.

18. T. Cīrulis, O. Lietuvietis. Degenerate matrix method with Chebyshev nodes for solving nonlinear systems of differential equations. Mathematical modelling and Analysis, vol. 4, Vilnius’ Technika’ (1999). – 51-57.

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19. T. Cīrulis, O. Lietuvietis. Degenerate matrix method for solving some stiff differential equations. Numrerical Mathematics and Advanced Applications, Proceedings of 3rd

European Conference, “World Scientific” (2000)– 456-461.20. H. Kalis, O. Lietuvietis. The numerical study of heating and burning process in glass

fabric manufacture. numrerical Mathematics and Advanced Applications, Proceedings of 3rd European Conference, “World Scientific” (2000). – 556-563.

21. D. Cīrule, T. Cīrulis, O. Lietuvietis. Multistep degenerate matrix method for ordinary differential equations. Mathematical Modelling and Analysis, vol. 6, Nr. 1, Vilnius’Technika’ (2001). – 58-67.

22. T. Cīrulis, O. Lietuvietis. Analysis of generalized multistep Adam’s methods by degenerate matrix method for ordinery differential equations. Mathematical Modelling and Analysis, vol. 6, Nr. 2, Vilnius’ Technika’ (2001). – 192-198.

23. T. Cīrulis, O. Lietuvietis. Application of DM methods for problems with partial differential equations. Math.Modelling and Analysis, vol.7, Nr.2 (2002). - 191-200.

24. T. Cīrulis, O. Lietuvietis. Application of DM methods for PDE with nonlocal boundary conditions. P. 14. Abstracts of the 4th Latvian Mathematical Conference, Ventspils, 2002.

25. T. Cīrulis, O. Lietuvietis. Small perturbations of free interface dynamics for gas bubble in the magnetic liquid on account of gravitational and magnetic forces. P. 40. Book of Abstracts of the 9th International Conference “Mathematical Modelling and Analysis”, May 27 – 29, 2004, Jurmala, Latvia. http://www.mma2004.lv/

26. T. Cīrulis, O. Lietuvietis. Application of DM methods for problems in mathematical physics. P. 25. Abstracts of the 5th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. Līdzautors T. Cīrulis.http://www.de.dau.lv/matematika/lmb5/

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LIST OF VYACHESLAVS STARCEV’S PUBLICATIONS

Scientific papers and report theses

1. О симметрической непрерывности и симметрической дифференцируемости относительно множества. ДАН СССР. – 1969., т. 185, № 6. – с. 1251-1253.

2. Symmetric continnuity and symmetric differentiability with respect to sets. Soviet Math. Dokl. - 1969, vol 10, Nr. 2. - 517- 519.

3. О симметрической непрерывности относительно множества. Ученые записки МГПИ. – 1971., № 277. – с. 162-167.

4. Об одном обобщении понятий симметрической непрерывности и симметрической дифференцируемости. Ж. “Математика”. Известия Высших учебных заведений. – 1971., № 3. – с. 92-100.

5. О симметрической непрерывности и симметрической дифференцируемости функции относительно множества. // Автореферат диссертации на соискание уч. степени канд. физико-математических наук. – Москва, 1971. – 12 с.

6. О симметрической непрерывности и симметрической дифференцируемости функции относительно множества. // Диссертация на соискание уч. степени канд. физико-математических наук. – Москва, 1971. – 124 с.

7. Об одном обобщении понятий симметрической непрерывности и симметрической дифференцируемости. Вопросы преподавания. – Рига, 1973., т. 16, вып. 1. – с. 27-29.

8. О измеримости равномерно симметрически непрерывной функции. Вопросы преподавания. – Рига, 1973, т. 16, вып. 1. – с. 19-26.

9. О некоторых проблемах изучения курса математического анализа студентов пединститутов специальности “Математика и физика” (соавторы: Дворецкий Б., Старожицкий М.). // Аннотации докладов участников II совещания семинара преподавателей математики вузов Белорусии, Латв. ССР, Лит. ССР, Эстонской ССР, Калининградской обл. – Таллин, 1973. – с. 29-30.

10. О гладкости функций относительно множества. Ж. “Математические заметки”. – Москва, 1974., т. 15, № 3. – с. 431-436.

11. Некоторые вопросы изучения курса “Математический анализ и теория функций”. // Межвузовская н/м конференция “Активизация мышления студентов в учебном процессе”. – Даугавпилс, 1974. – с. 59.

12. Некоторые вопросы преподавания математического анализа в пединституте в связи с переходом общеобразовательной школы на новые программы. // Н/м конф. “Усовершенствование подготовки учительских кадров”. – Даугавпилс, 1976. – с. 68-69.

13. Преемственность между пединститутом и школой при изучении интегрального исчисления. // Материалы респ. н/м семинара “Преемственность в учебно-воспитательной работе между вузом и школой по математике”. – Даугавпилс, 1977. – с. 113-114.

14. Изучение теории меры и интеграла в пединститутте. // III зон. сов.-семинар зав. каф. и ведущих лекторов мат. вузов Латвийской, Литовской, Эстонской СССР и Калининградской обл. – Минск, 1977. – с. 104-105.

15. Некоторые вопросы организации учебной работы при прохождении курса “Математический анализ и теория функций” (соавтор Дворецкий Б.). // Материалы межвуз. н/м конф. Метод. основы орг. учебно-восп. работы на з/о. – Даугавпилс, 1977. – с. 102-103.

16. Дифференциальные уравнения как факультативный курс в средней школе. Ж. “Вопросы преподавания математики”. – Рига, 1978, выпуск 4. – с. 49-58.

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17. Об операторном методе решения линейных дифференциальных уравнений с постоянными коэффициентами. Ж. “Вопросы преподавания математики”. – Рига, 1978, выпуск 4. – с. 66-77.

18. Опыт работы по новой программе математического анализа по специальности 2104 “Математика-физика”. // IV Зональное совещ.-сем. Содержание и методы препод. математ. курсов в вузах. – Рига, 1980. – с. 79.

19. Вопросы преемственности при изучении меры и интеграла в школе и пединституте. // Респ. н/м конф. Проблемы подготовки учительских кадров. – Даугавпилс, 1980. – 84 с.

20. Локальное и тотальное исследование функции. // Избранные темы школьной математики. Сборник трудов. – Рига, 1980. – с. 3-37.

21. Организация научно-исследовательской работы студентов физико-математического фак. ДПИ. // Респ. н/м конф. Содержание и структура модели учителя. – Даугавпилс, 1981. – с. 82-84.

22. Ряды Фурье в курсе математического анализа специальности 2104 пед. институтов. // Н/м конф. Методика преподавания мат. анализа в пед. институтах. – Ленинград, 1983.

23. О некоторых связях школьной и вузовской математики при изучении курса математического анализа пединститута. // Н/м конф. проблемы преемственности в работе общеобраз. шк. и педагог. вузов в подготовке учителя. – Даугавпилс, 1982. – с. 58.

24. Опыт подготовки студентов пединститута к ведению факультативных занятий в школе. // Н/м конф. Проблемы преемственности в работе общеобраз. шк. и педагог. вузов в подготовке учителя. – Даугавпилс, 1982. – с. 65.

25. Применение аддитивных функций ориентированного промежутка в изложении интегрального исчисления функций одного переменного. // V Зональн. сов.-сем. зав. каф. и вед. спец. мат. вузов Бел., Латв., Лит., Эст. ССР и Калинингр. обл. – Вильнюс, 1983. – с. 22-24.

26. Олимпиадные задачи и повышение математической культуры студентов. // Uzdevumu racionāla atlase kā matemātiskās izglītības uzlabošanas līdzeklis skolā un augstskolā: Metodiskie materiāli (līdzautori: V. Balanovs, A. Gricāns). - Daugavpils: DPI, 1984. - 11.-13. lpp.

27. Diferenciālvienādojumi. // Metodiskie materiāli matemātikas fakultatīvajam kursam vidusskolā. - Daugavpils: DPI, 1984. - 58.-92. lpp.

28. Аксиома непрерывности множества R в форме существования разделяющего числа и ее использование в курсе математического анализа пединститутов. // VI-е Зональное совещание-семинар зав. каф. и вед. преп. математики вузов Бел., Латв., Лит., Эст. ССР и Калинингр. обл. РСФСР, Таллин 31 марта-2 апреля 1987. – ч. 2. – Тарту: ТГУ, 1987. – с. 147-148.

29. Вопросы организации самостоятельной работы студентов. // совершенствование подготовки учительских кадров без отрыва от производства: тезисы республиканской научно-методической конференции, Даугавпилс 19-20 ноября 1987 г. – Даугавпилс: ДПИ, 1987. – с. 96-97.

30. О подготовке учителей математики в Даугавпилсском педагогическом университете. // VII Baltijas valstu zinātniski-metodiskā konference “Matemātiskā izglītība: vēsture un mūsdienas” (līdzautors A. Galiņš). - Daugavpils: DPU, 1993. - 24.lpp.

31. Об интегральном определении элементарных функций. // Zinātniski pētnieciskais darbs pedagoga profesijā. Zinātniskie raksti, 1. sējums. - Daugavpils: izd. ”Saule”, 1996. - 99.-103. lpp.

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32. “Научные основы начал математического анализа” как дисциплина для студентов-магистрантов специальности “Дидактика математики”. // Baltijas valstu zinātniski-metodiskā semināra tēzes “Matemātikas mācīšana un skolotāju sagatavošana ( vēsture un mūsdienas, problēmas). Liepāja 31. maijs-1. jūnijs 1996. - 53.-55. lpp.

33. Совершенствование теоретической и профессиональной подготовки учителя математики по математическому анализу (вопросы теории и опыт реализации). // ”Izglītības attīstība Latvijā: pagātne, tagadne, nākotne”. DPU 75. gd. veltītas zinātniskās konferences tēzes. - Daugavpils: izd. ”Saule”, 1996. - 37.-38. lpp.

34. Matemātiskās analīzes katedra (līdz 1971. g .- matemātikas katedra). // No pedagoģiskās skolas līdz universitātei (skolotāju sagatavošana Daugavpilī (1921.-1996.)) (līdzautors A. Gricāns) - Daugavpils: izd. ”Saule”, 1996. - 80.-81. lpp.

35. О некоторых способах определения числа . “Akadēmiskās izglītības problēmas universitātē” . Zinātniskie raksti 5. sējums. - Daugavpils: izd. ”Saule”, 1997. - 5.-12.lpp.

36. Интеграл Лебега векторнозначных функций и его обобщения. “Akadēmiskās izglītības problēmas universitātē”. Zinātniskie raksti 5. sējums. (līdzautore Ž. Kambalova) - Daugavpils: izd. ”Saule”, 1997. - 13.-18.lpp.

37. Об измеримых векторно-значных функциях. // 6. ikgadējās zin. konferences rakstu krājums A8.- Daugavpils: izd. ”Saule”, 1999. - 10.-14.lpp.

38. О некоторых обобщениях интеграла Лебега векторнозначных функций. // 6. ikgadējās zināt. konferences rakstu krājums A8.- Daugavpils: izd. ”Saule”, 1999. - 5.-10.lpp.

39. Trigonometriskās funkcijas: dažādi definēšanas paņēmieni un saskaitīšanas teorēmu pierādījumu īpatnības. // Daugavpils Pedagoģiskās universitātes 7. ikgadējās zinātniskās konferences rakstu krājums A9 (dabaszinātnes, dabaszinātņu didaktika, matemātika, datorzinātne). – Daugavpils: DPU izd. “Saule”, 1999. – 128.-129.lpp.

40. Loka garums un trigonometriskās funkcijas. // Daugavpils Pedagoģiskās universitātes 8. kgadējās zinātniskās konferences rakstu krājums A11 (dabaszinātnes, dabaszinātņu didaktika, matemātika, datorzinātne). – Daugavpils: DPU izd. “Saule”, 2000. – 98.-99.lpp.

Edited works

1. Вопросы преподавания математики. – Вып. 1 сб. ст. XVI, Р.: Звайгзне, 1973. – 88 с.2. Matemātikas mācīšanas jautājumi. - 2. laid. (r.krāj. XXIV). - R.: Zvaigzne, 1975. - 108

lpp.3. Matemātikas mācīšanas jautājumi. - 3. laid. - R.: Zvaigzne, 1976. - 120 lpp.4. Kontroldarbu krājums matemātiskajā analīzē un funkciju teorijā neklātienes

nodaļas studentiem. - Daugavpils: DPI, 1976. - 132 lpp.5. Преемственность в учебно-воспитательной работе между вузом и школой по

математике: Материалы республ. научно-метод. семинара. Даугавпилс 12-13 апреля 1977 г. – Даугавпилс: ДПИ, 1977. – 128 с.

6. Методические основы организации учебно-воспитательной работы на заочном отделении: Методические материалы межвузовской научно-методической конференции, Даугавпилс 25-27 октября 1977 г. – Даугавпилс: Дпи, 1977. – 170 с.

7. Matemātikas mācīšanas jautājumi. - 4. laid. - R.: Zvaigzne, 1978. - 112 lpp.8. Skolas matemātikas izvēlētās tēmas: Starpaugstskolu zinātnisko rakstu krājums. -

R.: LVU, 1980. - 155 lpp.9. Пути совершенствования подготовки учителя математики в условиях работы со

студентами, подготовленными школой в соответствии с новым содержанием школьного курса математики: Тезисы докладов математических секций Респ.

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научно-методич. конф., Даугавпилс 23-24 апреля 1980 г. – Даугавпилс: ДПИ, 1980. – 105 с.

10. Uzdevumu racionāla atlase kā matemātiskās izglītības uzlabošanas līdzeklis skolā un augstskolā: Metodiskie materiāli. - Daugavpils: DPI, 1984. - 95 lpp.

11. Kontroldarbu krājums matemātiskajā analīzē neklātienes nodaļas I un II kursa studentiem. - Daugavpils: DPI, 1984. - 105 lpp.

12. Kontroldarbu krājums matemātiskajā analīzē neklātienes nodaļas III un IV kursa studentiem. - Daugavpils: DPI, 1984. - 84 lpp.

13. Непрерывные функции на топологических пространствах: Сборник научных трудов (межвузовский). / Отв. ред. В. Старцев. – Р.: ЛГУ, 1986. – 191 с.

Teaching aids

1. Математический анализ в метрическом пространстве /избранные главы/. Учебное пособие. – Даугавпилс, 1973. – 83 с.

2. Математический анализ в метрическом пространстве /избранные вопросы/. Т. II. – Даугавпилс, 1975. – 101 с.

3. Matemātiskās analīzes izvēlētie jautājumi (matanalīze metriskā telpā). -Daugavpils, 1979. - 128 lpp.

4. Attēlojumi metriskajās telpās. - Rīga: LVU, 1981. - 52 lpp.5. Mērojamas kopas un integrālis. Mācību līdzeklis. - Rīga, LVU. - 1982. - 124 lpp.6. Измеримые множества и интеграл. Ч. I. – Даугавпилс: ДПИ, 1984. – 114 с.7. Измеримые множества и интеграл. Ч. II. – Рига: ЛГУ, 1986. – 68 с.8. Измеримые множества и интеграл. Ч. III. – Рига: ЛГУ, 1987. – 124 с.9. Основные структуры математического анализа (метрические пространства). –

Рига: ЛГУ, 1988. – 80 с.10. Основные структуры математического анализа (непрерывные отображения). –

Рига: ЛГУ, 1989. – 84 с.11. Дифференциальное исчисление функций нескольких переменных. – Рига: ЛГУ,

1990. – 108 с.12. Геометрические приложения определенного интеграла. – Даугавпилс: ДПИ, 1991. –

105 с.13. Физические приложения определенного интеграла. – Даугавпилс: ДПИ, 1991. –

35 с.14. Математический анализ. Дифференциальное исчисление функций одной

переменной. – Даугавпилс: ДПУ изд. “Сауле”, 1995. – 123 с. (соавтор Старожицкий М.).

15. Введение в математический анализ I. Теория пределов. - Даугавпилс: ДПУ изд. “Сауле”, 1996. – 139 с.

16. Введение в математический анализ II. Непрерывные функции и отображения. - Даугавпилс: ДПУ изд. “Сауле”, 1996. – 85 с.

17. Elementāro pamatfunkciju aksiomātiskā teorija. – Daugavpils, DPU izd. “Saule”, 2001. – 91 lpp. (līdzautors A. Gricāns).

Methodological aids

1. Сборник контрольных работ по математическому анализу и теории функций для студентов заочного отделения (соавторы: Дворецкий Б., Зариня А., Кокин Я., Парпуцис Я., Старожицкий М.). – Даугавпилс, 1976. – 32 с.

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2. Рабочая программа по математическому анализу (метод. разработка для студентов I курса) (соавтор Хилькевич Г.И.) – Даугавпилс: ДПИ, 1983. – 21 с.

3. Рабочая программа по математическому анализу (метод. разработка для студентов II курса) (соавтор Хилькевич Г.И.) – Даугавпилс: ДПИ, 1983. – 15 с.

4. Методические указания по изучению математического анализа. – Даугавпилс: ДПИ, 1984. – 19 с.

5. Рабочая программа по математическому анализу (метод. разработка для студентов III курса) (соавтор Гедроиц В.). – Даугавпилс: ДПИ, 1984. – 11 с.

6. Darba programma matemātiskajā analīzē (metodisks palīglīdzeklis III kursa studentiem) (līdzautors V. Gedroics). - Daugavpils: DPI, 1984. - 11 lpp.

7. Методические указания к программе государственного экзамена по математике (вопросы математического анализа). – Даугавпилс: ДПИ, 1984. – 13 с.

8. Сборник контрольных работ по математическому анализу для студентов I-II курсов заочного отделения (на рус. и лат. яз.) (соавторы: Дворецкий Б., Зариня А., Секацкий В., Гедроица В.). – Даугавпилс, 1984. – 105 с.

9. Сборник контрольных работ по математическому анализу для студентов III-IV курсов заочного отделения (на рус. и лат. яз.) (соавторы: Иванов Б., Гедроиц В.). – Даугавпилс: ДПИ, 1984. – 84 с.

10. Математический анализ. Ч. 1-2. // Cб. метод. материалов для самостоятельной работы студ. I курса физико-математ. факультета заочного отделения. – Даугавпилс: ДПИ, 1987. – с. 14-21.

11. Математический анализ. Ч. 3-4. // Cб. метод. материалов для самостоятельной работы студ. II курса физико-математ. факультета заочного отделения (соавторы: Гедроиц В., Ермаченко И.). – Даугавпилс: ДПИ, 1988. – с. 42-57.

12. Математический анализ. Ч. 5. // Cб. метод. материалов для самостоятельной работы студ. III курса физико-математ. факультета заочного отделения. – Даугавпилс: ДПИ, 1988. – с. 39-48.

13. Математический анализ. Ч. 6. // Cб. метод. материалов для самостоятельной работы студ. IV курса физико-математ. факультета заочного отделения (соавтор Ермаченко И.). – Даугавпилс: ДПИ, 1989. – с. 13-44.

14. Математический анализ. Ч. 7. // Cб. метод. материалов для самостоятельной работы студ. IV курса физико-математ. факультета заочного отделения. – Даугавпилс: ДПИ, 1989. – с. 42-52.

15. Программа и методические указания к бакалаврскому экзамену по математике (вопросы математического анализа). // рукопись. – Даугавпилс, 1995.

16. Научные основы начал математического анализа и алгебры. I Соответствия и отображения (функции). – Даугавпилс: ДПУ, 1999. – 26 с.

17. Научные основы начал математического анализа и алгебры (избранные темы). Числовые функции числового аргумента. Часть I. Основные элементарные функции (аксиоматическая теория). - Даугавпилс: ДПУ, 1999. – 82 с.

18. Научные основы начал математического анализа и алгебры (избранные темы). Числовые функции числового аргумента. Часть II. Основные элементарные функции (способы задания). - Даугавпилс: ДПУ, 2000. – 70 с.

19. Научные основы начал математического анализа и алгебры (избранные темы). Числовые функции числового аргумента. Часть III. Основные элементарные функции (способы задания). - Даугавпилс: ДПУ, 2001. – 74 с.

20. Maģistra eksāmena matemātikā jautājumi (rokrakstā). – Daugavpils: DPU, 2001.

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Teaching aids published electronically

Elementāro pamatfunkciju aksiomātiskā teorija (2002.) (līdzautors A. Gricāns)http://www.de.dau.lv/matematika/el.pdf

Lebega mērs un integrālis (2002.-2004.) (līdzautors A. Gricāns)http://www.de.dau.lv/matematika/lebega/lebint.pdf

Individuālie uzdevumi par kursu "Lebega mērs un integrālis" (2002.-2004.) (līdzautors A. Gricāns)http://www.de.dau.lv/matematika/lebega/patst.pdf

Uzdevumi ar atrisinājumiem par tēmu "Lebega mērs un integrālis" (2002.-2004.) (līdzautors A. Gricāns)http://www.de.dau.lv/matematika/lebega/lebparaugi.pdf

Pamatelementārās funkcijas kā Košī uzdevuma atrisinājumi (2004.) (līdzautors A. Gricāns)http://www.de.dau.lv/matematika/elfundefpan/elfundefpanKOSI.pdf

Curricula (1993-1996)

1. Augstākā matemātika (fiziķiem).2. Matemātiskā analīze. Vispārīgs kurss (matemātiķiem, inf.bak., fiz.bak.,

mat.bak.).3. Reālā un kompleksā mainīgā funkcijas (matemātiķiem, mat.bakalaurs) (līdzautors

A. Gricāns).4. Vispārīgās topoloģijas elementi(mat.bak., mat.maģ.) (līdzautors A. Gricāns).5. Izvēles kurss “Matemātiskās analīzes jautājumi” (mat.bak.,mat.maģ.).6. Funkcionālanalīze (mat.bak., mat.maģ.) (līdzautors A. Gricāns).7. Matemātiskās analīzes sākumu zinātnisko pamatu izvēles tēmas

(mat.bak., mat.maģ., mat.did.maģ.).8. Funkciju teorijas elementi (mat.maģ.).9. Uzdevumu risināšanas praktikums (mat.maģ.) (līdzautore G. Hiļķeviča).

Curricula (1999)(Programmas apstiprinātas DPU Senāta sēdē 1999. gada 29. novembrī,

protokols Nr. 9, akreditācija: 2000. gada 29. jūnijā)

1. Matemātiskā analīze I (mat. bak., mat. skolotājs).2. Matemātiskā analīze II (mat. bak., mat. skolotājs).3. Parastie diferenciālvienādojumi (mat. bak., mat. skolotājs).4. Funkcionālanalīze I (mat. bak.) (līdzautors A. Gricāns).5. Lebega mērs un integrālis (mat. bak.) (līdzautors A. Gricāns).6. Kompleksā mainīgā funkciju teorija (mat. bak.) (līdzautors A. Gricāns).7. Ievads vispārīgajā topoloģijā (mat. bak.) (līdzautors A. Gricāns).8. Diferencējami attēlojumi (mat. bak.).9. Lebega integrālis un primitīvās funkcijas (mat. bak.).

82

http://www.de.dau.lv/matematika/elfundefpan/elfundefpanKOSI.pdf

http://www.de.dau.lv/matematika/lebega/lebparaugi.pdf

http://www.de.dau.lv/matematika/lebega/patst.pdf

http://www.de.dau.lv/matematika/lebega/patst/index.html



10. Funkcionālanalīze II (mat. maģ.) (līdzautors A. Gricāns).11. Vispārīgā topoloģija (mat. maģ.) (līdzautors A. Gricāns).12. Matemātiskās analīzes sākumu un algebras zinātniskie pamati (mat. maģ.).13. Uzdevumu risināšanas praktikums (mat. maģ.) (līdzautore G. Hiļķeviča).14. Funkciju teorijas elementi (mat. maģ.).15. Mēra un integrāļa abstraktā teorija (mat. maģ.).16. Daži Lebega integrāļa vispārinājumi (mat. maģ.).

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LIST OF ARMANDS GRITSAN’S PUBLICATIONS

Scientific publications

1. Олимпиадные задачи и повышение математической культуры студентов (соавторы: З. Баланов, В. Старцев). // Мат. республ. научно-методическая конференция ДПИ 29-30 марта 1984 г. – Даугавпилс, 1984. – с. 11-13.

2. О семействе средних нормалей поверхности V2Es. // Дифференциальная геометрия многообразий фигур. Межвуз. темат. сб. научных трудов. Вып. 17. - Калининград: Калининградский ун-т, 1986. – с. 21-25.

3. Дифференциальное уравнение dxdt =Ax в банаховом пространстве. // Непрерывные

функции на топологических пространствах: Межвуз. сб. научных трудов/ Kfndbqcrbq ey-n/ - Рига, 1986. – с. 64-68.

4. О р-поверхностях в En с общим семейством средних нормалей. // Дифференциальная геометрия многообразий фигур: Межвуз. темат. сб. научных трудов. Вып. 18. - Калининград: Калининградский ун-т, 1987. – с. 25-27.

5. К геометрии семейства средних нормалей поверхности VpEn. // Дифференциальная геометрия многообразий фигур: Межвуз. темат. сб. научных трудов. Вып. 20. - Калининград: Калининградский ун-т, 1989. – с. 34-37.

6. О гиперсферическом отображении и преобразовании Петерсона поверхности VpEn с помощью орта средней нормали. // Latvijas universitātes zinātniskie raksti / LU. - Rīga, 1990., 552.sēj. - 152.-161.lpp.

7. О геометрии киллинговых f-многообразий. // Успехи математических наук. – М., 1990., т. 45, № 4. – с. 149-150.

8. О локально симметрических киллинговых f-многообразиях основного типа. // Мат. Вестн. школы “Понтрягинские чтения. Оптимальное управление. Геометрия и анализ”. – Кемерово, 1990. – с. 20.

9. О структурной теории киллинговых f-многообразий. // Тезисы доклада конф. “Проблемы теоретической и прикладной математики”. – Тарту, 1990. – с. 47-48.

10. О некоторых распределениях на киллинговых f-многообразиях. // Ткани и квазигруппы: сб. научных трудов. – Каклинин: Калининский ун-т, 1990. – с. 142-146.

11. К геометрии киллинговых f-многообразий. / МГПИ им. В.И. Ленина. – М., 1990. – 39 с. – Деп. в ВИНИТИ 08.06.90. № 3274-В90.

12. О конформно-плоских киллинговых f-многообразиях. // Тез. докл. ХХVII научн. конф. фак. физ.-мат. и естественных наук. / УДН. – М., 1991. – с. 145.

13. Killing f- structures on principal toroidal bundles. DPU 75. gadadienai veltītās zinātniskās konferences “Izglītības attīstība Latvijā: pagātne, tagadne, nākotne” tēzes. - Daugavpils: DPU izdevn. “Saule”, 1996.- 39. lpp.

14. Matemātiskās analīzes katedra. Krājumā “No pedagoģiskās skolas līdz universitātei (skolotāju sagatavošana Daugavpilī (1921.-1996.)”. - Daugavpils: DPU izdevn. “Saule”, 1996.- 80.-81. lpp.

15. Polinomu dalīšanas atlikums kā Ermita interpolācijas uzdevuma atrisinājums (coauthor I. Gedroica). // DPU pasniedzēju un 5.(39.) studentu zinātniski metodiskās konferences materiāli. – Daugavpils: DPU izd. “Saule”, 1997. – 36.-39. lpp.

16. Ierobežotība normētās telpās (coauthor I.Brokāne). // DPU pasniedzēju un 5.(39.) studentu zinātniski metodiskās konferences materiāli. – Daugavpils: DPU izd. “Saule”, 1997. – 31.-33. lpp.

84

17. Ķīniešu uzdevums par atlikumiem polinomu algebrā. // DPU pasniedzēju un 5.(39.) studentu zinātniski metodiskās konferences materiāli. – Daugavpils: DPU izd. “Saule”, 1997. – 40.-44. lpp.

18. On canonical connection of Killing f-manifold. Acta Societatis Mathematicae Latviensis, Abstrakts of the 4th Latvian Mathematical Conference, 26-27 April, 2002, Ventspils, Latvia.

19. Lemniscatic functions in the theory of the Emden – Fowler differential equation. Rakstu krājumā: "LU MII Zinātniskie raksti. Matemātika. Diferenciālvienādojumi", 3. sējums, Rīga, 2003. – 5.-27. (coauthor F. Sadirbajevs).http://www.lumii.lv/sbornik/contents.htmhttp://www.mathpreprints.com/math/Preprint/

20. Trigonometry of lemniscatic functions // In the paper collection “Mathematics. Differential equations.” – 2004. – Univ. of Latvia, Institute of Math. and Comp. Sci. – Vol. 4 – P. 22-29. (coauthor F. Sadirbajevs).

http://www.lumii.lv/sbornik1/contents.htm21. The Taylor series expansion coefficients of solutions of the Emden - Fowler type

equations. P. 32. Acta Societatis Mathematicae Latviensis, Abstrakts of the 5 th Latvian Mathematical Conference, 6-7 April, 2004, Daugavpils, Latvia. (coauthor F. Sadirbajevs).

22. The Taylor series expansion coefficients of solutions of the Emden - Fowler type equations. P. 20. Book of the Abstract of the 9th International Conference “Mathematical Modelling and Analysis” (May 27 - 29, 2004, Jurmala, Latvia). (coauthor F. Sadirbajevs).

23. Remarks on lemniscatic functions. – LU Zinātniskie raksti (pieņemts publicēšanai). (coauthor F. Sadirbajevs).

Teaching literature

1. Latviešu-krievu matemātisko terminu vārdnīca. - Daugavpils: DPU izd. “Saule”, 1996.- 66 lpp.

2. Krievu-latviešu matemātisko terminu vārdnīca - Daugavpils: DPU izd. “Saule”, 1996.- 64 lpp.

3. Kopu teorijas elementi. – Daugavpils: DPU izd. “Saule”, 1997. – 169 lpp.4. Elementāro pamatfunkciju aksiomātiskā teorija. – Daugavpils, DPU izd. “Saule”,

2001. – 91 lpp. (coauthor V. Starcevs).5. Lebega mērs un integrālis (coauthor V. Starcevs).

http://www.de.dau.lv/matematika/lebint.pdf6. Individuālie uzdevumi par kursu "Lebega mērs un integrālis" (coauthor V. Starcevs).

http://www.de.dau.lv/matematika/patst.pdf


1. Elementāro pamatfunkciju aksiomātiskā teorija (2002.) (coauthor V. Starcevs) http://www.de.dau.lv/matematika/el.pdf

2. Lebega mērs un integrālis (2002.-2004.) (coauthor V. Starcevs)http://www.de.dau.lv/matematika/lebega/lebint.pdf

3. Individuālie uzdevumi par kursu "Lebega mērs un integrālis" (2002.-2004.) (coauthor V. Starcevs) http://www.de.dau.lv/matematika/lebega/patst.pdf

85

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http://www.de.dau.lv/matematika/lebega/patst/index.html



http://www.de.dau.lv/matematika/patst.pdf





4. Uzdevumi ar atrisinājumiem par tēmu "Lebega mērs un integrālis" (2002.-2004.) (coauthor V. Starcevs) http://www.de.dau.lv/matematika/lebega/lebparaugi.pdf

5. Pamatelementārās funkcijas kā Košī uzdevuma atrisinājumi (2004.) (coauthor V. Starcevs) http://www.de.dau.lv/matematika/elfundefpan/elfundefpanKOSI.pdf

6. A. Gricāns. Krievu-latviešu matemātisko terminu vārdnīca (2002.) http://www.de.dau.lv/matematika/kr_latv.zip7. A. Gricāns. Diskrētā matemātika (2004.)Lineāri rekurenti vienādojumi ar konstantiem koeficientiem

http://www.de.dau.lv/matematika/dm/rekvien.pdfKombinatorika

http://www.de.dau.lv/matematika/dm/Kombinatorika.pdfGrafu teorija

1. nodaļa. Ievads grafu teorija 1.1. Grafa jēdziens http://www.de.dau.lv/matematika/dm/Grafa_Jedziens.pdf1.2. Grafa ģeometriskā interpretācija http://www.de.dau.lv/matematika/dm/Grafu_Geom_Interpret.pdf1.3. Grafu matricas http://www.de.dau.lv/matematika/dm/Grafu_Matricas.pdf1.4. Grafu izomorfisms http://www.de.dau.lv/matematika/dm/Grafu_Izomorfisms.pdf1.5. Grafu piemēri http://www.de.dau.lv/matematika/dm/Grafu_Piemeri.pdf1.6. Apakšgrafi http://www.de.dau.lv/matematika/dm/Apaksgrafi.pdf1.7. Operācijas ar grafiem http://www.de.dau.lv/matematika/dm/Grafu_Operacijas.pdf1.8. Grafa virsotnes pakāpe http://www.de.dau.lv/matematika/dm/Virsotnu_Pakapes.pdf1.9. Grafa jēdziena vispārinājumi http://www.de.dau.lv/matematika/dm/Grafa_Visparinajumi.pdf1.10. Orgrafi http://www.de.dau.lv/matematika/dm/Orgrafi.pdf

2. nodaļa. Sakarīgi grafi 2.1. Sakarīga grafa jēdziens http://www.de.dau.lv/matematika/dm/Sakariga_Grafa_Jedziens.pdf2.2. Pārlase plašumā neorientētos grafos http://www.de.dau.lv/matematika/dm/P_parlaseplasuma_nonor.pdf2.3. Pārlase plašumā orientētos grafos http://www.de.dau.lv/matematika/dm/P_parlaseplasuma_or.pdf2.4. Pārlase dziļumā http://www.de.dau.lv/matematika/dm/Parlase_Dziluma.pdf2.5. Virsotņu un šķautņu sakarīgums http://www.de.dau.lv/matematika/dm/Virsotnu_Skautnu_Sakarigums.pdf

3. nodaļa. Kokihttp://www.de.dau.lv/matematika/dm/koki.pdf

4. nodaļa. Grafi ar svariem

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http://www.de.dau.lv/matematika/dm/koki.pdf

http://www.de.dau.lv/matematika/dm/Virsotnu_Skautnu_Sakarigums.pdf

http://www.de.dau.lv/matematika/dm/Parlase_Dziluma.pdf

http://www.de.dau.lv/matematika/dm/P_parlaseplasuma_or.pdf

http://www.de.dau.lv/matematika/dm/P_parlaseplasuma_nonor.pdf

http://www.de.dau.lv/matematika/dm/Sakariga_Grafa_Jedziens.pdf

http://www.de.dau.lv/matematika/dm/Orgrafi.pdf

http://www.de.dau.lv/matematika/dm/Grafa_Visparinajumi.pdf

http://www.de.dau.lv/matematika/dm/Virsotnu_Pakapes.pdf

http://www.de.dau.lv/matematika/dm/Grafu_Operacijas.pdf

http://www.de.dau.lv/matematika/dm/Apaksgrafi.pdf

http://www.de.dau.lv/matematika/dm/Grafu_Piemeri.pdf

http://www.de.dau.lv/matematika/dm/Grafu_Izomorfisms.pdf

http://www.de.dau.lv/matematika/dm/Grafu_Matricas.pdf

http://www.de.dau.lv/matematika/dm/Grafu_Geom_Interpret.pdf

http://www.de.dau.lv/matematika/dm/Grafa_Jedziens.pdf

http://www.de.dau.lv/matematika/dm/Kombinatorika.pdf

http://www.de.dau.lv/matematika/dm/rekvien.pdf

http://www.de.dau.lv/matematika/dm/dm.html

http://www.de.dau.lv/matematika/kr_latv.zip

http://www.de.dau.lv/matematika/elfundefpan/elfundefpanKOSI.pdf

http://www.de.dau.lv/matematika/lebega/lebparaugi.pdf

4.1. Ievadshttp://www.de.dau.lv/matematika/dm/Grafi_ar_svariem.pdf4.2. Floida metodehttp://www.de.dau.lv/matematika/dm/Floida.pdf4.3. Dijkstras metodehttp://www.de.dau.lv/matematika/dm/Dijkstra.pdf4.4. Belmana-Forda metodehttp://www.de.dau.lv/matematika/dm/Belmana_Forda.pdf4.5. Belmana-Kalabas metodehttp://www.de.dau.lv/matematika/dm/Belmana_Kalabas.pdf4.6. Visīsākie un visgarākie maršrutiorgrafos bez kontūriemhttp://www.de.dau.lv/matematika/dm/Bez_konturiem.pdf

5. nodaļa. Planāri grafihttp://www.de.dau.lv/matematika/dm/Planari_grafi.pdf

6. nodaļa. Eilera grafihttp://www.de.dau.lv/matematika/dm/Eilera_grafi.pdf

7. nodaļa. Hamiltona grafihttp://www.de.dau.lv/matematika/dm/Hamiltona_grafi.pdf

8. nodaļa. Grafu krāsošanahttp://www.de.dau.lv/matematika/dm/Grafu_krasosana.pdf

9. nodaļa. Pakāpju virkneshttp://www.de.dau.lv/matematika/dm/Pakapju_virknes.pdf

10. nodaļa. Neatkarība. PārklājumiNeatkarīgas virsotņu kopas. Dominējošas virsotņu kopas. Kliķe. Virsotņu pārklājumihttp://www.de.dau.lv/matematika/dm/Neatkariba_virsotnu.pdfNeatkarīgas šķautņu kopas. Šķautņu pārklājumihttp://www.de.dau.lv/matematika/dm/Neatkariba_skautnu.pdfSapārojumi divdaļu grafoshttp://www.de.dau.lv/matematika/dm/Neatkariba_saparojumi.pdf

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http://www.de.dau.lv/matematika/dm/Neatkariba_saparojumi.pdf

http://www.de.dau.lv/matematika/dm/Neatkariba_skautnu.pdf

http://www.de.dau.lv/matematika/dm/Neatkariba_virsotnu.pdf

http://www.de.dau.lv/matematika/dm/Pakapju_virknes.pdf

http://www.de.dau.lv/matematika/dm/Grafu_krasosana.pdf

http://www.de.dau.lv/matematika/dm/Hamiltona_grafi.pdf

http://www.de.dau.lv/matematika/dm/Eilera_grafi.pdf

http://www.de.dau.lv/matematika/dm/Planari_grafi.pdf

http://www.de.dau.lv/matematika/dm/Bez_konturiem.pdf

http://www.de.dau.lv/matematika/dm/Belmana_Kalabas.pdf

http://www.de.dau.lv/matematika/dm/Belmana_Forda.pdf

http://www.de.dau.lv/matematika/dm/Dijkstra.pdf

http://www.de.dau.lv/matematika/dm/Floida.pdf

http://www.de.dau.lv/matematika/dm/Grafi_ar_svariem.pdf

LIST OF ANITA SONDORE’S PUBLICATIONS


1. On clp-compact and countably clp-compact spaces (coauthor Šostaks A.). - LU, Matemātika. Zinātniskie raksti, 595.sējums, 1994. – 123.-143.lpp.

2. On clp-Lindelöf and clp-paracompact spaces. - LU, Matemātika. Zinātniskie raksti, 595.sējums, 1994. – 143.-156.lpp.

3. On kB-compact spaces. - LU, Matemātika. Zinātniskie raksti, 606.sējums, 1997. – 61.-72.lpp.

4. CB-kompaktas, sanumurejami CB-kompaktas un CB-Lindelofa telpas. – 2.Latvijas matemātikas konferences tēzes, 1997. – 64.-65.lpp.

5. On CB-compact, countably CB-compact and CB-Lindelöf spaces. –“Математички весник”, 50, 1998., – p. 125-133.

6. Ar speciāliem vaļējiem pārklājumiem definētās kompaktības tipa topoloģiskās īpašības. // Daugavpils Pedagoģiskās universitātes 6.ikgadējās zinātniskās konferences materiāli, 6.sējums. – 1998. - 18.-24.lpp.

7. FB-компактные и CB-компактные пространства. – thesis of the International Conference “Teaching Mathematics: Retrospective and Perspective” at the Šiauliai University. – 1998. – p. 38-40.


A. Sondore. Varbūtību teorija un matemātiskā statistika (2004.)Testi par tēmu "Notikumu klasifikācija"

1. Neiespējami, gadījuma un droši notikumi http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija1tests.pdf

2. Savienojami un nesavienojami notikumi http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija2tests.pdf

3. Pretējā notikuma noteikšana http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija3tests.pdf

4. Labvēlīgi notikumi http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija4tests.pdf

5. Vienlīdziespējami notikumi http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija5tests.pdf

6. Pilna notikumu kopa http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija6tests.pdf

7. Notikumu summa un reizinājums http://www.de.dau.lv/matematika/anitavtms/testi/notikumi/notikumuklasifikacija7tests.pdf

88

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http://www.de.dau.lv/matematika/anitavtms/anitavtms.html




Individuālie darbi varbūtību teorijā

1. Notikumu varbūtība http://www.de.dau.lv/matematika/anitavtms/individualie/1indd.pdf

2. Atkārtoti mēģinājumi http://www.de.dau.lv/matematika/anitavtms/individualie/2indd.pdf

3. Gadījuma lielumi http://www.de.dau.lv/matematika/anitavtms/individualie/3indd.pdf

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LIST OF VITOLDS GEDROICS’ PUBLICATIONS


1. Daži elementāro funkciju teorijas jautājumi skolas un pedagoģisko institūtu matemātikas kursos. (В кн.: ”Проблемы преемственности в работе общеобразовательной школы и педагогических вузов в подготовке учителей”, ч. I). - Daugavpils, 1982. - 60. - 62.lpp.

2. Формы организации самостоятельной работы студентов при изучении курса математического анализа. (Сб. тезисов научно методического семинара Балтийских стран. Проблемы содержания, методики и форм организации обучения математике). - Шауляй, 1995. - с. 33 - 34.

3. Matemātikas profilkursa loma skolēna personības veidošanā. DPU 75. gadadienai veltītās zinātniskās konferences “Izglītības attīstība Latvijā: pagātne, tagadne, nākotne” tēzes. - Daugavpils: DPU izdevn. “Saule”, 1996. - 42. lpp.

4. Daži paņēmieni funkcijas ekstremālo vērtību atrašanā. “Akadēmiskās izglītības problēmas universitātē”. Zinātniskie raksti, 5. sēj. (līdzautore V. Gedroica). - Daugavpils: DPU izdevn. “Saule”, 1997. - 53. - 55. lpp.

Teaching literature

1. Matemātikas un fizikas iestājeksāmenu materiāli DPI 1978. g. (I daļa latviešu un krievu val.; līdzautors Š. Mihelovičs). - Daugavpils: DPI, 1979. - 22 lpp.2. Darba programma matemātiskajā analīzē II kursa matemātikas specialitāšu

studentiem (līdzautori: V. Gedroica, I. Bura). - Daugavpils: DPI, 1983. - 14 lpp.3. Matemātikas iestājeksāmenu materiāli DPI 1982. gadā (latviešu un krievu val. -

Daugavpils: DPI, 1983. - 24 lpp.4. Bezgalīgas kopas (gr. “Metodiskie materiāli matemātikas fakultatīvajam kursam

vidusskolā”). - Daugavpils: DPI, 1984. - 35. - 37. lpp.5. Metodiskie norādījumi Valsts eksāmena matemātikā programmai (matemātiskās

analīzes jautājumi). - Daugavpils: DPI, 1984. - 14 lpp.6. Kontroldarbu krājums matemātiskajā analīzē III-IV kursa n/n studentiem (latviešu un

krievu val.; līdzautori: B. Ivanovs, V. Starcevs). - Daugavpils: DPI, 1984. - 84 lpp.7. 1987. gada DPI matemātikas iestājeksāmenu materiāli (latviešu un krievu val.;

līdzautore: E. Laudiņa). - Daugavpils: DPI, 1988. - 28 lpp.8. Elementārās funkcijas. Metodiskie materiāli (līdzautore V. Gedroica). -Daugavpils:

DPI, 1988.- 78 lpp.9. Ievads matemātiskajā analīzē. Mācību līdzeklis. - Daugavpils: DPI, 1989.- 98 lpp.

10. Viena argumenta funkciju diferenciālrēķini. Mācību līdzeklis. - Rīga: LVU, 1990.- 90 lpp.

11. Viena argumenta funkciju integrālrēķini. Mācību līdzeklis. - Daugavpils: DPI, 1992.- 144 lpp.

12. Vairāku argumentu funkciju diferenciālrēķini. Mācību līdzeklis. -Daugavpils: DPU, 1995. - 73 lpp.

13. Daugavpils Pedagoģiskā universitāte. // Matemātikas uzdevumi augstskolu reflektantiem (sastādītāja B. Siliņa). – R.: Zvaigzne ABC, 1998. - 5.- 19. lpp.

14. Elementārā skaitļu teorija. Algebras profilkursa jautājumi. - DPU: izd. ”Saule”, 2000. - 54 lpp.

15. Kombinatorika. Algebras profilkursa jautājumi (datorsalikums). - 2001.16. Viena argumenta funkciju diferenciālrēķini. - DPU: izd. ”Saule”, 2002. - 100 lpp.

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V. Gedroics. Vairāku argumenta funkciju integrālrēķini (2004.)http://www.de.dau.lv/matematika/int2.pdf

V. Gedroics. Ievads matemātiskajā analīzē (2003.)http://www.de.dau.lv/matematika/ievmatanavit.pdf

V. Gedroics. Viena argumenta funkciju diferenciālrēķini (2002.)http://www.de.dau.lv/matematika/fun1.pdf

V. Gedroics. Viena argumenta funkciju integrālrēķini (2002.)http://www.de.dau.lv/matematika/int1.pdf

V. Gedroics. Vairāku argumentu funkciju diferenciālrēķini (2002.)http://www.de.dau.lv/matematika/fun2.pdf

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http://www.de.dau.lv/matematika/fun2/index.html


http://www.de.dau.lv/matematika/int1ht/index.html


http://www.de.dau.lv/matematika/fun1/index.html

http://www.de.dau.lv/matematika/ievmatanavit.pdf

http://www.de.dau.lv/matematika/ievmatanavit2ht/index.html


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