university of rajshahi numerical grade letter grade grade...

DEPARTMENT OF MATHEMATICS University of Rajshahi

Rajshahi-6205, Bangladesh

Syllabuses for B.Sc. (Honours)

Session : 2010-2014

211. Grading System:

The credit achieved by an examinee for 5, 75 & 10 unit shall be 2, 3 & 4 respectively. i) Table of Letter Grade, Grade Point for credit courses Numerical grade Letter Grade Grade Point 80% or its above A+ (A plus) 4-00 75% to less than 80% A (A regular) 3.75 70% to Less than 75% A- (A minus) 3.50 65% to less than 70% B+ (B plus) 3.25 60% to less than 65% B (B regular) 3-00 55% to less than 60% B- (B minus) 2.75 50% to less than 55% C+ (C plus) 2.50 45% to less than 50% C (C regular) 2-25 40% to less than 45% D 2.00 Less than 40% F 0.00 Incomplete I

Absence from the final examination shall be considered incomplete with the letter grade "I". Award of Degree, Promotions and Improvement of Results a) Award of degree: The degree of Bachelor of Science with Honours in any

subject shall be awarded on the basis of CGPA obtained by a candidate in B. Sc. Honours Part-1, Part-2, Part-3 and Part-4 examinations. In order to qualify for the B.Sc. Honours degree a candidate must have to obtain within 6 (six) academic years from the date of admission.

i) a minimum CGPA of 2.50. ii) a minimum GPA of 2.00 in the practical courses in each of Part-1, Part-2,

Part-3 and Part-4 examination. iii) a minimum TCP of 144 with fourth year Credit point 38. iv) "S" letter grade in English course (in 4 academic years from the date of

admission). The result shall be given in CGPA with the corresponding LG (Table of LG, GP and CP) in bracket. For instance, in the example cited above the result is "CGPA = 3.09 (B)" b) Publication of Results: The overall results of a successful candidate covering

all examinations of four years shall be declared on the basis of CGPA. The transcript in English shall show the course number, course title, credit, grade and grade point of individual courses, GPA of each year, CGPA and the corresponding LG for the overall result.

c) Promotions: In order to be eligible for promotion from one class to the next higher class, a candidate must secure

3 (i) at least 2.00 GPA in each of his/ her Part-1, 2.25 GPA in Part2,

and 2.50 GPA in Part-3 examinations, (ii) at least 2.00 GPA in each of his/her Part-1, Part-2 and Part-3

practical examinations, and class assignments/Tutorial/Home assignments Course Examinations and

(iii) 34 credits for each of part-1 and Part-2 and 38 credits in Part-3 examinations.

d) Course Improvement: A promoted student earning a grade less than 2.75 in individual courses, shall be allowed to improve the grades on courses, not more than two full unit courses including those of F grades, if any, of Part-1, Part-2 and Part-3 examinations or their equivalent courses (in case of changes in the syllabus), defined by the departmental academic committee, through the regular examination of the immediate following batch. However, if the candidate fails to clear his/her F grades in the first attempt, he/she shall get a second (last) chance in the immediate next year to clear the F grades No improvement shall be allowed in practical course examinations/ viva-voce/ class assessment/ tutorial/ terminal/ home assignment and thesis/ project/ in-plant training curses. If a candidate fails to improve his/her course grade, the previous grade shall remain valid. If a readmitted candidate fails to appear at the class assessment/ tutorial/ terminal/ home assignment and thesis/ project/ in-plant training courses, his/her previous grades shall remain valid.

e) Result Improvement: A candidate obtaining a CGPA of less than 2.75 at the end of the part-4 examinations within 5(five) academic shall be allowed to improve his/her result, on up to a maximum of 4(four) full units of the Part-4 theoretical courses in the immediate next regular examination after publication of his/her result. Regular improvement examinations have to be completed within six academic years. The year of examination, in the case of a result improvement, shall remain same as the regular examination. No improvement shall be allowed for practical courses/ viva-voce/class assessment/ tutorial/ terminal/ home assignment, thesis/ project/ in-plant training courses. If a candidate fails to improve CGPA with the block of new GP in total, the previous result shall remain valid.

f) Pass Degree: Candidates failing to obtain the required GPA, i) for promotion in Honours Part-3 examination in 4 (four) academic years, in

case of readmission in Part-3 course year, or 5 (five) academic years, with no readmission in Part-3 course year from the date of admission, or

ii) for Honours degree in Honours Part-4 examination in 6 (six) academic years from the date of admission,

but secure a) a CGPA of at least 2.00 ignoring TCP up to Honours Part-3 examination and, b) a minimum TCP of 80% of the total, and

4 c) a LG of "S" in the English Course in four academic years from the date of

admission, shall be awarded a B.Sc. Pass degree. Such candidates shall not be allowed to improve, on the B.Sc. Pass degree.

g) Dropping out : Candidates failing to earn the yearly required GPA after completing regular examinations and subsequently failed again after taking readmission in 1st, 2nd or 3rd year or to clear F grades in the stipulated period shall be dropped out of the programme.

16. Academic Calendar: The date of beginning and completion of courses, date of examination, publication of results etc. shall have to be declared by the department concerned through an academic calendar at the beginning of the session. In preparing the calendar the following points shall have to be considered:

a) Courses shall have to be completed within 8 (eight) months. b) Examination shall start after three weeks from the date of completion of the

courses c) At least. 2 (two) theoretical course examinations shall be held per week.

5 UNIVERSITY OF RAJSHAHI

FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS

B. Sc. (Honours) Syllabus Session: 2010-2014

The B. Sc. Honours course in Mathematics would be spread over Four academic years.

The B. Sc. Honours Examination in Mathematics for students of 2010-2014 session will be held in Four parts:

Honours Part-I Examination, 2011 will be held at the end of 2010-2011 session.

Honours Part-II Examination, 2012 will be held at the end of 2011-2012 session.

Honours Part-III Examination, 2013 will be held at the end of 2012-2013 session.

Honours Part-IV Examination, 2014 will be held at the end of 2013-2014 session.

The result of a candidate will be determined on the combined results of Part-1, Part-11, Part-III and Part-IV examinations.

6UNIVERSITY OF RAJSHAHI

FACULTY OF SCIENCE DEPARTMENT OF MATHEMATICS

B. Sc. (Honours) Part -I. Examination, 2011

Honours Part-I Examination will comprise of 950 marks (Theory courses-750, Math. Practical 100, Tutorial, Terminal and Class Records 50 and Viva-Voce 50). The duration of examination for each theory course is 4 hours for 75 and 100 marks and 3 hours for 50 marks. There is a noncredit English course of 50 marks.The duration of the practical examination is 6 hours.

Course No. Title of Courses Full Marks Credit Unit Math.-101 Algebra and Trigonometry 100 4 1 Math.-102 Geometry of Two and Three

Dimensions 100 4 1

Math.-103 Calculus -1 100 4 1 Math.-104 Set Theory & Matrix Algebra 100 4 1 Phy.-105 Mechanics, Properties of matter,

Wave and Sound 75 3 75

Phy.-106 Electricity and Magnetism 75 3 75 Stat.-107 Introductory Statistics 100 4 1 Stat.-108 Theory of Statistics 100 4 1

Math.-109 Tutorial, Terminal and Class Records

50 2 5

Math.-110 Viva-Voce 50 2 5 Math.-111 Math. Practical-I 100 4 1

Total 950 38 95 DM-112 Functional English 50 0 5

Courses for other Departments

Math.-115 Algebra, Trigonometry and Vector 75 Math.-116 Algebra and Trigonometry, 75 Math.-117 Differential and Integral Calculus 75

7 Math-101

Algebra &Trigonometry

1 Unit Full marks-100 Credit-4 [3 Lectures per week. Five questions to be answered out of eight]

Group-A 1. Arithmetic, Geometric and Harmonic means, Weierstrass, Cauchy's and

Chebyshev's inequalities. 2. Fundamental theorem of algebra, Relation between roots and coefficients, Descartes

rule of signs. 3. Solutions of cubic and biquadratic equations. 4. Difference equations, Summation of algebraic series. Group-B 5. Complex numbers and their properties. De Moivre's theorem and its applications. 6. Functions of complex arguments, Gregory's series. 7. Summation of trigonometric series. 8. Hyperbolic functions, Factorizations. BOOKS RECOMMENDED: 1. Bernard and Child : Higher Algebra 2. Burnside and Panton : Theory of equations 3. Hall and Knight : Higher Algebra 4. Das and Mukherjee : Higher Trigonometry 5. Sattar, M.A. : Higher Trigonometry

8Math-102

Geometry of Two & Three Dimensions

1 Unit Full marks-100 Credit-4

[3 Lectures per week. Five questions to be answered out of eight.]

Group-A 1. Transformation of coordinates. Pair of straight lines 2. Circles, System of circles 3. Parabola, Ellipse and Hyperbola. 4. The general equation of 2nd degree and reduction to standard forms. Identification

of conics. Group-B 5. Coordinate systems, Direction cosines and direction ratios, Planes. 6. Straight lines, shortest distance 7. Sphere, Cylinder and cone. 8. The general equations of second degree and reduction to standard forms. Identification of conicoids. BOOKS RECOMMENDED: 1. Askwith, H.H. : Analytic Geometry of Conic Sections 2. Smith, C : Analytic Geometry of Conic Sections 3. Loney, S. L. : Analytic Coordinate Geometry 4. Kar, J. M. : Analytic Geometry of Conic Sections 5. Bell, J. T : A Treatise on Three Dimensional Geometry 6. Smith, C : An Elementary Treatse on Solid Geometry 7. Wt wkwki Kzgvi fÆvPvh© : mœvZK wØgvwÎK R¨vwgwZ

9 Math-103 Calculus-I



Group-A 1. Functions: Domain, range, inverse and graphs of functions, Limits, continuity and

differentiability, Indeterminate forms. L'Hospital's rule. 2. Differentiation, Successive differentiations, Leibnitz theorem. 3. a) Expansions of functions : Rolle's theorem, Mean value theorem, Taylor's and

Maclaurin's theorems. b) Maxima and Minima of functions of one variable. 4. Partial differentiations, Euler's theorem, Tangents and normals. Group-B 5. Indefinite integrals: Method of substitutions, Integration by parts, Special

trigonometric functions and Rational fractions. 6. Definite integrals: Fundamental theorem, General properties, Evaluations of definite

integrals. 7. Reduction formulas. 8. Improper Integrals. BOOKS RECOMMENDED: 1. Edwards, J. : Differential Calculus 2. Ayres, F. : Calculus 3. Das and Mukherjee : Differential Calculus 4. Das and Mukherjee : Integral Calculus 5. Williamson : Integral Calculus 6. Spigel, M.R. : Advanced Calculus 7. Anton, H. : Calculus 8. Thomas, G.B. and : Calculus and Analytical Finny, R.L. Geometry 9. Stein and Bercellos : Calculus and Analytical Geometry

10

Math-104 Set Theory & Matrix Algebra



1. Sets: Relations, product, sets, equivalence relations, partitions, partial ordering

relations'. Functions, one-to-one and onto functions, invertible functions, composition functions, recursively defined functions, relations and functions. Set functions, operations, commutative, associative and distributive operations, identity and inverse elements.

2. Cardinal Number: Denumerable and countable sets. Cardinal numbers, ordering of cardinal numbers, cardinal arithmetic. Cantor's theorem, addition and multiplication of cardinal numbers.

3. Ordered sets: Definition and examples of ordered sets, dual order, quasi-order, product sets and order, partial and total order, minimal and maximal elements, first and last elements, supremum and infimum.

4. Well Ordered Sets: Definition and examples, principle of Mathematical induction, Principle of transfinite induction, limit elements, similar sets, initial segments.

5. Ordinal numbers: Definition, inequalities and ordinal numbers, addition and multiplication of ordinal numbers, structure of ordinal numbers.

6. Axiom of Choice, Zorn's Lemma and well ordering theorem, Logical truth table. 7. Types and kinds of matrices: Definitions and properties of different kinds of

matrices, adjoint, inverse and rank of a matrix. 8. System of linear equations: Echelon, normal and canonical forms of matrices,

consistency and solutions of homogeneous and non-homogeneous systems of linear equations by matrix methods.

BOOKS RECOMMENDED: 1. Lipschutz, S. : Set Theory and Related Topics 2. Zehuna, W. and Johnson, L. : Elements of Set Theory. 3. Lipschutz, S. : Linear Algebra. 4. Ansary, M. A. : Matrix.

11

Phys-105 Mechanics, Properties of Matter, Wave & Sound



Group A: Mechanics and Properties of Matter 1 . Conservation of Energy and Linear Momentum: Conservative and non-

conservative forces and systems; conservation of energy and momentum; center of mass; collision problem.

2. Rotational Motions: Rotational variable; rotation with constant angular acceleration; torque on a particle; angular moment of inertia; combined translational and rotational motion of rigid body; conservation of angular momentum.

3. Oscillatory Motions: Hook's law and vibration; simple harmonic motion; motion combination of harmonic motions; damped harmonic motion; forced oscillation and resonance.

4. Gravitation: Center of gravity of extended bodies; gravitational field and potential and their calculations; determination of gravitation constant and gravity; compound and Kater's pendulum; motion of planets and satellites; escape velocity.

5. Surface Tension: Surface tension as a molecular phenomenon; surface tension and surface energy; capillary rise or fall of liquids; pressure on a curved membrane due to surface tension; determination of surface tension of water; mercury and soap solution : effect of temperature.

6. Elasticity: Moduli of elasticity, Poisson's ratios; relations between elastic constants and their determination; cantilever; flat spiral spring.

7. Fluid Dynamics: Viscosity and coefficient of viscosity Poiseale's equation, determination of the coefficient of viscosity of liquid by Stock's method, Bernoulli's theorem and its applications, Torricelli's theorem; venturimeter.

Group B: Wave and Sound 8. Wave in Elastic Media: Mechanical waves; types of waves, superposition

principle, wave velocity; power and intensity in wave motion ; interference of waves ; complex waves; standing waves and

resonance. 9. Sound Waves: Audible, ultrasonic, and infrasonic, waves; propagation and speed of

longitudinal waves; vibrating systems and source of sound; beats; Doppler effect. BOOKS RECOMMENDED: 1. Ahmed and Nath : Mechanics and Properties of Matter 2. Bandopadhya and Ghose : Padartha Bidya (Bengali) 3. Constant : Theoretical Physics ( Part 1)

124. Emran, et al : General Properties of Matter

5. Halliday and Resnick : Physics ( I and II) 6. Haque : General Physics 7. Mathur : Elements of Properties of Matter 8. Newman and Searle : General Properties of Matter 9. Spiegel, M. R. : Vector Analysis 10. Symon : Mechanics 11. Halliday and Resnick : Physics ( I and 11) 12. Coulson : Waves 13. Saha : Text Book of Sound 14. Wood : Text Book of Sound.

Phys-106

Electricity & Magnetism



1. Electrostatistics: Electric dipole; electric field due to a dipole: dipole on external electric field ; Gauss's Law and its applications.

2. Capacitors: Parallel plate capacitors with dielectrics; dielectrics and Gauss's Low; susceptibility, permittivity and dielectric constant; energy stored in an electric field.

3. Electric Current: Electron theory of conductivity: Conductor, semiconductors and insulators; superconductors: current and current density; Kirchhoffs Law and its applications.

4. Magnetism: Magnetic dipole; mutual potential energy of two small- magnets: magnetic, shell; energy in a magnetic field; magnetometers.

5. Electromagnetic Induction: Faradays experiment; Faraday's; Ampere's Law, motional e.m.f; self and mutual inductance; galvanometers- moving cell ballistic and deadbeat types.

6. Thermoelectricity: Thermal 9. m. f.; Seebeck, Peltier and Thomson Effects; laws of thermal e.m.f.s. Thermoelectric power.

7. D.C and A.C circuits: D.C circuits wifth.1-R, RC, LC and LCR in series; A.C circuits with LR, RC, LC and LCR in series.

BOOKS RECOMMENDED : 1. Acharyya : Electricity and Magnetism 2. Adams and Page : Principles of Electricity 3. Bopadhyys and Ghose : Padarthavidya (Bengali) 4. Constant : Theoretical Physics (Electromagnetism)

13 5. Din : Electricity and Magnetism 6. Emran, et al : Text book of Magnetism, Electricity and Modern Physics. 7. Halliday and Resnick : Physics (I and II) 8. Huz, et al : Concepts of Electricity and Magnetism 9. Islam, et al : Tarit Chumbak Tatwa O Adhunik Padartha vijnan (Bengali) 10. Kip : Fundamentals of Electricity and Magnetism.

14Stat-107

Introductory Statistics Full marks-100

Number of Lecturer - Minimum 60 (Duration of Examination : 4 Hours)

1 Unit Credit-4


Statistics: Meaning and Scope, Variables and Attributes, Collection and presentation of Statistical data, Frequency Distribution and Graphical Representation.

Analysis of Statistical Data : Location, Dispersion and their measures. Skewness, Kurtosis and their measures. Moment, Cumulants and Practical examples.

Probability : Concept of Probability, sample Space, Events. Union and Intersection of Events. Probability of Events. Laws of Probability, Conditional Probabilities. Bose Einstein Statistics. Bay`s Theorem, Chebysec's Inquality, and Practical examples.

Random Variables And Probability Distribution : Basic Concepts. Discrete and continuous random variables. Density and distribution functions. Mathematical Expectation and variance. Joint, marginal and conditional density functions. Conditional expectation and conditional variance. Moments and Cumulant generating functions. Characteristic function. Study of Binomial, Poisson, Normal and Bivariate Normal distribution and Practical example.

Bivariate Distribution : Bivariate data, Scatter Diagram, Marginal and conditional Distribution. Correlation, Rank correlation.. Partial and Multiple correlation, Contingency, Analysis and Practical applications.

Linear Regression: Linear Regression for two variables, Principle of Least Squares Method, Lines of best fit, Residual Analysis and examples.

Test of Significance : Basic Idea of Null Hypothesis, Alternative hypothesis, Type-I error, Type-II error, level of significance degree of freedom, Rejection region and Acceptance region. Test of single mean, Single variance, Two sample means and Variances. Test for 2X2 Contingency tables, Independence test and Practical example.

BOOKS RECOMMENDED :

Anderson, A.J.B.(1989) : Interpreting Data, Chapman & Hal, London. Cramer, H.(1955): The Elements of Probability Theory, Wiley, N.Y. Gupta, S.C. and Kapoor,V.K.(2001) : Fundamental of Applied Statistics, 3rd Ed.. Sultan Chand and Son's, New Delhi, India. Hool, P. G. (1993): Introductory Statistics, Wiley & Sons, N.Y. Lipschutz, S. (1987) : Probability, McGraw-Hill, N.Y. Mosteller, F., Rourke and Thomas (1970) : Probability with Statistical Applications, 2nd Ed., Addison-Wesley, N.Y. Ross, S.M.(2002) : Introduction to Probability Model's. 3rd Ed, Academic Press, N.Y. Yule, G. U. and Kendall, M. G.(1994): An Introduction to the Theory of Statistics, 14th ed., Charles Griffin, London.

15

Stat-108 Theory of Statistics

Full marks-100 Number of Lecturer - Minimum 60

(Duration of Examination : 4 Hours) 1 Unit Credit-4


Sampling Distributions : Fisher's Lemma . Study of 2- distribution. t-distribution

and F- distribution. Properties, uses and application. Distribution of sample regression coefficient and correlation coefficient in null case. Point Estimations: Basic concepts. Sufficiency, Consistency, Unbiasedness, Efficiency, Minimum variance bound estimate, Cramer-Rao Lower bound. Principle of maximum likelihood. Method of moments, Illustration from Binomial, Poisson and Normal distribution.

Hypothesis Testing :Basic concepts. Simple hypothesis, Composite hypothesis, Critical region, Best Critical region, Most Powerful test, Uniformly most Powerful test, Likelihood Ratio test and Examples. Large Sample Test :Equality of K 2 Proportions. Means and Variances. Test for regression and Correlation Coefficients. Test for r×c Contingency tables. Exact Test for 2×2 Contingency tables Examples. Non -parametric Test : Sign test, Run test and Rank Sum test. Examples.

BOOKS RECOMMENDED:

Hogg and Tanis (2001). Probability and Statistical Inference, 6th ed ., Prentice Hall, N.J.

Hogg R.V. and A.T. Craig (2002) : Introduction to Mathematical Statistics, 5th ed., Pearson, Education, Asia.

Kendall, M.G. and Stuart, A.(2004) : Advanced Theory of Statistics, 14th ed., Edward Arnold, N.Y.

Lehmann, E.L.(2000) : Testing of Statistical Hypothesis 4th ed., Wiley, N.Y.

Lehmann, E.L. and H.J.MD' Abrera (1981) : Non parametric Statistics. McGraw-Hill, N.Y.

Mood, A.M., F.A. Graybill and D.C. Boes (1974) : Introduction to the Theory of Statistics, 3rd ed., McGraw-Hill, N. Y.

Wonnacott, T.H and Wonnacott, R.J. (1977) : Introductory Statistics, 3rd ed., Wiley, N.Y.

Zacks, S. (1971) : Theory of Statistical Inference, Wiley, N.Y.

16

Math-111

Math Practical-I


[Six hours practical examination using MatLab.] A. Computer-75 Marks 1. Matrix manipulation: Construction of matrices, linear combination of matrices,

multiplication of matrices, inversion of nonsingular matrices, solving system of linear equations and polynomial equations. Testing the continuity and differentiability of a function only by the observation of the graphs.

2. Graphs: Plotting a set of points, line drawing joining consecutive points, Plotting of curves of some well-known functions in Cartesian and polar coordinates.

3. Conics: Identification and graphs of conics and conicoids. 4. Programming: (i) Area and perimeter of triangles, square, rectangles, rhombus,

circles etc. (ii) Summation of finite series and product of a finite number of factors. 5. Word Processing: Composition of letters, Type of Mathematical equations, drawing

etc. 6. Excel: Graphs of different functions and statistical analysis of data. B. Practical Note Book - 25 Marks

Syllabus for other departments

Math-115

Algebra, Trigonometry and Vector

0.75 Unit Full marks-100 Credit-4

[3 Lectures per week. Five questions to be answered out of eight.] Group-A 1 a) Algebra of sets, DeMorgans rule, relation and function. b) Determinants: Properties and Cramer's rule. 2. a) Inequalities. b) Summation of Algebraic Series. 3. Theory of Equations:

17 a) Theorems and relation between roots and coefficients. b) Solution of cubic equations. Group-B 4. a) De Moivre's theorem. b) Deduction from De Moivre's theorem. 5. a) Functions of complex arguments. b) Gregory's series. 6. a) Summation of series. b) Hyperbolic functions. Group-C 7. Vector addition, multiplication and differentiation. 8. Vector differential operators-grad., div. and curl. BOOKS RECOMMENDED: 1. Barnside and Panton OX: : Theory of Equations 2. Bernard and Child : Higher Algebra 3. Hall and Knight : Higher Algebra 4. Das and Mukherjee : Higher Trigonometry 5. Sattar, M. A. : Higher Trigonometry 6. Spiezel, M. R. : Vector Analysis 7. Sattar, M. A. : Vector Analysis

Math-116 Algebra and Trigonometry



1. Algebra of sets, De Morgan's rule, relation and function, 2. Determinants: Properties and Cramer's rule. 3. Inequalities: Arithmetic, Geometric and Harmonic means, Weierstrass, Cauchy's

and Chebyshev's inequalities. 4. Theory of equations: a) Theorem and relation between roots and coefficients, b)

Solution of cubic equations. 5. a) Summation of algebraic series b) Difference equations. 6. a) De Moiver's theorem, b) Deduction from De Moivers theorem. 7. a) Functions of complex arguments,

18 b) Gregory's series.

8. a) Summation of trigonometric series, b) Hyperbolic functions. BOOKS RECOMMENDED: 1. Bernard and Child : Higher Algebra 2. Barnside and Panion : Theory of Equations 3. Hall and Knight : Higher Algebra 4. Das and Mukherjee : Higher Trigonometry 5. Sattar, M.A. : Higher Trigonometry

Math-117 Differential & Integral Calculus



Group-A 1. Functions: Domain, range, inverse function and graphs of functions, limits,

continuity and indeterminate forms. 2. Ordinary Differentiation: Differentiability, differentiation, successive

differentiation and Leibnitz theorem. 3. a) Expansions of functions: Rolle's theorem, mean value theorem, Taylors and

Maclaurin's formulae. b) Maxima and minima of functions of one variable. 4. a) Partial Differentiation: Euler’s theorem, tangents and normals. b) Asymptotes. Group-B 5. Indefinite Integrals: Method of substitution, Integration by parts, special

trigonometric functions and rational fractions. 6. Definite Integrals: Fundamental theorem, general properties, evaluations of definite

integrals. 7. a) Reduction formulas. b) Improper integrals. 8. Multiple Integrals: Determination of lengths, areas and volumes. BOOKS RECOMMENDED :

19 1. Ayres : Calculus 2. Das and Mukherjee : Differential Calculus 3. Das and Mukherjee : Integral Calculus 4. Edwards : Differential Calculus 5. Williamson : Integral Calculus 6. Muhammad and Bhattacherjee : Differential Calculus 7. Muhammad and Bhattacherjee : Integral Calculus

MD-112 Functional English

[Five questions to be answered out of eight.]

0.5 Unit Full marks-50 Credit-00 Group-A

Review of parts of speech; Articles; Basic sentence structures, Verb; Tense and its forms (conjugation); Punctuations; Structure of simple, compound and complex sentences; Narrations; Voice-Change of voice; Corrections.

Group-B

Translations; Paragraph writing; Report writing on a small project. BOOK RECOMMENDED : Ahmed Sadruddin : Learning English, the Easy Way Thomson A.J. and : A Practical English Grammar Martinet A. V. Swales John : Writing Scientific English. Swan Michad : Practical English Uses. Wren and Martin : English Grammar and Composition Vallins, G. H. : Good English Homby, A. S. : The Teaching of Structural Words and Sentence Patems (Stages 1 and 2) Homby, A. S. : The Teaching of Structural Words and Sentence Patems (Stages 3 and 4) Homby, A. S. : A Guide to Patterns and Usage of English Homby, A. S. : The Advanced Learner's Dictionary.

20B.Sc. (Honours) Part - II Examination, 2012

Honours Part-II Examination will comprise of 950 marks (Theory course-750,

Mathematics Practical - 100, Tutorial, Terminal and Class Record - 50 and Viva-Voce -50). The duration of examination for each theory course is 4 hours for 75 and 100 marks and 3 hours for 50 marks. The duration of the practical examination is 6 hours.

Course No. Course Title Full Marks Unit No. Credit Math - 201 Calculus - II 100 1 4 Math - 202 Real Analysis - I 100 1 4 Math - 203 Vector and Tensor

Analysis 100 1 4

Math - 204 Ordinary Differential Equations

100 1 4

Math - 205 Computer Programming (Fortran 90)

100 1 4

Phys - 206 Heat, Radiation and Optics 75 75 3 Phys - 207 Modern Physics and

Thermodynamics 75 75 3

Stats - 208 Statistical Methods and Demography

100 1 4

Math - 209 Tutorial , Terminal and Class Records

50 05 2

Math - 210 Viva-Voce 50 05 2 Math - 211 Math Practical-II 100 1 4

Total 950 95 38

Courses (Related Subjects) for other Departments Math - 214 Geometry of Two and Three Dimensions 75 Math - 215 Vector and Differential Equations 75 Math - 216 Matrices and Differential Equations 75 Math - 217 Algebra and Geometry 75 Math - 218 Special Functions and Numerical Methods 75

21 Math-201 Calculus -II



1. Functions of several variables: Partial differentiation, total. differentiation,

differentials, Euler's. Theorem of homogeneous function, Taylor's series for functions of several variables, Jacobians.

2. Singular points: Concave and convex curves. Node cusp, conjugate points. The point of inflexion. Curve tracing.

3. Maxima and Minima of functions of several variables, Lagrange’s undetermined multipliers.

4. Curvature of plane curves, asymptotes. Group-B 5. Definite integration: Integration under the sign of differentiation and integration,

Leibnitz rule, Improper integrals. Theorem of Frullani. 6. Gamma and Beta functions. 7. Multiple integrals: Double integration, triple integration. 8. Dirichlet's Theorem, Change of order of integration. BOOKS RECOMMENDED : 1. Edwards, J. : Differential Calculus 2. Williamson : Integral Calculus 3. Spiegel, M.R. : Advanced Calculus 4. Wider : Advanced Calculus

22Math-202

Real Analysis-I 1 Unit Full marks-100 Credit-4

[3 Lectures per week. Five questions to be answered out of eight.] 1. Real number system: Rational number, field, ordered set, ordered field, least upper

bound and greatest lower bound, the least upper bound property and its applications. 2. Real number system: The existence theorem and its proof. Dedekind theorem and

its equivalence to the least upper bound property and its applications. 3. Set Theory: Finite and infinite sets, equivalence of sets, denumerable and countable

sets, uncountable sets 4. Metric spaces: Metric spaces, open and closed sets, compact sets. Perfect set.

Cantor set. 5. Sequence: Convergence sequence, bounded sequence, subsequence, Cauchy

sequence and completeness of R. 6. Series: Convergent series, Cauchy's criteria for convergent series, comparison test,

Cauchy's condensation test, Root and Ratio test, Integral test, Raabi's test, Leibnitz's test, Absolutely convergence.

7. Continuity: Continuous function, continuity and compactness, uniform continuity. 8. Differentiation: Derivative of a function, Rolle's theorem, Generalized mean value

theorem, Taylor's Theorem. BOOKS RECOMMENDED : 1. Rudin, W. : Principles of Mathematical Analysis 2. Procter and Morey, C.R. : Modern Mathematical Analysis 3. Bortle : Real Analysis 4. Royden : Mathematical Analysis

23 Math-203

Vector and Tensor Analysis


[3 Lectures per week. Five questions to be answered out of eight.] Group-A 1 . Vectors and scalars, definitions and fundamental laws. Product of vectors.

Reciprocal Vectors. Vector Geometry: Equation of planes, straight lines and spheres.

2. Vector differentiation, Vector differential operators, gradient, divergence and curl. 3. Vector integration, Green's theorem, Gauss' theorem and Stoke's theorem and their

applications. 4. Curvilinear co-ordinates. Group-B 5. Tensor and coordinate transformations. Covariant and contravariant vectors and

tensors. Mixed and invariant tensors. Addition, subtraction and multiplication of tensors, contraction, symmetric and skew-symmetric tensors, Quotient law.

6. Line element and metric tensor, Conjugate and associated tensors, Christoffel's symbols and their transformation laws.

7. Geodesics and Parallelism, Covariant derivative of a vector and a tensor, Intrinsic derivative, Tensor form of gradient, divergence, and curl.

8. Riemann Christoffel tensor, Curvature tensor, Ricci tensor, Bianchi identity, Flat space and Einstein space.

BOOKS RECOMMENDED : 1. Spain, B. : Tensor Calculus 2. Agarwal, D.C. : Tensor Calculus and Riemannian Geometry 3. Spiegel, M.R. : Vector and Tensor Analysis 4. Sattar, S.A. : Vector Analysis 5. Synge and Schild : Tensor Calculus 6. Ansary, M.A. : Tensor

24Math-204

Ordinary Differential Equations


[3 Lectures per week. Five questions to be answered out of eight.] 1 . Definitions and classifications of differential equations, problems and solutions.

Formation of differential equation. Existence and uniqueness theorem (Statement and application only). Separable and homogeneous equations.

2. Exact equation. Integrating factor. Equations made exact by integrating factor. First order linear equation. Bernoulli equation. Riccati equation.

3. First order higher degree equations-solvable for x, y and p. Clairaut's equation. Singular solutions. Orthogonal and oblique trajectories.

4. Higher order linear homogeneous equation with constant coefficients. Reduction of order. Basic theorems.

5. Linear nonhomogeneous equation with constant coefficients, Method of undetermined coefficients, Method of variation of parameters, Operator method.

6. Linear equation with variable coefficients: Cauchy-Euler equation, Legendre equation, Operational factoring, Exact equation.

7. Series solutions of linear differential equations: Taylor series method, Frobenius method.

8. Systems of linear differential equations: Method of elimination, Euler's method, Matrix method.

BOOKS RECOMMENDED: 1. Ross, S.L. : Differential Equations 2. Simmons, G.F. : Differential Equations 3. Frank Ayres : Differential Equations 4. Piaggio, H.T.H. : An Elementary Treatise on Differential Equations and Their Application. 5. Sharma, B.D. : Differential Equations 6. Ansary, M.A. : Ordinary Differential Equations.

25 Math-205

Computer Programming with Fortran '90



1 . First steps in Fortran 90 Programming, number system (binary, octal, hexadecimal), conversion and algebra.

2. Essential data handling. 3. Basic building blocks. 4. Controlling the flow of a program. 5. Repeating parts of a program. 6. Introduction to arrays. 7. More control over input and output. 8. Using files to preserve data. BOOKS RECOMMENDED : 1. Ellis, T.M.R. and Philips, I.R. : Fortran 90 Programming Lahey,

T.M. 2. Cooper Redwine : Upgrading to Fortran 90 3. Rajaraman, V. : Computer programming in Fortran 90 and 95

Phys-206 Heat, Radiation and Optics


[3 Lectures per week. Five questions to be answered out of eight.] Group A: Heat and Radiation 1 Thermometry: Gas thermometers and their corrections; measurement of low and

high temperatures; platinum resistance thermometer; thermocouple. 2. Kinetic Theory of Gases: Kinetic theory of gm deduclion of Boyle's; Charle's and

Avogardo's laws, determination of gas constants; mean free path. 3. Equation of states for gases: Equation of state for a perfect gas its experimental

study; Vander Waal's equation deduction; physical significance of 'a' and 'b' defects.

264. Liquefaction of gases: Different methods of liquefaction of air and nitrogen;

refrigeration. 5. Thermal conduction: Thermal conductivity; Fourier's equations of heat flow; thermal

conductivities of good and bad conductors. 6. Radiation: Radiation pressure; Kirchhoffs law, Black body radiation;

Stefan-Boltzmann's Wein's law. Rayleigh-Jean's law; Planck's quantum law. Group B: Optics 1. Geometrical optics: Fermats principle, theory of equivalent lenses; defect of

images; optical instruments, dispersion; rainbow. 2. Nature and propagation light: Properties of light, wave theory and Huygen's

principles, theories of light. 3. Interference: Young's experiment, biprism; colour of thin film, Newton's ring;

Michelson and Fabry-peret interferometers. 4. Diffraction: Fresnet and Fraunhofer types, diffraction through single slit, double slit

and diffraction grating; dispersive and resolving powers of gratings. 5. Polarization: Plane, elliptic and circular polarization double refraction; rotatorary

polarization, polarimeter. BOOKS RECOMMENDED : 1. Bhulyah and Rahnift : Text Book of Heat, Thermodynamics and Radiation 2. Hallidary and Rasnlak : Physics (I and II) 3. Sahel and Srivastava : A treatise on Heat 4. Leo grid Sears : Thermodyna miics 5. Zeman6ky : Heat and Thermodynamics 6. Din : Text Book of optics 7. Mathur : Principles of optics 8. Mazumder : Text Book of Light 9. Sears : Optics 10. Bandopadhyya and Ghose : Padatihavidya (Bengali)

27 Phys-207

Thermodynamics and Modern Physics



Group A: Thermodynamics 1. First law of Thermodynamics: Internal energy; work done by expanding fluid';

specific heats of perfect gases; ratio of Cp to C, isothermal and adiabatic expansions.

2. Second law of Thermodynamics and Entropy ; Reversible and irreversible processes; cantor cycle; efficiency of heat engines; absolute scale of temperature; Clausius and Clapegron's theorem; entropy; change of entropy in reversible and irreversible processes.

3. Thermodynamics Function: Thermodynamics potentials at constant volume and pressure; Maxwell's thermodynamics relations; specific heat equation; Joule-Thomson effect; production of low temperature.

Group B: Modern Physics: 1. Atomic Physics: Motion of electrons under electric and magnetic fields;

measurement of e/m and ' e ', positive sign: Thermodynamics emission; photoelectric emission; Bohr's atom model; atomic spectra; x-rays; Matter waves.

2. Nuclear Physics: Basic concept and properties of the nucleus; nuclear size, binding energy; radioactivity; elementary knowledge of fission, fusion, and reactors cosmic rays.

3. Electronics: Vacuum diodes and triodes; p-type and n-types, semiconductors; p-n junctions; transistor biasing; transistor amplifiers; transmitters and receivers.

BOOKS RECOMMENDED : 1. Hossain T : Text Book of Heat 2. Haque : Text Book of Heat Thermodynamics and Radiation. 3. V.K. Mehta : Principles of Electronics. 4. Beiser : Concepts of Modern Physics 5. N.Suabrahmanyam : Atomic and Nuclear Physics and Brijlal

28

Stat-208 Statistical Methods and Demography

Full marks-100 Number of Lecturer - Minimum 60

(Duration of Examination : 4 Hours) 1 Unit Credit-4

[3 Lectures per week. .5 questions are to be answered out of 8]

Regression Analysis: 3-variable regression and Multiple linear regression model, Estimation of parameters by OLS Method. Properties of OLS estimators, Analysis of Residuals Estimation with restriction. Analysis of Variance: Concept of Randomization, Replication, Treatments, Analysis of variance corresponding to one-way, two-way and three-way classification, completely Randomized. Block designs and Latin square designs. Missing observation, Factorial experiment, Concept of confounding and examples. Sample Surveys : Basic Concept of Sample Surveys, Preparation of questionnaire, Schedules, Probability and non-probability sampling, Sampling with and without replacement, Sampling and non sampling error, Study of Simple random sampling, Stratified random sampling, Systematic sampling, Cluster sampling, Ratio and regression methods of estimation.. Demography : Basic Concept of Demography, Birth and death rates, growth rates. Components of population growth rates, migration, population projection.

BOOKS RECOMMENDED :

Biswas S. (1994) : Stochastic Process in Demography and Applications, Wiley Eastern. Chatterjee, S. and Hadi, A.S. (2006) : Regression Analysis by Example, 3rd ed., Wiely, N.Y. Cochran, W.G. (2002) : Sampling Techniques, 4th ed., Wiley, N.Y. Cochran and Cox (2000) : Experimental Designs, 2nd ed., Wiley, N.Y. Draper, N.R. and H. Smith (2003) : Applied Linear Regression, 3rd ed., Wiley, N.Y. Des Raj. (1968) : Design Surveys, McGraw-Hill, N.Y. Fisher, R.A. (1995) : The Design of Experiments,8th ed., Hafner, N.Y. Hensen, Harwitz, Madaw (1953) : Sample Survey Methods and Theory, Wiley Eastern. Hitson, A. (1995) : The Analysis of Variance, 3rd ed., Wiley, N.Y. Hans Raj (1988) : Fundamentals of Demography. Keyfitz, N. (1977) : Introduction to Mathematics of Population, Addison Wesley, N.Y. Kish,L. (1995) : Survey Sampling Wiley, N.Y. Mukhopadhayay (2000) : Theory and Methods of Survey Sampling, Prentice- Hall, New Delhi. Murthy, M.N. (1977) : Sampling Methods. 2nd ed., Montgomery, D.C., Peck, F. and Vining, G.G. (2003) : An Introduction to Linear Regression Analysis, 3rd ed., Wiley, N.Y. Montgomery, D.C. (2005) : Design and Analysis of Experiments, 6th ed., Wiley. Sukhatme, P.V., V.V. Sukhatme, S. Sukhatme and C. Ashok (1954) : Sampling Theory of Surveys with Application, 2nd ed., IOWA State University Press. Shryock, H.J.S. Siegel and Associates (1980) : The Methods and Materials of Demography; Cond., ed., Academic Press, N.Y. Siegal : Vol. I and II U.S. Department of Commerce U.S. Govt. Spigelman, M. (1968) : Introduction to Demography; Harvard University Press, Cambridge, London..

29 Math-211

Math Practical-II


[Six hours practical examination using Fortran 90.]

A. Computer-75 Marks

1. Elementary Programs: Solving a quadratic equation, identification of conics, circumference and area of circles and triangles, testing a leapyear.

2. Programs using do loops: Summation of series, product of factors,, testing of prime numbers.

3. Programs using select case: Printing number of days if the year and month in given, printing result of students if the marks of different courses are given, printing weather condition if the temperature is given, etc.

4. Programs of arrays: Printing Fibonacci numbers, sorting in ascending / descending order of a given array, searching the highest and lowest number in a given array, addition and multiplication of matrices, transposing of matrices.

5. Using Functions and subroutine: Defining a given function and printing its values at a set of equally spaced points. Calculation of A.M., G.M, H.M, S.D., M.D etc. of an array of numbers. Elementary row operations of matrices, solving a system of linear equations.

6. File Processing: Printing an array of numbers in a file, reading two matrices from a file and printing the addition/ subtraction / multiplication in another file. Creating, editing, appending files of students records.

B. Practical Note Book-25 Marks

Syllabus for other Departments

Math-214: Geometry of Two and Three Dimensions


[3 Lectures per Week. 5 questions are to be answered out of 8] Group-A 1. Transformation of coordinates, pair of straight lines. 2. Circles, system of circles. 3. Parabola, ellipse and hyperbola. 4. The general equation of 2nd degree and reduction to standard forms. Identification of

conics.

30

Group-B 5. Coordinate systems: Direction cosines and ratios, planes. 6. Straight lines, shortest distance. 7. Sphere, cylinder and cone. 8. The general equations of second degree and reduction to standard forms.

Identification of conicoids. BOOKS RECOMMENDED: 1. Askwith, H.H. : Analytic Geometry of Conic Sections 2. Smith, C. : Analytic Geometry of Conic Sections 3. Loney, S. L. : Analytic Coordinate Geometry 4. Kar, J.M. : Analytic Geometry of Conic Sections 5. Bell, J.T. : A Treatise on Three Dimensional Geometry 6. Smith, C. : An Elementary Treatises on Solid Geometry.

Math-215

Vector and Differential Equations


[Three lectures per week. Five questions are to be answered out of eight.]

1. Definitions and theorems on vectors and scalars, product of vectors. 2. Vector differentiation and integration. 3. Vector differentiatial operators. 4. Green’s, Gauss’s and Stokes’s theorems. 5. Solution of first order & first degree differential equations. 6. Singular solutions, orthogonal and oblique trajectories. 7. Solution of higher order linear differential equations. 8. Series solution of linear differential equations. BOOKS RECOMMENDED : 1. Spiegel, M.R. : Theory and problems of matrices 2. Sattar, M.A. : Vector Analysis 3. Ross, S. L. : Differential Equations 4. Ayres, F. : Differential Equations 5. Sharma, B.D. : Differential Equations

Math-216

Matrices and Differential Equations

31 0.75 Unit Full marks-75 Credit-3


1. Definitions and properties of matrices. 2. Adjoint, inverse and rank of a matrix, properties and evaluation. 3. Elementary transformation: Echelon, canonical and normal forms, solution of

system of linear equations by matrix method. 4. Green's, Gauss & Stoke's theorem. 5. Solution of first order & first-degree differential equations. 6. Singular solutions, orthogonal and oblique trajectories. 7. Solution of higher order linear differential equations. 8. Series solution of linear differential equations. BOOKS RECOMMENDED : 1. Ayres, F. : Theory and problems of vector Analysis 2. Khanna, M.L. : Differential Equations 3. Ross, S. L. : Differential Equations. 4. Ayres, F. : Differential Equations. 5. Sharma, B.D. : Differential Equations. 6. Lipschutz, S : Linear Algebra.

Math-217

Algebra and Geometry



Group-A 1. Algebra of sets: De-Morgan's rule, relation and function. 2. Theory of Equations: a) Theorems and relation between roots and coefficients, b)

Solution of cubic equations. 3. Inequalities. Group-B 4. Change of axes, general equations of second degree, pair of straight lines. 5. Circle and parabola. 6. Ellipse and hyperbola. 7. Direction cosines; straight line and plane. 8. Sphere and cone.

32

BOOKS RECOMMENDED : 1. Barnside and Pantion : Theory of Equations 2. Bernard and Child : Higher Algebra 3. Hall and Knight : Higher Algebra 4. Askwith, H.H. : Analytic Geometry of Conic Sections 5. Smith, C. : Analytic Geometry of Conic Sections 6. Khanna, M.L. : Coordinate Geometry 7. Bell, J.T. : A treatise on Three dimensional Geometry 8. Smith, C. : Elementary Trealises on Solid Geometry 9. Vashishta and Agarwal : Analytic Solid Geometry.

Math-218

Special Functions, Numerical Methods



Group-A 1. Gamma and Beta Functions: Bessel's equation, Bessel's functions of first, second and

third kind; recurrence relations; Legendre's differential equations and Legendre polynomials; Hermite's differential equation, Hermite's and Laguerrie polynomials; Hypergeometric function and its properties; Fourier series and Fourier integral; Fourier and Laplace transform.

Group-B Numerical Methods: 1. Matrix Algebra and Simultaneous Equations: Elementary operations of matrices;

Gauss-Jordan elimination method; Direct method; Necessity of normalization; Zero diagonal elements and positioning of size; Matrix-inversion; Gauss-Seidel iterative method; Computer Algorithm and Program for matrix algebra.

2. Polynomial Interpolation: The Lagrange polynomials; Lagrange's interpolation formula for unequally spaced data; Polynomial interpolation by computer algorithm and program.

3. Solution of Partial Differential Equations: Introduction, Examples of Partial differential equations, the approximation of derivatives of finite differences, Parabolic Differential, equations, Derivation of the Elliptic Differences Elliptic Differences, Laplace equation, Iterative Method, Successive Over-relaxation and Alternating and Direction Methods.

33 BOOKS RECOMMENDED : 1. Rajput, B. S. and Prakash, P. : Mathematical Physics 2. Sokolnikoff, I.S.and : Mathematical Physics Redheffer, R.M. and Modern Engineering 3. Jeffreys and Jeffreys : Methods of Mathematical Physics 4. Vasistha A.R : Numerical Methods. 5. Sastry, S.S. : Methods of Numerical Analysis

34B-Sc.(Honours) Part - III Examination, 2013

Honours Part-III Examination will comprise of 1050 marks (Theory courses -

850, Math. Practical -100, Tutorial, Terminal and Class Record -50 and Viva-Voce-50). The duration of examination for each theory course is 4 hours for 75 and 100 marks. The duration of the practical examination is 6 hours.

Course No. Title of Courses Full Marks Unit No. Credit Math - 301 Real Analysis - II 100 1 4 Math - 302 Complex Analysis 100 1 4 Math - 303 Mechanics 100 1 4 Math - 304 Mathematical Methods 100 1 4 Math - 305 Partial Differential 100 1 4

Equations Math - 306 Discrete Mathematics 100 1 4

and Programming with C Math - 307 Linear Algebra 100 1 4 Math - 308 Methods of Numerical

Analysis 75 75 3

Math - 309 Topology & Functional Analysis

75 75 3

Math - 310 Tutorial, Terminal and Class Record

50 05 2

Math - 311 Math Practical-III 100 1 4 Math - 312 Viva-Voce 50 05 2

Total 1050 105 42

35 Math-301

Real Analysis -II


[Three lectures per week. Five questions are to be answered out of 8.]

1. Euclidean space Rk: Definition and properties, K-cell, Heine-Borel theorem,

Wierstrass theorem. Cantor set.

2. Functions of several variables: Limit and continuity of two variables, partial differentiation, Schwarz's theorem & Young's theorem.

3. Linear Transformation, differentiation, the contraction principle, the inverse function theorem, the implicit function theorem, the rank theorem.

4. The Riemann and the Riemann stieltjes integral: Definition and existence of the integrals, properties, integration and differentiation.

5. Sequences and series of functions: Discussion of main problem, uniform convergence, uniform convergence and continuity.

6. Uniform convergence and integration, uniform convergence and differentiation, the Stone-Weierstrass theorem.

7. The Lebesgue theory: Set functions, construction of the Lebesgue measure, Measure spaces, Measurable functions.

8. Simple function, Integration, comparison with the Riemann integral, integration of complex functions.

BOOKS RECOMMENDED :

1. Rudin, W. : Principles of Mathematical Analysis

2. Royden : Mathematical Analysis

3. Apostol : Mathematical Analysis

36Math-302

Complex Analysis


[Three lectures per week. Five questions are to be answered out of 8.]

1. The complex number system: Complex plane, the extended plane and its spherical

representation (Riemann sphere). 2. Topology of C: Sequences, completeness, uniform convergence.

3. Complex function : Single and many valued function, branch point, limit, continuity and differentiability of complex functions.

4. Analytic functions : Necessary and sufficient conditions, Mobius transformation, power series. harmonic function.

5. Complex Integration : Power series representation of analytic functions, zeros of analytic functions. Cauchy's theorem. Morera's theorem. Cauchy integral formula. Singularities: classification of singularities

6. Complex integration : Maximum modulus theorem, the homotopic version of cauchy's theorem and simple connectivity, the open mapping theorem, Taylor's and Laurent series, Fundamental theorem of algebra, Rouches theorem. The argument principle, The Residue theorem contour integration.

7. Conformal mapping, bilinear mapping. The application of the conformal mapping. 8. Riemann Mapping theorem, Riemann zeta function, analytic continuation, Riemann

surface. BOOKS RECOMMENDED : 1. Conway, J. B. : Functions of one complex variable 2. Ahlfors, L.V. : Complex Analysis. 3. Sarason, D. : Notes on complex function theory.

37 Math-303 Mechanics 1 Unit Full marks-100 Credit-4

[3 Lectures per week. 5 questions are to be answered out of 8] Statics: 1. Forces acting in a plane, parallel forces, moments and couples. 2. Equilibrium of coplanar forces. Astatic, stable and unstable equilibrium. 3. Work and virtual work. 4. Centre of gravity, forces in three dimensions. Dynamics: 5. Motion in a straight line, simple harmonic motion 6. Motion in a plane referred to cartesian and polar coordinates. Radial and transverse

velocities; central, tangential and normal accelerations & central forces. 7. Motion in a resisting medium. 8. Motion in three dimensions; accelerations in terms of polar and cartesian

coordinates. BOOKS RECOMMENDED : 1. Loney, S. L. : Statics 2. Loney, SI : Dvnamics Of Darticle 3. Ramsey, A.S. : Dynamics 4. Gupta, P P. : Statics 5. Malik, S. : Dynamics of particles

Math-304 Mathematical Methods 1 Unit Full marks-100 Credit-4

[3 Lectures per week. Five questions are to be answered out of 8] 1 . The Laplace Transform: (i) Definition, existence and basic properties (ii)

Differentiation and integration (iii) Inverse Laplace transform and convolution (iv) Solution of linear differential equations with constant coefficients and linear systems.

2. Bessel's Equations: Solution, Generating function, Recurrence relation, values of Bessel's function, Orthogonality, Neuman and Hankel function, Modified Bessel's function.

a) Legendre's Equation: Solution, Generating function, Recurrence relation, Rodrigue's formula and Orthogonality of Legendre polynomials.

38 b) Hermite's Equation: Solution, Integral and Recurrence formula,

Orthogonaity, Differential formula. 4. a) Leguerre's Equation: Solution, Integral and Recurrence formula, Differential

forms, Orthogonality, b) Hypergeometric Equation : Solution, Hypergeometric function and its

properties, Integral formula and transformations of hypergeometric functions. 5. Fourier series: Fourier coefficients, sine and cosine series, Dirichlet's theorem,

Properties and applications. 6. Sturm-Lioville problem: Self adjoint differential equation, Characteristic values

and characteristic function. Orthogonality; Green's function. 7. Fourier transforms: Fourier sine and cosine transforms, Complex Fourier

transform, convolution theorem, Applications to boundary value problem 8 a) Asymptotic expansions (b) Calculus of variations. BOOKS RECOMMENDED: 1. Jeffreys and Jeffreys : Methods of Mathematical Physics 2. Courant and Hilbert : Methods of Mathematical Physics 3. Rajput, B.S. : Mathematical Physics 4. Spiegel, M R : Laplace Transforms 5. Lighthill, M J : Asymptotic Expansion 6. dii“L Lwjj : MvwYwZK c×wZ| 7. Ansary, M.A. : Methods of Applied Mathematics

Math-305 Partial Differential Equations


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Total Differential Equations: Integrability condition, Solution method for

R

dz

Q

dy

P

dxand0 Rdz Qdy Pdx

2. Formation of PDEs, First order linear PDEs. 3. First Order quasilinear and nonlinear PDEs, 4. Second Order homogeneous and nonhomogeneous PDEs. 5. Second order nonlinear PDEs. 6. Classification of general second order PDEs and canonical forms. 7. Solutions of Laplace's equations in cartesian, cylindrical and Spherical coordinates. 8. Solutions of diffusion (or heat flow) equation and wave equation.

39 BOOKS RECOMMENDED : 1. Ayres, F. : Differential Equations. 2. Sneddon, I.N. : Elements of Partial Differential Equations 3. Dennemeyer, R. : Introduction to Partial Differential Equations 4. Myint, U.T. : Partial Differential Equations 5. Sharma, B.D. : Partial Differential Equations

Math-306 Discrete Mathematics and Programming with C


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Proposition, Relations and Functions: Propositions, A relational model for data

bank, Properties of binary relations,, Equivalence relations and Partitions, Partial ordering relations and lattices, chains and antichains, Functions and the Pigeonhole Principle.

2. Graphs and planar Graphs: Introduction, Basic terminology, Multigraphs and weighted graphs, Paths and circuits, Shortest Paths in weighted graphs, eulerian Paths and circuits, Hamiltonian Paths and circuits.

3. Trees and Cut Sets: Trees, Rooted trees, Path lengths in rooted trees, Binary search trees spanning trees and cutsets, Minimum spanning trees.

4. Boolean Algebra: Lattices and Algebraic systems, Principle of duality, Basic Properties of Algebraic system defined by lattices, Distributive and complemented lattices, Boolean lattices and Boolean algebras, Boolean functions and boolean expressions Propositional calculus, Design and implementation of digital Networks, Switching circuits.

5. C. Fundamentals 6. Operators and expressions, data input/output 7. Different Control statements. 8. Functions and arrays. BOOKS RECOMMENDED : 1. Liu, C.L. : Elements of Discrete Mathematics 2. Robert, J. McElice : Introduction to Discrete Mathematics 3. Alan Doer : Applied discrete structure for computer Science 4. Donald, F. Stanat : Discrete Mathematics in computer Science 5. Byron, S. Gotteried : Programming with C 6. Stephen, G. Kochan : Programming with C 7. Stan Kelly Botle, : Mastering Turbo C 8. Kumar Agrawal : Programming in ANSI C

409. Herbert Schildt : Turbo C/C++, The complete reference

Math-307 Linear Algebra


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Vector space, subspace, sum and direct sum. 2. Linear dependence and independence, basis and dimension. 3. Linear transformation : Range, kernel, nullity, rank, singular and non-singular

transformations. 4. Matrix representation of a linear operator. Change of basis, similarity. Matrices and

linear mappings. 5. Characteristic roots and vectors of linear transformations, Theorems and problems;

Characteristic and Minimum Polynomials of square matrices. 6. Linear functionals and dual vector spaces, Annihilators. 7. Norms and inner products, Orthogonal complements, orthonormal sets,

Gram-schmidt orthogonalization process. 8. Adjoint operators, Hermitian, Unitary, Orthogonal and Normal operators. BOOKS RECOMMENDED : 1. Lipschutz, S : Linear Algebra 2. Herstein, L.N. : Topics in Algebra

Math-308 Methods of Numerical Analysis


[3 Lectures per week. 5 questions are to be answered out of 8] 1 . Solution of Algebraic and Transcendental Equations. 2. Interpolation. 3. Curve Fitting, Cubic Splines and Approximation. 4. Numerical Solutions of Linear and Nonlinear Systems of Equations. 5. Numerical Differentiation and Integration. 6. Numerical Solutions of Ordinary Differential Equations. 7. Numerical Solutions of Partial Differential Equations.

41 BOOKS RECOMMENDED: 1. Sastry, S.S. : Introductory Methods of Numerical Analysis 2. Henrici, P. : Elements of Numerical Analysis 3. Burden, Faires and Reynolds : Numerical Analysis 4. Bashishthe, A R : Numerical Analysis 5. †gvt b~i“j û`v : mvswL¨K MwYZ c×wZ

Math-309 Topology and Functional Analysis


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Elements of topology: Topological space, Base, Subbase, Lindelof theorem, Baire

theorem. Continuous mapping. 2. Compactness. 3. Separation axioms: T0,T1, T2 spaces. 4. Connectedness. 5. Normed linear spaces, Quotient norm and Quotient spaces. 6. Banach Spaces. 7. Hilbert spaces, elementary properties of Hilbert spaces. 8. Operators of Hilbert spaces. BOOKS RECOMMENDED : 1. Munkers, J.R. : Topology, A first course 2. Simmons, G.F. : Introduction of topology and Modern Analysis 3. Dugundgi, J. : Topology 4. Taior, A. : Functional Analysis

42Math-311: Math Practical-III

1 Unit Credit-4

[Six hours practical examination using C/C++.] A. Computer-75 Marks 1. Array And string: Arithmetic mean, geometric mean, harmonic mean, Variance of

some numbers, Sorting of a list of numbers and strings, searching, finding out put. 2. Matrices and determinations: Addition, subtraction and multiplication of matrices,

determinant of a square matrices, echelon form, row canonical form, elementary transformation of matrices.

3. File : Out put of a file and read from the file and drawing of graphs of some function using the data.

4. Solution of transcendental and algebraic equations by i) bisection, ii) false position, iii) iterative and iv) Newton- Raphson methods.

5. Interpolation: i) Newton forward , ii) Newton backward , iii) stir line and iv) Lagrange interpolation formulae.

6. Numerical differentiation: By using Newton forward and backward interpolation formula and numerical integration by simple 1/3, 3/8 and trapezoidal rules.

B. Practical Note Book-25 Marks

43

B.Sc.(Honours) Part - IV Examination, 2014

Honours Part - IV Examination will comprise of 1050 marks (Theory Courses- 850; Math. Practical - 100; Tutorial, Terminal and Class Records - 50 and Viva-Voce-50). Math. 401-404 courses are compulsory for all students. In addition, students must take any five optional courses from either of the following two groups with the approval of the department. The duration of examination for each theory course is 4 hours for 75 and 100 marks. The duration of practical examination is 6 hours.

Compulsory Courses Course No. Title of Courses Full Marks Unit No Credit Math - 401 Operations Research 100 1 4 Math - 402 Group Theory 75 75 3 Math - 403 Differential Geometry 100 1 4 Math - 404 Classical Mechanics 75 75 3 Math - 416 Tutorial, Terminal and

Class Records 50 05 2

Math - 417 Viva-Voce 50 05 2 Math - 418 Math. Practical-IV 100 1 4

Optional Courses: Group - A

Course No. Title of Courses Full Marks Unit No Credit Math - 405 Ring Theory 100 1 4 Math - 406 Advanced Topology 100 1 4 Math - 407 Number Theory 100 1 4 Math - 408 Theory of Modules 100 1 4 Math - 409 Graph Theory 100 1 4

Optional Courses :Group - B

Math - 411 Hydrodynamics 100 1 4 Math - 412 Astronomy 100 1 4 Math - 413 Quantum Mechanics 100 1 4 Math - 414 Electromagnetic Theory 100 1 4 Math - 415 Integral Equations 100 1 4

Total 1050 10.5 42

44Math-401

Operations Research 1 Unit Full marks-100 Credit-4

[3 Lectures per Week. 5 questions are to be answered out of 8] 1. Basic Concepts : Introduction, the nature, meaning, scope and role of operation

Research. Main phases of operation Research, study, modeling in operation Research. General methods for solving operation Research models, decision making in operation Research.

2. Mathematical Programming: Linear programming; formulations and graphical solutions. The simplex method, revised simplex method.

4. Duality, sensitivity and parametric analysis, transportation model & net working. 5. Integer linear programming, dynamic programming. 6. Decision Theory: Decision under risk. 7. Decision trees, decision under uncertainty. 8. Game Theory: Operational solution of two-person zero-sum games, mixed

strategies, graphical solution of (2n) and (m2) games, solution of (mn) games by linear programming & dominance property.

BOOKS RECOMMENDED: 1. Berger, J.O. : Statistical Decision Theory 2. Charles, A : Decision Making under Uncertainty Models and Choices 3. Gass, S.1 : Linear Programming 4. Hudly, G. : Linear Programming 5. Lindly, D.V. : Making Decision 6. Taha, H.A : Operations Research An Introduction 7. Raiffa, H : Decision Analysis, Introductory Lectures on Choices and Uncertainty. 8. Vajda, S : Game Theory

45 Math-402

Group Theory 75 Unit Full marks-75 Credit-3

[3 Lectures per week. 5 questions are to be answered out of 8] 1 . Definition and properties of groupiods, quasi-groups, semi groups, monoids; and

groups. The symmetric and alternating groups, permutation groups, cyclic groups, Lagrange's theorem.

2. Normal subgroups, homomorphism, isomorphism and their theorems. 3. Direct product of groups, the centralizer and the normalizer of subset of a group, the

centre of a group. 4. The commutator subgroups, solvable groups, normal, subnormal and composition

series, Jordan-Holder theorem, Schreier's theorem, nilpotent groups. 5. Conjugacy classes, p-group's theorem. sylow subgroups and sylow theorems, free

groups. 6. Structure theory of finite abelian groups. 7. Group representations. 8. Group extensions. BOOKS RECOMMENDED : 1. Kurosh, A.G. : Lectures in abstract algebra 2. Jacobson, H. : Lectures in abstract algebra 3. Scoff : Group theory 4. Hall, M. : The theory of groups 5. Dakua, K.A. : Introduction to Modern Abstract Algebra.

Math-403 Differential Geometry


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Curves : Parametric representation, are length, tangent, osculating plane, normal,

principal normal, binormal and fundamental planes. 2. Curves : Curvature and torsion, Frenet- serret formula, helices, osculation circle,

osculating sphere, involute and evolute. 3. Surface : Parametric equation, parametric curves, tangent plane, normal and envelope,

two and three parameter family of surfaces. 4. First and second fundamental forms, direction coefficients, orthogonal trajectories,

double family of curves. 5. Curves on a surface : Normal curvature and section, Mousnicer's theorem, principal

sections, curvature and directions, Rodrigue's formula, Euler’s theorem, minimal surface.

6. Developable, Monge's theorem, conjugate direction, asymptotic lines, theorem of Beltrami and Enneper.

467. Ruled and skew surfaces, parallel surfaces and Bonnet's theorem, isometric lines.

8. Geodesics : Definitions, differential equation of geodesics, canonical geodesic equation, geodesic on a surface of revolution, Clairaut's theorem, normal property, geodesic curvature, Bonnet's theorem, Gauss-Bonnet Theorem.

BOOKS RECOMMENDED : 1. Guggen'heimer, H. : Differential Geometry 2. Struik, D.J. : Classical Differential Geometry 3. Sharma, J.N. and : Differential Geometry Basishtha, A.R. 4. Khanna, M.L. : Differential Geometry 5. Weathcrburn, C. : Differential Geometry of three Dimensions.

Math-404

Classical Mechanics 75 Unit Full marks-75 Credit-3

[3 Lectures per week. 5 questions are to be answered out of 8] 1. Generalized coordinates : Holonomic and non-holonomic systems. Langranges

equation for holonomic systems. 2. Elementary principles : Mechanics of a particle and system of particles constraints,

D-Alembert's principle and Lagrange’s equation. simple applications of Lagrange's equation.

3. Introduction to calculus of variation, Euler-Lagrange differential equation, applications.

4. Motion in rotating frames, motion relative to earth. Foucault's pendulum. 5. Inpulsive motion, ignoration of coordinates, small oscillation, constant of motion. 6. Phase space, Hamilton’s equation, Hamilton's principle, principle of least action,

Hamilton’s principle function and Hamilton-Jacoby equation. 7. Lagrange & poisson brackets, contact transformation, commutator. 8. Introduction to the Lagrangian and Hamiltonian formulations for continuous systems and fields. BOOKS RECOMMENDED : 1. Goldstein, H. : Classical Mechanics 2. Rutherford : Classical Mechanics 3. Gupta, Kumar & Sharma : Classical Mechanics 4. Gupta, B.D. and Saha, S. : Classical Mechanics

47

Math.-405 Ring Theory


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Rings, integral domains, ideal and quotient rings, field and imbedding theorem. 2. Homomorphism and isomorphism theorems of rings, polynomial rings. 3. Euclidean rings 4. Principal ideal rings. 5. Noetherian rings : Hilbert basis theorems. 6. Wedder-bum's commutativity theorem. 7. Artinian rings: Radicals, semi simple rings, 8. Simple rings, wedderbum's structure theorem. BOOKS RECOMMENDED : 1. Jamback, J. : The theory of rings 2. Herstein, I.N. : Topics in Algebra 3. Vander Waerden, B.L. : Modem Algebra V-I 4. Curtis and Reiner : Representation of groups and associative Algebras. Math-406: Advanced Topology


[3 Lectures per week. 5 questions are to be answered out of 8] 1. Metric spaces, completeness of metric spaces 2. Compactness and connectedness of metric spaces 3. Topological spaces, product topology, metric topology, quotient topology, compact

open topology, order topology, lens spaces. 4. Separation axioms: R0, R1, regular and normal spaces, Urysohn lemma, the Urysohn

metrization theorem, completely regular spaces. 5. Compact spaces, Tychonoff theorem, locally compact spaces, Stone-Cech

compactification., one point compactification 6. Connected spaces, local connectedness. Path connected and locally path connected

spaces. 7. Fundamental group, covering spaces, 8. Weierstrass approximation theorem, Bernstein polynnomial BOOKS RECOMMENDED :

481. Munkres, J. R. : Topology, A first Course

Simmons, G. F. : Introduction of topology and Modem Analysis 3. Dugandji : Topology.

Math-407 Number Theory-4


[3 Lectures per week. 5 questions are to be answered out of 8] 1 . The number system, Euclidian algorithm, Diophantine equation. 2. Congruences and their solutions, Euler's function, The theorems of Fermat, Euler and Wilson. 3. Primitive roots and indices, an application to Fermats conjecture. 4. Quadratic residues, Gaussian integers. 5. Continued fractions, nonlinear congruences. 6. Elementary theory of the distribution of primes. 7. The proof of the prime number theorem. 8. Quadratic fields: Simple fields; Euclidian fields. BOOKS RECOMMENDED : 1. Leveque, W.J. : Topics in Number Theory Vol-1. Addison- Wesley co. New York. 2. Hardy, G.H. and : Oxford University Press. London. Wright, E.M. 3. Leveque, W.J. : Fundamentals of Number theory

Math 408 Theory of Modules


[3 Lectures per week. 5 questions are to be answered out of 8] 1 Modules, submodules, factor modules, module homomorphisms. 2. Exact and short exact sequences. 3. Cartesian products, direct sums free modules. 4. Projective and injective modules. 5. Hom (A, B) and its properties. 6. Tensor product, adjoint associativity 7. Diagram lemmas. 8. Torsion product of abelian groups. BOOKS RECOMMENDED : 1. Lambek, J. : Lectures on rings and Modules 2. Jans, J.P. : Rings and Homology. 3. Maclane : Homology

49

Math-409 Graph Theory

1 Unit Full marks-100 Credit-4 [3 Lectures per week. 5 questions are to be answered out of 8] 1. Discovery of graph Theory : Definition and examples of graphs, multigraphs,

digraphs, bigraphs, walks and connectedness, intersection graphs, operation of graphs.

2. Blocks: Cut points, bridges, and blocks, block graphs and cut point graphs. 3. Trees 4. Connectivity and traverability, Eulerian and Hamiltonian graphs. 5. Line graphs, special line graphs, total graphs. 6. Plane and planar graphs 7. Color ability: The chromatic numbers, the five color theorem, statement of the four

color theorem. 8. Matrices: The adjacency matrix, the incident matrix, the cycle matrix. BOOKS RECOMMENDED : 1. Frank Harary : Graph Theory, Narosa Publishing House New Delhi 2. West : Graph Theory 3. Parthasarathy : Graph Theory 4. Calaude Berge : Introduction to Graph Theory.

Math-411 Hydrodynamics

1 Unit Full marks-100 Credit-4 [3 Lectures per week. 5 questions are to be answered out of 8] 1. Velocity and acceleration of fluid particles, relation between local and individual

rates; steady and unsteady flows, uniform and non-uniform flows, stream lines, path lines, vortex lines, velocity potential.

2. Rotational and irrotational flows, equations of continuity, equation of continuity in spherical and cylindrical polar coordinates, boundary surface.

3. Euler's equation of motion, conservative field of force, Lamb's hydrodynamical equations of motion, Bernoulli equation, motion under conservative body force, vorticity equations.

4. Motion in two-dimensions, stream function, physical meaning of stream function, velocity in polar-coordinates, relation between stream function and velocity.

5. Sources, sinks and doublets, complex potential and complex velocity stagnation points, complex potential due to a source and a doublet, image in two and three dimensions, Stoke's, stream function.

506. Circulation and vorticity, relation between circulation and vorticity, Kelvin's

circulation theorem, permanence of irrotational motion, equation of energy, Kelvin's minimum energy theorem

7. Circle's theorem, Blasius theorem, motion of a circular cylinder, pressure at points on a circular cylinder, application of circle theorem.

8. Vortex motion, vortex tube, strength of a vortex, vortex pair, complex potential due to vortex motion, vortex rows, free vortex, forced vortex, spiral vortex, compound vortex.

BOOKS RECOMMENDED : 1. Chorlton, F. : Fluid dynamics Vari-Nostrand 2. Milne Thomosn, I.M. : Theoretical Hydrodynamics 3. Gupta, P.P. : Hydrodynamics 4. Khalil, F. : Ashanghnamah Prabasha

Math-412 Astronomy

1 Unit Full marks-100 Credit-4 [3 Lectures per week. 5 questions are to be answered out of 8]

1. Elements of spherical trigonometry: cosine, sine and cotangent formulas. 2. Celestial sphere and celestial coordinates Transformation of celestial coordinates. 3. Refraction, planetory motion 4. Time, seasons 5. Parallax, aberration 6. Precession and nutation 7. Eclipses 8. The solar system. BOOKS RECOMMENDED : 1. Smart : Spherical Trigonometry 2. Godtrey : Spherical Trigonometry 3. Kar, J.M. : Astronomy 4. Datta and Choudhary : Astronomy 5. Todhunter : Spherical Trigonometry 6. Khan and Sikder : Astronomy 7. Dey, A.K. : Astronomy

51

Math-413 Quantum Mechanics


1 . Black body radiation : Plank's radiation law, Einstein photon theory, compton effect. 2. De Broglie wave : Phase and group velocities. wave packets. Uncertainty Principle. 3. Rutherford atom model : Alpha particle scattering, Bohr's theory; Correspondence

principle. 4. Wave mechanical concepts : Schrodinger wave equation, interpretation of wave function

: expectation value and Ehrenfest's Theorem. 5. Eigenfunctions, Potential steps, linear harmonic oscillator, spherically symmetric

potentials, interpretative postulates and energy eigenfunctions. 6. Momentum eigenfunctions, Box normalization, Dirac delta function, motion of a

free wave packet: minimum uncertainty product and form of minimum packet. 7. Linear harmonic oscillator, Spherically potentials in three dimensions, angular

momentum. 8. Hydrogen atom : Three-dimensional square potential barrier. BOOKS RECOMMENDED : 1. Arther Beiser : Concept of Modern physics 2. Schiff, L.I. : Quantum Mechanics 3. Mathews, P.T. : Introduction of Quantum Mechanics 4. Powell and Crassmann : Quantum Mechanics 5. Gupta, Kumar and Sharma : Quantum Mechanics 6. Anderson, E.E : Introduction to Quantum Mechanics 7. Donald Rao : Quantum Mechanics

Math-414 Electromagnetic Theory


[3 Lectures per week. 5 questions are to be answered out of 8] 1 . Electrostatics : The electrostatic field of force, conductors, condensers and dipole,

systems of conductors, electrical images, electrostatic energy. 2. Dielectrics : Electro potential and displacement minimum energy of the field,

uniqueness theorem, polarization.

523. Capacitance and electric energy : Capacitances of a conductors, capacitors in

series and parallel, combination of capacitors, electric energy in terms of Q.V. and C.

4. Steady electric current : Electro magnetic force or e.m.f, field aspect, network aspect, resistance and conductors, general net work theorem and Kirchhoff's law.

5. Magnetism : Fundamental of magnetostatics, magnetic field poles and strength volume vector and vector potential, mutual and self inductance, force on a current, Faraday's law. .

6. Steady current in magnetic material: Equations of magnetic field and energy, magnetic dipole, electromagnetic Induction, amperes circuital theorem, Biot Savat law.

7. Maxwell's equations : Derivations, general solutions, and deductions, scalar and vector potentials, electromagnetic potentials, poynting theorem.

8. Electromagnetic waves: Plane electromagnetic waves in an isotropic non-conducting media, equation of telegraphy, Fresnel's relation.

BOOKS RECOMMENDED : 1. Coulson : Electricity 2. Ferraro, V.C.A. : Electromagnetic Theory 3. Gupta and Sharma : Mathematical Theory of Electricity and Magnetism 4. Duffin, W.J. : Electricity and Magnetism

Math-415 Integral Equations


1 . Introduction, Abel's problem, types of IEs, differentiation under an integral sign, relation between differential and integral equations.

2. Solution of VIEs of the first and second kinds. 3. Solution of FIEs of the first and second kinds. 4. Fredholm's first, second and third fundamental theorems. 5. Fundamental function, IEs with degenerate kernels, eigenvalues and eigen functions. 6. Symmetric kernel, orthogonal and normalized systems, Schmidts solution of

nonhomogeneous IEs, Hilbert Schmidt theorem. 7. Green's function, construction of Green's function, Influence function, IE and

Green's function for BVPs. 8. Singular integral equations, Abel IE, cauchy principlal integral, Poincare Bertrand

formula, Hilbert kernel and Hilbert formula. Solution of Hilbert type IEs of the first and second kinds.

BOOKS RECOMMENDED : 1. Shanti Swarup : Integral Equations 2. Raishinghania, M.D. : Linear Integral Equations

53 3. Vashishtha, A.R. : Integral Equations 4. Kanwal, R.P. : Linear Integral Equations 5. Tricomi, T.G. : Integral Equations.

Math-418 Math Practical-IV

1 Unit Credit-4

[Six hours practical examination using C Matlab.] A. Computer-75 Marks

1. Solution of polynomial and transcendental equations and system of nonlinear

equations. 2. Interpolation and polynomial approximation. 3. Matrices and solution of systems of linear equations. 4. Numerical differentiation and integration. 5. Numerical solution of ordinary differential equations and system of ordinary

differential equations. (IVP and BVP) 6. Numerical solution of partial differential equations and integral equations, heat

equations, wave equations, Laplace Equation. 7. Curve fitting. B. Practical Note Book - 25 Marks

university of rajshahi numerical grade letter grade grade...

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