EGM 4313- Intermediate Engineering Analyses Spring 2011

Catalog Description: 3 credits - Ordinary differential equations, systems of ordinary differential equations, partial differential equations, Fourier series, complex analysis. Equations of heat conduction, wave propagation and Laplace. Prerequisites: MAP 2302, EGM 3344 Text and Other Material: Text: Advanced Engineering Mathematics by E.Kryszig, J.Wiley and Co, 9th Ed, New York.

Contact Information:

• Instructor: David Mikolaitis • Office: 316 MAE-A • Phone: 392-7632 • E-mail: mollusk@ufl.edu • Office Hours: MWR, 7th period • Teaching Assistants:

• Name: Camila Francolin o Office Location: o Telephone: o Email Address: francoli@ufl.edu o Office Hours:

• Name: Brian Roberts o Office Location: 321 MAE-A o Telephone: o Email Address: brianroberts@ufl.edu o Office Hours:

Meeting Times: 8th Period (3:00 to 3:50 PM) MWF

Meeting Location: NEB 100

Course Objectives: In EGM 4313 the student will learn introductory analytical techniques for the solution of (mostly) linear differential systems commonly found in engineering analysis. Included in the analytical techniques are Fourier series, Fourier Transforms, solution of systems of ordinary differential equations by matrix methods, and solution of systems of ordinary differential equations by Laplace transform methods. Solution methods will also be learned for some partial differential equations of importance in engineering (Laplace, heat conduction, wave) by separation of variables and d’Alembert’s method as a special case of the method of characteristics. Complex variables and the Cauchy-Riemann conditions will be studied with particular attention paid to the connection between analytic functions and solutions to Laplace’s equation.

Contribution of course to meeting the professional component:

This course contributes to the students becoming proficient in the analysis of engineering systems. In particular it supports several program outcomes enumerated in the Mission Statement of the Department of Mechanical and Aerospace Engineering, including

(A1) and (M1): Using knowledge of chemistry and calculus based physics with depth in at least one of them

(A2) and (M2): Apply knowledge of advanced mathematics through multivariate calculus and differential equations

(A3) and (M3): Apply statistics and linear algebra

Relationship of course to program outcomes: (a) Apply knowledge of mathematics, science, and engineering – High coverage, 85% of course grade. (A2, M2, A3, M3) (e) Identify, formulate, and solve engineering problems – Medium coverage, 15% of course grade. (A1, M1)

Class Schedule and Grading Policy: Monday, Wednesday, Friday 8th Period (3:00 to 3:50 PM) NEB 100. Grade Determination: weekly homework 16%, best 7 of 8 quizzes at 12% each (total of 84%) Averages greater than or equal to will guarantee minimum grades of: 90 - A, 80 - B, 70 - C, 60 - D. B+ and C+ grades may be assigned in some borderline cases. Any regrade requests must be submitted within one week after return of the graded paper.

Make-up Exam Policy:

A student having a documentable illness or emergency must, if possible, contact the instructor before missing an exam or quiz. Emergencies will be handled individually.

Miscellaneous Policies:

• The use of cell phones during class is prohibited. Please turn all cell phones and pagers off before class begins.

• Eating and drinking are prohibited during lecture.

• Lecture attendance is not mandatory and attendance will not be taken or used in assigning grades.

• Homework for EGM 4313 is to be turned in at the end of lecture on Friday. You may turn homework assignments in early. Late homework is not accepted without a strong reason. Homework handed in after solutions are posted will not be accepted.

• Please make a diligent effort to solve homework problems BEFORE asking about them during office hours. You may be asked to produce your effort so that we can be efficient in pinpointing the difficulty you are facing.

• Getting the answer to a problem is only half the effort. The other half is verifying the answer. Having numerical answers available to all the homework problems teaches you poor skills in checking your work. After all we don't put the answers to the quiz and examination problems on the back of the exam!

• Several of the homework exercises in EGM 4901 will require the use of Matlab. You will not need to purchase Matlab and none of the quizzes or examinations will require it. You can use Matlab on any of the Circa computer lab PC’s. There are PC’s at Architecture 118, Bldg 105 (CBD) – Room 110, CSE E211, and Weil Hall 408. (Norman Hall’s lab has only Apple computers and do not have Matlab.)

• All quizzes and exams will be open book, closed notes, no calculators or computers.

Honesty Policy: All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a UF student and to be honest in all work submitted and exams taken in this course and all others. Accommodation for Students with Disabilities: Students requesting classroom accommodation must first register with the Dean of Students Office. That office will provide the student with documentation that he/she must provide to the course instructor when requesting accommodation. UF Counseling Services: Resources are available on-campus for students having personal problems or lacking clear career and

academic goals. The resources include:

• University Counseling Center, 301 Peabody Hall, 392-1575, Personal and Career Counseling. • SHCC mental Health, Student Health Care Center, 392-1171, Personal and Counseling. • Center for Sexual Assault/Abuse Recovery and Education (CARE), Student Health Care Center,

392-1161, sexual assault counseling. • Career Resource Center, Reitz Union, 392-1601, career development assistance and counseling.

Software Use: All faculty, staff and student of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to uphold ourselves and our peers to the highest standards of honesty and integrity. Lecture Topics to be Covered and Tentative Schedule EGM 4313:

January 5 Fourier Series 11.1-11.6

January 7 Fourier Series (continued)

January 10 Fourier Series (continued)/ Fourier Integrals and Transforms

11.7-11.10

January 12 Fourier Integrals and Transforms (continued)

January 14 Wave Equation – Separation of variables 12.1-12.4

January 17 MLK Day

January 19 Wave Equation – Separation of variables and d’Alembert’s solution– Quiz 1

January 21 Heat Equation – Separation of variables and Fourier Transforms

12.5-12.6

January 24 Heat Equation – Separation of variables and Fourier Transforms

January 26 Heat Equation – Separation of variables and Fourier Transforms (continued)

January 28 Systems of equations from engineering problems – Introduction to linear algebra

7.1-7.6

January 31 Introduction to linear algebra (cont.)

February 2 Introduction linear algebra (continued) - QUIZ 2 7.7-7.8

February 4 Introduction linear algebra (continued)

February 7 Eigenvalues and eigenvectors 8.1-8.5

February 9 Eigenvalues and eigenvectors (continued)

February 11 Eigenvalues and eigenvectors (continued)

February 14 Systems of linear ODE’s 4.1-4.3

February 16 Systems of linear ODE’s (continued)

February 18 Systems of linear ODE’s – Analytical methods– Quiz 3 4.4-4.6 (+supplementary)

February 21 Systems of linear ODE’s – Analytical methods

February 23 Systems of linear ODE’s – Analytical methods

February 25 Laplace transforms of systems of ODE’s, Analytic functions of a complex variable

6.7, 13.1-13.7

February 28 Analytic functions of a complex variable (continued)

March 2 Analytic functions of a complex variable (continued) – Quiz 4

March 4 Complex integration 14.1-14.4

March 14 Complex integration

March 16 Power series representations of complex functions 15.1-15.4

March 18 Power series representations of complex functions (continued

March 21 Power series representations of complex functions (continued)

March 23 Laurent Series and the residue integration– Quiz 5 16.1-16.2

March 25 Laurent Series and the residue integration (continued)

March 28 Laurent Series and the residue integration (continued)

March 30 Residue Integration 16.3

April 1 Residue Integration (continued)

April 4 Evaluation of real integrals 16.4

April 6 Evaluation of real integrals (continued) – Quiz 6

April 8 Evaluation of real integrals (continued)

April 11 Inversion of Laplace Transforms (simple cases) Supplementary material

April 13 Potential Theory 18.1

April 15 Applications to electrostatics, heat conduction, and fluid flow

18.3-18.5

April 28 Applications (continued)

April 20 Quiz 7 and 8