# math handout

**Topics:**Partial differential equation, Boundary value problem, Fourier transform

**Pages:**6 (547 words)

**Published:**September 25, 2013

COURSE HANDOUT (PART-II)

Date: 03.08.2013

In addition to part I (General Handout for all courses appended to the time table) this portion gives further specific details regarding the course. Course No. : MATH C241/MATH F211

Course Title :MATHEMATICS - III

Instructorincharge: M S RADHAKRISHNAN

Instructors :A Ramu, M S Radhakrishnan, TSL Radhika, P K Sahoo, K Venkata Ratnam, Manish Kumar, PTV Praveen Kumar, Sumit Kumar Vishwakarma

1. Scopes and Objective of the Course:

This Course reviews and continues the study of differential equations with the objective of introducing classical methods for solving boundary value problems. This course serves as a basis of the applications for differential equations, Fourier series and Laplace transform in various branches of engineering and sciences. This course emphasizes the role of orthogonal polynomials in dealing with Sturm-Liouville problems.

2. Text Book: Simmons G.F., Differential Equations with Applications and Historical Notes, TMH Edition 2003, Twelfth reprint 2008 Reference Book: 1. Kreider D.L. and Others: An Introduction to Linear Analysis, A.W., 1966.

2. Shepley L. Ross: Differential Equations, John Willy & Sons, 1984. 3. Course Plan: (Sections/Articles refer to Text Book)

Lect No.

Learning Objectives

Topic

Sections

Home work (Pageproblems)

1

To introduce the classical methods to solve 1st order equations First order eqns

1-7

Review & Self study

2

First order equations

8,9,10

All Pages 53-54

1 to 6, Pages 59-60

1 to 10, Page 61-62

3

Reduction of order

11

1 to 3, Page 65

1 to 50, Pages 75-76

4-5

To introduce the classical methods to solve 2nd order equations

Second order equations

14,15

All Pages 86-87 1-10, Pages 91-92

6

Use of a known solution

16

All Pages 94-95

8-11

Various methods to solve diff. Eqns

17,18,19,22,23

1-2, Page 97 & 5-8, Page 98

All Page 103, All Page 106, 1-13, Pages 127, All Pages 135-136

12-13

Properties of solutions

Sturm Separation Theorem and Sturm Comparison Theorem

24, 25

2-4, Page 161

All Page 164

14-16

To introduce Series Solutions method to 2nd order diff. Equation with variable coefficients Series Solutions

26 to 30

1-2, Page 175

All Page 182-184

All Pages 191-192

1 – 5, Page 198

17-18

Hypergeometric equation

31

All Pages 203-204

19-20

Legendre Polynomials

44,45

All Pages 341-343

1-5, Page 347

21

Chebyshev Polynomials

Appendix D

Pages 230-236

Hermite Polynomials (Self-study)

Appendix B

Pages 211-221

22-24

Bessel functions

46,47

All Pages 356-359

All Pages 363-365

25-28

Use LT to solve DE and IE

Laplace Transforms

48,49,50,51,53

All Pages 384-385

All Pages 388-389

All Page 394

All Pages 398-399 2 to4, Page 410

29-30

To introduce systems of equations

Systems of Equations

54,55,56

1-2, Page 420

5-9, Pages 426-427

1-5, Page 433

31-34

To introduce trigonometric series expansion of a function

Fourier Series

33,34,35,36

All Pages 256-257

1-5, Pages 263-264

All Pages 269-272

1-7, Page 274

35-36

To introduce classical methods to solve PDE

Eigen values and Eigen functions Sturm Liouville Problems

43

1, 2 Page 308

5, 7 Page 310

All Pages 316-317

37

One dim. Wave eqn

40

38

One dim. Heat eqn

41

39-40

Laplace’s eqn (Self Study)

42

4. Home Assignment: All problems listed are for Home work.

5. Evaluation Scheme :...

Please join StudyMode to read the full document