# math handout

Topics: Partial differential equation, Boundary value problem, Fourier transform Pages: 6 (547 words) Published: September 25, 2013
INSTRUCTION DIVISION, FIRST SEMESTER 2013-2014
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
Instructorincharge: 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 (Pageproblems)
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 :...