Grader: Kunal Krishna

Grader Office Hours: email him for appointment

The course will discuss the solution of Boundary Value Problems for classical Partial Differential Equations.

The text that will be used is:

David L. Powers, **Boundary Value Problem** 5th Edition,
Harcourt Academic Press

There will be two midterm the first of which will be on Thursday September 27th.

The exercise listed are for HW collection. I will collect them every two weeks and grade 2 or 3 exercises among the one assigned.

The final greade will be based on the following rules: 50% final, 40% midterms, 10% HW. Curving will be done on the final result.

**Assignments for the Long Distance students are due 1 weeks after the normal
students due date.**

- Ordinary Differential Equation (review material)
- Fourier Series and Integrals
- The Heat Equation
- The Wave Equation
- Problem in Several Dimension (time permitting)
- Numerical Methods (time permitting)

**First week**

Material covered:

- 0.1 (Homogeneous Linear Equations)
- 0.2 (Nonhomogeneous Linear Equations)
- 0.3 (Boundary Value Problems)
- 0.5 (Green's Function)
- 0.4 (Singular Boundary Value Problem)

Exercises:

- (0.1) 3, 11, 12, 18, 22
- (0.2) 3, 7, 12, 16
- (0.3) 3, 7, 14
- (0.4) 1, 4, 8
- (0.5) 3, 4, 8, 13

**Second week**

Material covered:

- 1.1 (Periodic Functions and Fourier Series)
- 1.2 (Arbitrary Period and Half Range Expansions)
- 1.3 (Convergence of Fourier Series)

Exercises:

- (1.1) 1, 6,7
- (1.2) 1, 7, 8, 9, 15
- (1.3) 2, 3

First HW collection **Thursday September 6 (13 for DL student)**

**Third week**

Material covered:

- 1.4 (Uniform convergence)
- 1.10 (Complex Methods)
- 1.5 (Operation on Fourier Series)

Exercises: (number in [] are for people with the 4th edition)

- (1.4) 1, 2, 4
- (1.10) 1 [3], 3 [5], 6 [2]
- (1.5) 6, 8, 9

**Fourth week**

Material covered:

- 1.6 (Mean, Error and Convergence in Mean)
- 1.8 (Numerical Determination of Fourier Coefficients)
- 1.9 (Fourier Integral)

Exercises: (number in [] are for people with the 4th edition)

- (1.6) 2, 3, 4
- (18) 3
- (1.9) 3, 5 [9], 6

Second HW collection **Thursday September 20 (27 for DL student)**

**Fifth and Sixth week**

Material covered:

- 2.1 (Derivation and Boundary Conditions)
- 2.2 (Steady States Temperatures)
- 2.3 (Example: Fixed Ends Temperatures)

Exercises:

- (2.1) 3, 5, 8
- (2.2) 1, 3, 7, 9
- (2.3) 3, 9

**First Midterm** will be on **Thursday September 27**.

See last term first miterm and solution.

**Seventh week**

Material covered:

- 2.4 (Example: Insulated bar)
- 2.5 (Example: Different Boundary Conditions)
- 2.6 (Example: Convection)

Exercises:

- (2.4) 1, 5, 8
- (2.5) 5 [9], 10 [6,8], 11 [3], 12 [4]
- (2.6) 3, 7, 8

Third HW collection ** Thursday October 11th (18 for DL student)**

**Eighth week**

Material covered:

- 2.7 (Sturm-Liouville Problems)
- 2.8 (Expansion in Series of Eigenfunctions)
- 2.9 (Generalities on the Heat Conduction Problem)

Exercises:

- (2.7) 1, 5, 7, 8
- (2.8) 1, 2
- (2.9) 1

Material covered:

- 2.10 (Semi-Infinite Rod)
- 2.11 (Infinite Rod)

Exercises:

- (2.10) 2, 6
- (2.11) 1, 4, 5

Material covered:

- 3.1 (The Vibrating String)
- 3.2 (Solution of the Vibrating String Problem)
- 3.3 (D'Alembert Solution)

Exercises:

- (3.1) 3
- (3.2) 7 [5], 8 [6], 11 [9], 13 [11]
- (3.3) 9, 12 [10], 13 [12]

Fourth HW collection ** Thursday November 1st (8th for DL student)**

**Eleventh week**

Material covered:

- 3.4 (One Dimensional Wave Equation: Generalities)
- 3.5 (Estimation of Eigenvalues)
- 3.6 (Wave Equation in Unbounded Region)

Exercises:

- (3.4) 4, 6, 8
- (3.5) 3, 6
- (3.6) 3, 6, 8

**Twelfth week**

Material covered:

- 4.1 (Potential Equation)
- 4.2 (Potential in a Rectangle)
- 4.3 (Further Example for a Rectangle) copy for people with 4th edition
- 4.5 (Potential in a Disk)

Exercises:

- (4.1) 3, 8
- (4.2) 2, 6
- (4.3) 1, 4, 5, 9
- (4.5) 1, 2, 9

**Second Midterm** will be on **Thursday November 15**.
The dead line for DL student is **Monday November 25**. Preparation material: last year second midterm with solution; retake for second midterm with solution; last year final.

Fifth HW collection ** Thursday November 29th (December 6th for DL student)**