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** Harcourt Academic Press

There will be two midterm the first of which will be on Monday September 20th.

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 2 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)
- 1.4 (Uniform Convergence)

Exercises:

- (1.1) 1, 6,7
- (1.2) 1, 7, 8, 9, 15
- (1.3) 2, 3
- (1.4) 1, 2, 4

**Third week**

Material covered:

- 1.5 (Operations on Fourier Series)

Exercises:

- (1.5) 2, 6, 8, 9

**Fourth week**

Material covered:

- 1.6 (Mean Error and Convergence in Mean)
- 1.10 (Complex Methods)
- 1.9 (Fourier Integrals)

Exercises:

- (1.6) 2, 3, 4
- (1.9) 3, 6, 9
- (1.10) 2, 5

** First midterm on Monday 26th September**

**
****Practice test for the September 26th midterm.
It is a collection of exercise like the one you may find in the test but considerably
longer the the test will be.
**

**
Fifth and Sixth week
**

**
Material covered: **

**
**

**1.11 (Applications of Fourier Series and Integrals)****2.1 (Derivation and Boundary Conditions)****2.2 (Steady States Temperatures)****2.3 (Example: Fixed Ends Temperatures)****2.4 (Example: Insulated Bar)**

Exercises:

- (Miscellaneous Exercise) 1, 2, 3
- (2.1) 3, 5, 8
- (2.2) 1, 3, 7, 9
- (2.3) 3, 9
- (2.4) 1, 5, 8

**Third HW due Wednesday October 13. Sections due are 1.10 and 2.1-2.4**

**Seventh and Eighth week**

Material covered:

- 2.5 (Example: Different Boundary Conditions)
- 2.6 (Example: Convection)

Exercises:

- (2.5) 3, 4, 5, 6, 8, 14
- (2.6) 3, 7, 8

Material covered:

- 1.8 (Numerical Fourier Coefficient)
- 2.7 (Sturm-Luiville Problems)
- 2.8 (Expansion in series of Eigenfunction)
- 2.9 (Generalities on the Heat Conduction Problem)

- (1.8) 3
- (2.7) 1, 5, 8
- (2.8) 1, 2
- (2.9) 1

**Second midterm on Wednesday November 2nd**

** The Midterm will cover up to
section 2.9. There will be a review class on Monday at 5pm in ESM 212.
Last year second midter.
**

**
?? week
**

**
Material covered: **

**
**

**3.1 (The Vibrating String)****3.2 (Solution of the Vibrating String Problem)****3.3 (D'Alembert's Solution)****3.4 (One Dimensional Wave Equation: Generalities)****3.5 (Estimation of the Eigenvalues)****3.6 (Wave Equation in Unbounded Regions)**

Exercises:

- (3.1) 3
- (3.2) 5, 6, 9, 11, 13
- (3.3) 9, 10, 11
- (3.4) 4, 6, 8
- (3.4) 3, 6
- (3.6) 3, 6, 8

**Forth HW due on Wednesday December 7.** Exercise due from sections
3.1-3.6.

**?? week**

Material covered:

- 5.3 (Two Dimensional Heat Equation: Solution)
- 5.4 (Problems in Polar Coordinates)
- 5.5 (Bessel's Equation)
- 5.7 (Vibration of a Circular Membrane)
- 7.1 (Boundary Value Problem)

Exercises:

- (5.3) 3, 5, 7
- (5.4) 3, 5, 6
- (5.5) 1, 4
- (5.7) 1, 2, 3

Solution set for the retake exam

Last term test. I'll go over this test on Wednesday and Friday.