Grader: TBA

Grader Office Hours: TBA

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** 6th
Edition, Harcourt Academic Press. If you have the fifth edition you can
use it. There are only minor differences with the newest edition. Some
of the exercises have changed number. Incase one such exercise is
assigned has a HW the number relative to the fifth edition will appear
in square brakets (e.g. [12]).

There will be two midterm. The first midterm will be on Friday 6/18 and the second on Friday 7/9. The midterms will test all the material covered up to the Friday before the test date.

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.**

Arguments Covered

- 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)
- 1.1 (Periodic Functions and Fourier Series)

Exercises:

- (0.1) 3, 11, 12, 18, 22
- (0.2) 3, 7, 11, 16
- (0.3) 3, 7, 16 [14]
- (1.1) 1, 6,7

**Second week**

Material covered:

- 1.2 (Arbitrary Period and Half Range Expansions)
- 1.3 (Convergence of Fourier Series)
- 1.4 (Uniform convergence)
- 1.5 (Operation on Fourier Series)

Exercises:

- (1.2) 1, 7, 8, 9, 15
- (1.3) 2, 3
- (1.4) 1, 2, 4
- (1.5) 6, 8, 9

**Third week**

Material covered:

- 1.10 (Complex Methods)
- 1.6 (Mean, Error and Convergence in Mean)
- 1.8 (Numerical Determination of Fourier Coefficients)

Exercises:

- (1.10) 1, 3, 6
- (1.6) 2, 3, 4
- (1.8) 3

The first midterm will be on Friday 18/6. It will cover all the material up to section 2.2. You may use a scientific calculator but no laptop or calculator able to do symbolic differentiation or integration. No cheat sheet will be allowed.

Here is some preparation material: fall 2005 miterm and solution set and a practice test with solution set.

Material covered:

- 1.9 (Fourier Integral)
- 1.11 (Applications of Fourier Series and Integrals)
- 2.1 (Derivation and Boundary Conditions)

Exercises:

- (1.9) 3, 5
- (2.1) 3, 5

Fifth week

Material covered:

- 2.2 (Steady States Temperatures)
- 2.3 (Example: Fixed Ends Temperatures)

Exercises:

- (2.2) 3, 7, 9
- (2.3) Project 2.2 [9]

Sixth 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 , 10 , 11 , 12
- (2.6) 7, 10

Solution set for the first midterm.

The first midterm will be on Friday 9/7. It will cover all the material up to section 2.9. You may use a scientific calculator but no laptop or calculator able to do symbolic differentiation or integration. No cheat sheet will be allowed.

Here is some preparation material: fall 2004 miterm and fall 05 midterm with solution set.

Seventh 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 [9], 11 [7]
- (2.8) 1, 2, 3
- (2.9) 1

Eighth week

Preparation for midterm and midterm.

Nineth week

Material covered:

- 3.1 (The Vibrating String)
- 3.2 (Solution of the Vibrating String Problem)
- 3.3 (D'Alembert Solution)
- 3.4 (One Dimensional Wave Equation: Generalities)

Exercises:

- (3.1) 4
- (3.2) 7, 8, 12 [14]
- (3.3) 1, 4 [9], 12
- (3.4) 8

Material covered:

- 4.1 (The Potential Equation)
- 4.2 (Potential in a Rectangle)
- 4.3 (Further Example for a Rectangle)
- 4.5 (Potential in a Disk)

Exercises (suggested):

- (4.1) 2, 6, 8
- (4.2) 5, 6
- (4.3) 1, 10, 11
- (4.5) 1, 7, 8

Material covered:

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

Exercises (suggested):

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

The final exam will be on Monday August 2 at 8:00am in the usual lecture room. The exam will cover all the material of the class. The sections of the book covered by the exam are the one listed above.

Preparation material: Final from fall 04, fall 05 and fall 07.