MW 3:00 - 4:15 Skiles 249

Instructor: Federico Bonetto

Office Hours: MW 2:00 - 3:00, Skiles 133B

Grader: Eric Sabo

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. In case one such exercise is
assigned has a HW the number relative to the fifth edition will appear
in square brakets (e.g. [12]).

The syllabus can be found here. You can see how the class will develop on the webpage of the previous time I teached it.

There will be two midterms tentatively scheduled for 2/28 and 3/28.

The exercise listed are for HW collection. I will collect them every two weeks.

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

**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 - Third 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, 22
- (0.2) 3, 7, 16
- (0.3) 3, 7, 16 [14]
- (1.1) 1, 6,7

**First HW** due on **January 29**.

**Fourth week**

Material covered:

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

Exercises:

- (1.2) 1, 7, 8
- (1.3) 2, 3

Material covered:

- 1.4 (Uniform convergence)
- 1.5 (Operation on Fourier Series)
- 1.6 (Mean, Error and Convergence in Mean)
- 1.8 (Numerical Determination of Fourier Coefficients)

Exercises:

- (1.4) 1, 2
- (1.5) 6, 8
- (1.6) 2, 4
- (1.8) 3

**Second HW** due on **February 12**.

**Sixth week**

Material covered:

- 1.9 (Fourier Integral)
- 1.10 (Complex Methods)
- 1.11 (Applications of Fourier Series and Integrals)

Exercises:

- (1.9) 3, 5
- (1.10) 1, 3, 6

**Seventh week**

Material covered:

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

Exercises:

- (2.1) 3, 5
- (2.2) 3, 7
- (2.3) Project 2.2 [9]
- (2.4) 1, 5, 8

**Third HW** due on **February 26**.

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

Solution set for the first midterm.

**Eighth week**

Material covered:

- 2.6 (Example: Convection)
- 2.7 (Sturm-Liouville Problems)

Exercises:

- (2.6) 7, 10
- (2.7) 1, 5, 7 [9], 11 [7]

**Eighth week**

Material covered:

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

Exercises:

- (2.8) 1, 2, 3
- (2.9) 1

**Forth HW **due on** April 2. **

The **second midterm ** will be on Wednesday April 4. It will cover all the material up to Chapter 2 included.
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.

Solution set for Midterm 2

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]

Material covered:

- 3.4 (One Dimensional Wave Equation: Generalities)
- 4.1 (Potential Equation)
- 4.2 (Potential in a Rectangle)

Exercises:

- (3.4) 4, 6, 8
- (4.1) 3, 8
- (4.2) 2, 6

The exercise posted since the last HW will **not be collected**. They are intended for **practice** only.

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