TTr 10:00-11:45 Skiles 268

Professor Federico Bonetto

Office Hours: TTr 12-1, Skiles 123B

Grader: Melissa Hopkins

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 Tuesday 6/19. 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.

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)

Exercises:

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

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

Exercises:

- (1.5) 6, 8, 9
- (1.10) 1, 3, 6
- (1.6) 2, 3, 4
- (1.8) 3

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

Material covered:

- 2.2 (Steady States Temperatures)
- 2.3 (Example: Fixed Ends Temperatures)
- 2.4 (Example: Insulated bar)
- 2.6 (Example: Convection)

Exercises:

- (2.2) 3, 7, 9
- (2.3) Project 2.2 [9]
- (2.4) 1, 5, 8
- (2.6) 7, 10

Sixth 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