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

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.

**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

- 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

**Third week**

Material covered:

- 1.4 (Uniform Convergence)
- 1.5 (Operations on Fourier Series)

Exercises:

- (1.4) 1, 2, 4
- (1.5) 2, 6, 8, 9

Material covered:

- 1.6 (Mean Error and Convergence in Mean)

Exercises:

- (1.6) 2, 3, 4

Practice test for the September 20th 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:

- 1.8 (Numerical determination of Fourier Coefficients)
- 1.9 (Fourier Integrals)
- 1.10 (Complex Methods)
- 1.11 (Applications of Fourier Series and Integrals)

Exercises:

- (1.8) 3
- (1.9) 3, 6, 9
- (1.10) 2, 5
- (Miscellaneous Exercise) 1, 2, 3

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

Exercises:

- (2.1) 3, 5, 8
- (2.2) 1, 3, 7, 9
- (2.3) 3, 9
- (2.4) 1, 5, 8
- (2.5) 3, 4, 5, 6, 8, 14
- (2.6) 3, 7, 8

** Next Midterm on November 3rd** No HW collection on the week of the midterm.

**Tenth week**

Material covered:

- 2.10 (Semi-infinite rod)
- 2.11 (Infinite rod)

Exercises:

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

**Last week**

Material covered:

- 3.1 (The Vibrating String)
- 3.2 (Solution of the Vibrating String Problem)
- 3.3 (D'Alembert's Solution)
- 3.6 (Wave Equation in Unbounded Regions)

Exercises:

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