Office Hours: MW 12-13,

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

Second week

Material covered:

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
Fourth week

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)
• 2.3 (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