### Office Hours: MW 12-13,

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 Harcourt Academic Press

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.

Assignments for the Long Distance students are due 2 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)
• 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:

• 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 (Operations on Fourier Series)

Exercises:

• (1.5) 2, 6, 8, 9
Second HW due Wednesday September 21

Fourth week

Material covered:

• 1.6 (Mean Error and Convergence in Mean)
• 1.10 (Complex Methods)
• 1.9 (Fourier Integrals)

Exercises:

• (1.6) 2, 3, 4
• (1.9) 3, 6, 9
• (1.10) 2, 5

First midterm on Monday 26th September

Practice test for the September 26th 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:

• 1.11 (Applications of Fourier Series and Integrals)
• 2.1 (Derivation and Boundary Conditions)
• 2.3 (Example: Fixed Ends Temperatures)
• 2.4 (Example: Insulated Bar)

Exercises:

• (Miscellaneous Exercise) 1, 2, 3
• (2.1) 3, 5, 8
• (2.2) 1, 3, 7, 9
• (2.3) 3, 9
• (2.4) 1, 5, 8

Third HW due Wednesday October 13. Sections due are 1.10 and 2.1-2.4

Seventh and Eighth week

Material covered:

• 2.5 (Example: Different Boundary Conditions)
• 2.6 (Example: Convection)

Exercises:

• (2.5) 3, 4, 5, 6, 8, 14
• (2.6) 3, 7, 8
Nineth week

Material covered:

• 1.8 (Numerical Fourier Coefficient)
• 2.7 (Sturm-Luiville Problems)
• 2.8 (Expansion in series of Eigenfunction)
• 2.9 (Generalities on the Heat Conduction Problem)
Exercises:

• (1.8) 3
• (2.7) 1, 5, 8
• (2.8) 1, 2
• (2.9) 1
Third HW due on Monday October 31 Exercise due from sections 1.8, 2.5, 2.6, 2.7, 2.8, 2.9.

Second midterm on Wednesday November 2nd

The Midterm will cover up to section 2.9. There will be a review class on Monday at 5pm in ESM 212. Last year second midter.

?? week

Material covered:

• 3.1 (The Vibrating String)
• 3.2 (Solution of the Vibrating String Problem)
• 3.3 (D'Alembert's Solution)
• 3.4 (One Dimensional Wave Equation: Generalities)
• 3.5 (Estimation of the Eigenvalues)
• 3.6 (Wave Equation in Unbounded Regions)

Exercises:

• (3.1) 3
• (3.2) 5, 6, 9, 11, 13
• (3.3) 9, 10, 11
• (3.4) 4, 6, 8
• (3.4) 3, 6
• (3.6) 3, 6, 8

Forth HW due on Wednesday December 7. Exercise due from sections 3.1-3.6.

?? week

Material covered:

• 5.3 (Two Dimensional Heat Equation: Solution)
• 5.4 (Problems in Polar Coordinates)
• 5.5 (Bessel's Equation)
• 5.7 (Vibration of a Circular Membrane)
• 7.1 (Boundary Value Problem)

Exercises:

• (5.3) 3, 5, 7
• (5.4) 3, 5, 6
• (5.5) 1, 4
• (5.7) 1, 2, 3

Final Preparation Material

Last term test. I'll go over this test on Wednesday and Friday.