MATH 4581
Fall 2004
MWF 11:05-11:55 Skiles 202
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
Solutions to the HW.
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)
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:
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.
Solution set for HW
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