MATH 4581

Fall 2011

MW 3:05-4:25 Engr Science & Mech, room 212

Professor Federico Bonetto

Office Hours: MW 12-1, Skiles 133b
Grader: Chenchen Mou

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. In case one such exercise is assigned as a HW the number relative to the fifth edition will appear in square brakets (e.g. [12]).

There will be two midterm.  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.

Assignments for the Long Distance students are due 1 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)
• 2.1 (Derivation and Boundary Conditions)

Exercises:

• (0.1) 3, 11, 12, 18, 22
• (0.2) 3, 7, 11, 16
• (0.3) 3, 7, 16 [14]
• (2.1) 3, 5

Second week

Material covered:

• 1.1 (Periodic Functions and Fourier Series)
• 1.2 (Arbitrary Period and Half Range Expansions)

Exercises:

• (1.1) 1, 6,7
• (1.2) 1, 7, 8, 9, 15

Third week

Material covered:

• 1.4 (Uniform convergence)
• 1.5 (Operation on Fourier Series)

Exercises:

• (1.4) 1, 2, 4
• (1.5) 6, 8, 9

Fourth week

Material covered:

• 1.6 (Mean, Error and Convergence in Mean)
• 1.8 (Numerical Determination of Fourier Coefficients)

Exercises: 

• (1.6) 2, 3, 4
• (1.8) 3

• 1.10 (Complex Methods)
• 1.9   (Fourier Integral)
• 1.11 (Applications of Fourier Series and Integrals)

• (1.10) 1, 3, 6
• (1.9) 3, 5 
• (2.1) 3, 5

• 2.2 (Steady States Temperatures)
• 2.3 (Example: Fixed Ends Temperatures)

Exercises: 

• (2.2) 3, 7, 9
• (2.3) Project 2.2 [9]

• 2.4 (Example: Insulated bar)
• 2.5 (Example: Different Boundary Conditions)
• 2.6 (Example: Convection)

Exercises: 

• (2.4) 1, 5, 8
• (2.5) 5 , 10 , 11 , 12
• (2.6) 7, 10

• 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

• 3.1  (The Vibrating String)
• 3.2 (Solution of the Vibrating String Problem)
• 3.3 (D'Alembert Solution)
• 3.4 (One Dimensional Wave Equation: Generalities)

Exercises: 

• (3.1) 4
• (3.2) 7, 8, 12 [14]
• (3.3) 1, 4 [9], 12
• (3.4) 8

• 4.1 (The Potential Equation)
• 4.2 (Potential in a Rectangle)
• 4.3 (Further Example for a Rectangle)
• 4.5 (Potential in a Disk)

Exercises (suggested): 

• (4.1) 2, 6, 8
• (4.2) 5, 6
• (4.3) 1, 10, 11
• (4.5) 1, 7, 8

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

Exercises (suggested): 

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