Math 454 Boundary Value Problems for PDEs

Section 001, Winter 2001

Instructor:	Warren Weckesser 4859 East Hall, 936-9995 Email: weckwg@math.lsa.umich.edu
Office Hours:	Tuesday, 1:30-3:00 PM, in 1211 EECS
	Wednesday, 2:30-4:00 PM, in 4859 East Hall
Lecture:	Tue, Thu 12-1:30, Room 1371 GGBL (North Campus)
Text:	Math 454 Coursepack: Boundary Value Problems for Partial Differential Equations, by Tim Callahan
Web Page:	http://www.math.lsa.umich.edu/~weckwg/math454/

Final Exam is Friday, April 20, 4-6 PM in 1371 GGBL

Course Content

This course covers methods of solving partial differential equations (e.g. the heat, wave, Helmholtz and Laplace equations) with specified boundary conditions in various geometries. We will cover separation of variables, Fourier series, Bessel functions, spherical harmonics, orthogonal polynomials, Sturm-Liouville theory, eigenfunctions of the Laplacian in several different coordinate systems, conformal mapping, etc. These methods have applications in fields as diverse as mechanics, finance, thermodynamics, aerodynamics, electromagnetism, and many others, and we will take our examples from such disciplines.

We will start at the beginning of the course pack written by Tim Callahan, and proceed through as far as we can. There is certainly more there than we will be able to cover in one semester.

General Information

Prerequisites: Math 216, 256, 286, or 316. You should have a solid understanding of ordinary differential equations.
Your grade will be calculated using: 40% Homework, 25% Midterm Exam, 35% Final Exam.
You are responsible for all announcements and material covered in class. Attendance is not mandatory, but is strongly encouraged.

Exams

There will be a midterm exam in class on Thursday, Feb. 22.
There will be a comprehensive final exam.
Exams will be based on the text, the homework assignments, and the lectures.
Travel plans are not a valid reason for missing an exam.

Homework

There will be weekly homework assignments. Homework will be assigned on Thursday, and will be due the following Thursday.
The assignments will be available on the web page.
Late homework is not accepted.
The lowest homework score will be dropped before computing your course grade.
You may work together on the homework. In fact, I encourage you to work together in study groups. However, each person must write up and submit their own answers--no copying!
Your homework should be either written with a word processor or very neatly hand-written. Explanations must be given in clear and complete sentences. Anything that I can't read or understand will be not be given credit.
All graphs must have a title and clearly labeled axes.

Homework Assignments

Assignment	Due Date	Hints and Frequently Asked Questions	Solutions
1: Postscript or PDF	January 16	Last update 01/15, 04:55 PM	Postscript or PDF
2: Postscript or PDF	January 25	Last update 01/24, 05:05 PM	Postscript or PDF
3: Postscript or PDF	February 1	Last update: Jan. 31, 03:55 PM	Postscript or PDF
4: Postscript or PDF	February 8	Last update: Feb. 7, 1:30 PM	Postscript or PDF
5: Postscript or PDF	February 15	Last update: ---	Postscript or PDF
6: Postscript or PDF	March 15	Last update: ---	Postscript or PDF
7: Postscript or PDF	March 22	Last update: March 20, 6:20PM	Postscript or PDF
8: Postscript or PDF	April 3 (Tuesday!)	Last update: ---	Postscript or PDF
9: Postscript or PDF	April 10 (Tuesday!)	Last update: Thursday, April 5, 6:40 PM	Postscript or PDF
10: Postscript or PDF	April 17 (Tuesday!)	Last update: Monday, April 16, 3:30 PM	Postscript or PDF

Additional Class Handouts

Jan. 4	Course Information (an early version of this web page)	Postscript or PDF
Jan. 23	Plots of solution to the heat equation	Postscript or PDF
Feb. 15	Midterm Review Sheet	Postscript or PDF
Feb. 20	Midterm Review Problems -- Solutions	Postscript or PDF
April 12	Final Exam Practice Problems	Postscript or PDF