AMATH 353
SLN 1205, MWF 10:30-11:20, Loew Hall 113
(Prerequisites: AMATH 351 or MATH 307)

Fourier Analysis and Partial Differential Equations

Instructors:
Professor K.K. Tung Guggenheim 412C tel: 685-3794 fax: 685-1440 tung@amath.washington.edu office hours: M: 11:30 - 12:30, Tu: 11:00 - 12:00				Professor Randall J. LeVeque Guggenheim 408A Tel: 685-3037 fax: 685-1440 rjl@amath.washington.edu office hours: M: 11:30 - 12:30, Tu: 11:00 - 12:00
TA: Jihwan Kim Guggenheim 416 tel: 685-8068 jkim@amath.washington.edu office hours: T, F: 1:00 - 2:00

Course Description

Heat equation, wave equation, and Laplace's equation. Separation of variables. Fourier series in context of solving heat equation. Fourier sine and cosine series; complete Fourier series. Fourier and Laplace transforms. Solving partial differential equations in infinite domains. D'Alembert's solution for wave equation.

Textbook

Tung, K.K.: Partial Differential Equations and Fourier Analysis--A Short Introduction. Available on the Web (free).

Not Required: Farlow, S.J.: Partial Differential Equations for Scientists and Engineers. Dover Publishing, New York, 1993. Available at the University Bookstore.

Syllabus

Introduction to partial derivatives and partial differential equations. Physical origins of partial differential equations in heat conduction, pollutant transport, random walk, stock prices, guitar strings, bridges, and waves in the atmosphere. Separation of variables. Fourier series in the context of solving the heat equation, as in Fourier's original work on heat conduction. Fourier sine and cosine series, and complete Fourier series. Fourier and Laplace transforms. Solving partial differential equations in infinite domains. D'Alembert's solution for the wave equation.

Learning Objectives and Instructor Expectations

Although the subject matter of Fourier Analysis and Partial Differential Equations can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be presented. Applications will be emphasized.

I will let you know clearly what you need to learn and what can be skipped. Homeworks are used to reinforce class lectures, but not as a way to introduce material not covered in class. Exams will emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or

Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Homework and Exams	Homework Assigned	Homework Due	Homework Problem Sets	Homework Solutions
First day of classes	Wednesday, January 4
Homework #1	Wednesday, January 11	Wednesday, January 18	Homework #1 (.ps, .pdf)	HW #1 Solutions (.ps, .pdf)
Martin Luther King Day	Monday, January 16		No class
Homework #2	Wednesday, January 18	Wednesday, January 25	Homework #2 (.ps, .pdf)	HW #2 Solutions (.ps, .pdf)
Homework #3	Wednesday, January 25	Wednesday, February 1	Homework #3 (.ps, .pdf)	HW #3 Solutions (.ps, .pdf)
*Exam I (one hour)*	Monday, February 6	Sample Exam I (.ps, .pdf)	Exam #1 (.ps, .pdf)	Exam 1 Solutions (.ps, .pdf)
Homework #4	Wednesday, February 8	Wednesday, February 15	Homework #4 (.ps, .pdf)	HW #4 Solutions (.ps, .pdf)
Homework #5	Wednesday, February 15	Wednesday, February 22	Homework #5 (.ps, .pdf)	HW #5 Solutions (.ps, .pdf)
President's Day	Monday, February 20		No class
Homework #6	Wednesday, February 22	Wednesday, March 1	Homework #6 (.ps, .pdf)	HW #6 Solutions (.ps, .pdf)
Homework #7	Wednesday, March 1	Wednesday, March 8	Homework #7 (.ps, .pdf)	HW #7 Solutions (.ps,.pdf)
Last day of classes	Friday, March 10
*Exam II (one hour)*	Monday, March 13 9:20am - 10:20am	Sample Exam II (.ps, .pdf) Sample Exam II Solution (.ps, .pdf)	Exam #2 (.ps, .pdf)	Exam 2 Solutions (.ps, .pdf)

Grading

Your course grade will be calculated by weighing your homework, first and second exam grades in the proportions 1/3, 1/3, and 1/3, respectively. There will be no comprehensive final exam. You are guaranteed a grade of 3.0 if your marks total 50%.

You may view your homework and exam grades on-line.

Lecture Notes on the Web

Tung, K.K.: Partial Differential Equations and Fourier Analysis--A Short Introduction.

Title: (.ps, .pdf).
Table of Contents: (.ps, .pdf).
Chapter 1: (.ps, .pdf).
Chapter 2: (.ps, .pdf).
Chapter 3: (.ps, .pdf).
Chapter 4: (.ps, .pdf).
Chapters 5: (.ps, .pdf).
Chapter 6: (.ps, .pdf).
Chapter 7: (.ps, .pdf).
Chapter 8: (.ps, .pdf).
Chapter 9: (.ps, .pdf).
Chapter 10: (.ps, .pdf).
Chapter 11: (.ps, .pdf).
Chapter12: (.ps, .pdf).
Chapter 13: (.ps, .pdf).
Chapter 14: (.ps, .pdf).

Links of interest:

Biography of Joseph Fourier

Tutorials

Animations
If you have a relatively slow internet connection the animations play better if you save the file locally and then view it with a browser.
For a simulation of the traveling wave with a boundary at x=0 (homework #2, exercise #2) see semi-infinite wave.
For a simulation of the diffusion equation (homework #3, exercise #1) see diffusion.
For a simulation of the plucked string (homework #4, exercise #2) see pluck.
For a simulation of the collapsing bridges (chapter 11 of the course notes) see resonance.

MATLAB
A short MATLAB tutorial is available in the MATLAB script file plot1.m. To run the tutorial save the file in a directory that is in the MATLAB path.

For those unfamiliar with the path, start MATLAB and type "path" at the MATLAB prompt. This should provide a list of the directories in the MATLAB path.

Then type "plot1" at the MATLAB prompt to run the script.

String Simulation
A simulation of the string problem from homework #4 is available in the MATLAB script file string353.m. To run the simulation, save the file in a directory that is in the MATLAB path. Then type "string353" at the MATLAB prompt to run the script.

Homework Solution Plots
Homework #2:
Homework #5:
Homework #6
Homework #7

Report problems or direct questions to <tung@amath.washington.edu>, or <rjl@amath.washington.edu>

Mon Dec 20 14:10:34 1999 -->