AMATH 353
SLN 1188, MWF 10:30-11:20, Loew 115

Fourier Analysis and Partial Differential Equations

(Prerequisite: AMATH 351 or MATH 307)

Instructor:

 Professor W. Criminale
Guggenheim 405A
tel: 543-9506
fax: 685-1440
lascala@amath.washington.edu
office hours: 3:30-4:30pm or by appointment
   

Teaching Assistant:

 David George
Johnson 436
tel: 221-6652
fax: 685-1440
dgeorge@amath.washington.edu
office hours: T,Th 3:30-5:00

Homework Grades Message Board 2002 Web Page
Course description Textbook Syllabus Objectives Schedule

Course Description

Foundations and definitions; Heat equation, wave equation, and Laplace's equation; Separation of variables technique for solutions; Initial-value, boundary-value problems; 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; method of characteristics.

Textbook

Farlow, S.J. Partial Differential Equations for Scientists and Engineers. Dover Publications, 1993.
Additional Notes: From time to time, additional notes and supplements will be put on course web.

Syllabus

(a) Introduction, Bases
(b) Physical Origins of Partial Differential Equations
(c) Types of Partial Differential Equations
(d) Diffusion Examples; Solutions by Separation of Variables
(e) Fourier Series, Eigenfunction Expansions
(f) Wave Examples; Solutions by d'Alembert's Method
(g) Nonhomogeneous Partial Differential Equations
(h) Utility of Fourier and Laplace Transforms
(i) First Order Partial Differential Equations; Method of Characteristics

Learning Objectives and Instructor Expectations

Although the subject matter of partial differential equations can be made rather difficult, I will attempt to present the course material in as simple manner as possible. More theoretical aspects, such as proofs, will not be given or reequired. Instead, applications and the physical bases will be emphasized.

I will let you know what you need to learn and can be omitted. Homework is used to reinforce class lectures and not as a way to introduce material that is not covered in class. Exams will emphasize basic techniques as applied to simple and fundamental problems. No obscure questions will be on exams that cater to mental dexterity.

Class time should be thought of as interactive and questions are encouraged at all times.

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 Quizzes Homework Due Date Homework Problem Sets Homework Solutions
First day of classes Monday, January 6
Homework#1 due Friday, January 17 Homework #1 (.ps, .pdf) HW #1 Solutions (.ps, .pdf)
Martin Luther King Day Monday, January 20 No class
Homework#2 due Monday, January 27 Homework #2 (.ps, .pdf) HW #2 Solutions (.ps, .pdf)
homework#3 due Friday, January 31 Homework #3 (.ps, .pdf) HW #3 Solutions (.ps, .pdf)
Homework#4 due Friday, February 7 Homework #4 (.ps, .pdf) HW #4 Solutions (.ps, .pdf)
Quiz I Wednesday, February 12
President's Day Monday, February 17 No class
Homework#5 due Friday, February 21 Homework #5 (.ps, .pdf) HW #5 Solutions (.ps, .pdf)
Homework#6 due Friday, February 28 Homework #6 (.ps, .pdf) HW #6 Solutions (.ps, .pdf)
Homework#7 due Friday, March 7 Homework #7 (.ps, .pdf) HW #7 Solutions (.ps, .pdf)
Problem1 Quiz II due before Quiz II
Last day of classes Friday, March 14
Quiz II Monday, March 17 at 8:30am

Grading

Your course grade will be based on an equal balance of (a) all homework assignments (1/3), and (b) two quiz scores at 1/3 each.

You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password.

Tutorials

No on-line tutorials have been assigned for AMATH 353.

<lascala@amath.washington.edu> Mon Feb 3 10:50:42 2003