AMATH 353
SLN 1171, MWF 10:30-11:20, Loew Hall 115

Fourier Analysis and Partial Differential Equations

(Prerequisites: AMATH 351 or MATH 307)

Instructor:

 Professor W. Criminale
Guggenheim 405A
tel: 543-9506
fax: 685-1440
lascala@amath.washington.edu
office hours: MWTHF 3:30 - 4:30pm,
                     T 4:30 - 5:30pm, or by appointment.

Homework Grades Message Board 2001 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.

Textbook

Farlow, S.J. Partial Differential Equations for Scientists and Engineers. Dover Publications, 1993.

Syllabus

(a) Introduction, Bases
(b) Physical Origins of Many 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

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. Quizzes will emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in quizzes 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 quiz 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 7
Homework#1 due Friday, January 18 Homework #1 (.ps, .pdf) HW #1 Solutions (.ps, .pdf)
Martin Luther King Day Monday, January 21 No class
Homework#2 due Friday, January 25 Homework #2 (.ps, .pdf) HW #2 Solutions (.ps, .pdf)
Homework#3 due Friday, February 1 Homework #3 (.ps, .pdf) HW #3 Solutions (.ps, .pdf)
Homework#4 due Friday, February 8 Homework #4 (.ps, .pdf) HW #4 Solutions (.ps, .pdf)
Quiz I Friday, February 15
President's Day Monday, February 18 No class
Homework#5 due Friday, February 22 Homework #5 (.ps, .pdf) HW #5 Solutions (.ps, .pdf)
Homework#6 due Friday, March 1 Homework #6 (.ps, .pdf) HW #6 Solutions (.ps, .pdf)
Homework#7 due Friday, March 8 Homework #7 (.ps, .pdf) HW #7 Solutions (.ps, .pdf)
Homework#8 due Friday, March 15 Homework #8 (.ps, .pdf) HW #8 Solutions (.ps, .pdf)
Last day of classes Friday, March 15
Quiz II Monday, March 18 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 quiz 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> Fri Mar 15 15:16:42 2002