AMATH 353
SLN 10199, MWF 2:30-3:20, GLD 322
(Prerequisites: AMATH 351 or MATH 307)
Fourier Analysis and Partial Differential Equations
Instructor: |
Professor Nathan Kutz
Condon Hall 708
kutz@amath.washington.edu
office hours: W 3:30-5, Th 3-5, F 8-9
|
TA: | Mingyuan Zhong
Condon Hall
zhongmy@amath.washington.edu
office hours: by appointment
|
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 and Notes
The text for the course is: S. J. Farlow, Partial Differential Equations for Scientists and Engineers (Dover)
I will also post my scanned lecture notes on the appropriate lecture below.
Syllabus
- (1) Diffusion Type Problems 3 lectures
- Lecture 1 (3/26): Introduction to Partial Differential Equations (PDEs) (Lesson 1, 2, 4) 353lec1.pdf
- Lecture 2 (3/28): The Diffusion Equation and Separation of Variables (Lesson 3, 5) 353lec2.pdf
- Lecture 3 (3/30): Fourier Analysis (Lesson 5) 353lec3.pdf
- Lecture (4/2): CANCELLED
- Lecture 4 (4/4): Boundary Conditions (Lesson 6, 7) 353lec4.pdf
- Lecture 5 (4/6): Nonhomogeneous PDEs and Eigenfunction Expansions (Lesson 9) 353lec5.pdf
- Lecture 6 (4/9): Eigenfunction Expansions: Generalities 353lec6.pdf
- Lecture 7 (4/11): Sturm-Liouville Theory: nonhomogeneous problems 353lec7.pdf
- Lecture 8 (4/13): The Dirac Delta Function and Green's Functions 353lec8.pdf
- Lecture 9 (4/16): Review of Eigenfunction Expansions 353lec9.pdf
- Lecture 10 (4/20): General Theory for Green's Functions 353lec10.pdf
- Lecture 11 (4/23): Integral Transforms (Lesson 10, 11) 353lec11.pdf
- Lecture 12 (4/25): Fourier Transforms (Lesson 11, 12) 353lec12.pdf
- Lecture 13 (4/27): Laplace Tranform (Lesson 13) 353lec13.pdf
- Lecture 14 (4/30): Application of Laplace Transforms (Lesson 15) 353lec14.pdf
- Lecture 15 (5/2): The Wave Equation (Lesson 16, 17) 353lec15.pdf
- Lecture 16 (5/4): Method of Images (Lesson 18) 353lec16.pdf
- Lecture 17 (5/7): Bounded Domains and Standing Waves (Lesson 20) 353lec17.pdf
- Lecture 18 (5/9): Solving the Wave Equation via Transforms 353lec18.pdf
- Lecture 19 (5/11): Higher Order Equations (Lesson 21) 353lec19.pdf
- Lecture (5/14): Midterm 2 review
- Lecture 20 (5/18): 2D and 3D Wave Equation 353lec20.pdf
- Lecture 21 (5/21): First-order Equations: Method of Characteristics 353lec21.pdf
- Lecture 22 (5/23): Nonlinear Waves and Shocks 353lec22.pdf
- Lecture 23 (5/25): Vibrating Drum Head 353lec23.pdf
- Lecture 24 (5/30): Poisson's Equation 353lec24.pdf
- Lecture (6/1): Final review
Schedule and Homework
Follow links in
the table below to obtain a copy of the homework in 
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.
| Homework and Exams |
Homework Due
Date |
Homework Problem Sets |
| First day of class |
Monday, March 26 |
| Homework#1 |
due Friday, March 30 |
Homework #1 (.pdf) |
| Homework#2 |
due Friday, April 6 |
Homework #2 (.pdf) |
| Homework#3 |
due Friday, April 13 |
Homework #3 (.pdf) |
| Midterm 1 |
Wednesday, April 18 |
Midterm 1
| Homework#4 |
due Friday, April 20 |
Homework #4 (.pdf) |
| Homework#5 |
due Friday, April 27 |
Homework #5 (.pdf) |
| Homework#6 |
due Friday, May 4 |
Homework #6 (.pdf) |
| Homework#7 |
due Friday, May 18 |
Homework #7 (.pdf) |
| Midterm 2 |
Wednesday, May 16 |
Midterm 2
| Memorial Day |
Monday, May 28 |
no
classes |
| Homework#8 |
due Wednesday, May 30 |
Homework #8 (.pdf) |
| Last day of classes |
Friday, June 1 |
| Final Exam |
Tuesday, June 5, 2:30-4:30pm |
Final
Exam
|
| |
Grading
You may view your homework and exam grades online:
grades
on-line.
Your course grade will be calculated by weighing the homework,
the Midterms, and the Final in the proportions 50%, 15%, 15%, and 20%,
respectively. Homework problem
sets will be assigned weekly. Homework
constitutes 50% of your final grade.
There will also be two one-hour-long
midterm and comprehensive final
for 30% and 20% or your grade respectively.
The test schedule is as follows:
Midterm 1: Wednesday, April 18, 2007 (15% - 1 hour)
Midterm 2: Wednesday, May 16, 2007 (15% - 1 hour)
Final: 2:30 p.m. - 4:20 p.m. - Tuesday, June 5,
2007 (20% - 2 hours)
The ten homework sets will determine remaining
50% of grade.
LATE HOMEWORK WILL NOT BE ACCEPTED.