Mathematics 33
Spring 2004
Syllabus
Date
Topics
Homework
| 3-29 | Review PDEs | Problem 1, solving the heat equation. |
| 3-31 | More review, Start Gibbs' phenomenon | Problems 2, 3a,b, Gibbs' phenomenon for a step function. |
| 4-2 |
Gibbs' phenomenon |
Problems
3c,d
Week 1 homework solutions. |
| 4-5 |
Exponential
form of Fourier series |
Problems 4,5 |
| 4-7 |
Fourier transform |
Problems 6,7 |
| 4-9 |
Some properties
of the Fourier Transform |
Problem 8 and p. 61 of our text, Kammler
(Baker reserve, math 83), problem 1.1 (a) and (b) only.
Week 2 homework solutions. |
| 4-12 |
Transforming
PDEs |
p. 72:
1.20 and Problem 9 |
| 4-14 |
Convolutions |
p. 116:
2.1(c), 2.3a,b,c and Problem
10 (optional: p. 122: 2.28) |
| 4-16 |
More properties, transforming
the gaussian |
Problems 11,12 and p. 156: 3.2e,j;
p. 157: 3.5d,e,f,h. Week 3 homework solutions. |
| 4-19 |
Inhomogenous heat
equation |
Problems 13,14 |
| 4-21 |
More properties |
p. 156:
3.2(f); p. 158: 3.11 (Look up the Fourier
transforms of the functions d and f on page A-3.);
p. 161: 3.20a,b,c,d,e,f, p. 122: 2.26(a) |
| 4-23 |
Start distributions |
Problem 15 and p. 157:
3.4(f) and 3.6(a) Week 4 homework solutions. |
The first test on Wednesday, the 28th, in Bradley 105 covers up to here. Solutions to the first test.
| 4-26 |
Differentiating distributions |
Problems 16,17,18 |
| 4-28 |
Schwartz functions |
Take-home portion of exam due in
class on Friday. |
| 4-30 |
Basic calculus |
Problems 19-22 20 is
optional. Week 5 homework solutions. |
| 5-3 |
Fourier transforms of distributions |
Problem
23(a) |
| 5-5 |
More operations on distributions |
Problems
23(b),24, 25 |
| 5-7 |
Convolving distributions
with functions |
Problems
26,27 Week 6 homework solutions. |
| 5-10 |
Solving linear ODEs |
Problem
28 |
| 5-12 |
Uncertainty principle |
Problem
29 |
| 5-14 |
More uncertainty |
Problem
30 Week 7 homework solutions. |
| 5-17 |
Schrodinger equation |
Problem 31 |
| 5-19 |
More Schrodinger |
Problems
32, 33 Week 8 homework solutions
(M,W). |
| 5-21 |
Problem 34 |
| 5-24 |
Laplace's equation |
Problem 35 |
| 5-26 |
||
| 5-28 |
The wave equation |
Problem 36
Week 9 homework solutions. |
| 6-2 |
no homework |