Mathematics 33
Spring 2003
Syllabus
Date
Topics
Homework
| 3-26 | Review PDEs | Problem 1, solving the heat equation. |
| 3-28 | More review, Start Gibbs' phenomenon | Problems 2,3(a), Gibbs' phenomenon for a step function. |
| 3-31 |
Gibbs'
phenomenon |
Problems 3b,c,d |
| 4-2 |
Start exponential form of Fourier
series |
Problem 4 |
| 4-4 |
Continue |
Problem 5 |
| 4-7 |
Fourier
transform
|
Problems 6,7 |
| 4-9 |
Some
properties of the Fourier Transform |
Problem 8 and p. 61
of our text (Baker reserve), problem 1.1 (a) and (b) only. |
| 4-11 |
Transforming PDEs |
p. 72: 1.20 and Problem 9 |
| 4-14 |
Convolutions
|
p. 116: 2.1(c), and p. 117: 2.4a,b,c and Problem 10 (optional: p. 122: 2.28) |
| 4-16 |
properties
of the Fourier Transform |
Problem 11 and p. 156: 3.2e,j;
p. 157: 3.5d,e,f,h. (You will need the Fourier
transform of the gaussian for many of these. See problem
11 for it.) Also do Problem
12, but don't turn it in. |
| 4-18 |
Inhomogenous
heat equation |
Problem 5 |
| 4-21 |
More properties |
Due Friday:
Problem 13 and p. 156: 3.2(f); p. 158: 3.11 (Use p. A-3 to
find the known Fourier transforms of the functions d and f.); p. 161: 3.20a,b,c,d,e,f, p. 122: 2.26(a) |
| 4-23 |
Start distributions |
Due Friday or Monday:
p. 157: 3.4(f) and 3.6(a) |
| 4-25 |
Differentiating distributions |
Problems 14,15,16 |
| 4-28 |
Schwartz functions |
Problem
17 and optional (due 5-5): Problem 18 |
| 4-30 |
Product rule |
Problems
20, 21(a) |
| 5-2 |
Fourier transforms |
Problems
22, 23 |
| 5-5 |
Start convolutions of distributions |
|
| 5-7 |
Convolutions |
Problems 24, 25,26 |
| 5-9 |
Solving linear ODEs |
Problem
27 |
| 5-12 |
Schrodinger equation |
Problems
28, 29 (29 due Wed., 28 on Friday) |
| 5-14 |
review |
|
| 5-16 |
Derivation of heat equation |
Problems
30, 31 |
| 5-19 |
Laplace's equation |
Problem
32 (due Friday, the 23rd) |
| 5-21 |
just
problem 32 |
|
| 5-23 |
The wave equation |
Problem
33 |
| 5-28 |
Wave equation |
none
|