course information


 

    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

Solutions to the second test.

5-24
Laplace's equation
Problem 35
5-26


5-28
The wave equation
Problem 36  Week 9 homework solutions.


6-2

no homework