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