course information

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

The exam on Wednesday,  April  23, in Bradley 105, from 7:00 to 9:00pm covers up to here.

 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

The final exam will cover the entire course, but will emphasize material covered since the second exam.