course information

Mathematics 33                Spring 2002           Syllabus

Date             Topics                                                                                 Homework

 3-27 Review PDEs Problem 1, solving the heat equation. 3-29 More review,  Gibbs' phenomenon Problems 2,3(a), Gibbs' phenomenon for a step function.

 4-1 Gibbs' phenomenon Problem 3b,c,d 4-3 Guest lecture Problem 4,  Heat flow smooths. 4-5 Fourier series, exponential form Problem 5   solution

 4-8 Fourier sine transform Problems 6, 7 4-10 Fourier transform Problem 8, heat flow in a semi-infinite rod, and p. 61: 1.1a,b;  p. 67: 1.16(a) 4-12 Transforming PDEs p. 72: 1.20 and Problem 9

 4-15 Convolutions Problem 10, and p. 116: 2.1c, 2.3abc;   (optional: p. 122:  2.28) 4-17 Properties of Fourier transforms          The exam covers up to here. Problems 11, 12,  and p. 156:  3.2e,j;  p. 157:  3.5d,e,f,h 4-19 More properties p. 156: 3.2(f);  p. 158:  3.11 (Use p. A-3 to find the known  Fourier transforms of d and f.);  p. 161: 3.20a,b,e,f

exam: Monday, the 22nd, 6:30-8:00, Bradley 102.

 4-22 Review p. 122: 2.26(a) 4-24 More properties, applications Problems 13, 14,  and p.157: 3.4(f), 3.6(a);  p. 161: 3.20(c),(d) 4-26 Generalized functions or distributions Problems 15, 16, 17,  Just find the first derivative in Problem 17 for Monday.

 4-29 More distributions Finish Problem 17,  Problem 18 and optional (due 5-6):  Problem 19 5-1 More distributions Problems 20,  21,  solution to 21(b) 5-3 Fourier transforms of distributions Problem 22(a)

 5-6 More Fourier transforms, convolutions Problem 22(b), 23, 24 5-8 More convolutions of distributions Problems 25, 26 5-10 Free Schrodinger equation Problems 27, 28

exam: Wednesday, the 15th, 6:30-8:00, Bradley 102.    Solutions: page 1page 2

 5-13 More Schrodinger Problems 29 5-15 review Problems 30 5-17 Laplace's equation Problems 31

 5-20 Uniqueness of solutions to Laplace's equation Problem 32 5-22 The wave equation Problem 33 5-24 Week solutions to PDEs Problem 34

 5-29 Solving the wave equation No homework