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 17Problem 18 and optional (due 5-6):  Problem 19
5-1 More distributions Problems 20,  21solution 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