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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 1, page 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

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

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

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