Announcements:
Final class on Monday May 7. We will meet for the final time on Monday May 7 from 5:55pm to 7:10pm to finish up the last bit of Wednesday's lecture and also to answer any questions you might have about the course or about the final exam.
Final Exam. The final exam for this course will be given on Wednesday May 9, 730-1015 in the same room where we have class. The final exam will cover Sections 2.1-2.5, 3.1, 5.1, 5.3 of Stein and Shakarchi. The exam will be closed book and will emphasize computational problems similar to the Exercises in the book. You should also understand the proofs of some basic results including results on approximation using good kernels, orthogonality, and Poisson summation.
Deadlines. Please be aware of all relevant deadlines. Details may be found here.
Mini-Projects. Below are a list of particularly challenging problems from the Stein and Shakarchi text. You are to choose one of these projects, solve the problem in detail, and hand in a neat write-up by Wednesday March 7. Here is the list of "mini-projects" that you are to choose from.
Project #1. Exercises #7 and #8, page 60.
Project #2. Exercises #14 and #17, page 62-63.
Project #3. Exercise #9, page 90.
Project #4. Exercise #11, page 90.
Project #5. Exercise #15, page 92.
Project #6. Exercise #16, page 92.
Project #7. Exercise #4, page 126
Project #8. Exercise #20, page 94.
Homework:
Homework #1 (due 01-31-07) pdf, Homework 1 solutions.
Homework #2 (due 02-07-07) pdf, Homework 2 solutions.
Homework #3 (due 02-21-07) #11, 12, and 15, p. 61-63 of Stein and Shakarchi, also prove Proposition 3.1 (iv) of Stein and Shakarchi, p. 45. Homework 3 solutions.
Homework #4 (due 02-28-07) #10, p. 27, #16, p. 63, #18, p. 64, Problem 1.46 from D. Kammler (reference below). Homework 4 solutions.
Homework #5 (due 03-21-07) pdf, Homework 5 solutions.
Homework #6 (due 03-28-07) #2, #3(a), #4, p. 161-162 of Stein and Shakarchi, Homework 6 solutions.
Homework #7 (due 04-11-07) #9, #14, #17, #21, p. 163-167 Homework 7 solutions.
Homework #8 (due 04-18-07) #8, p. 163 (Hint: You may use the fact that if f(x) is continuous and of moderate decrease and if its Fourier transform vanishes everywhere, then f(x) is identically zero), #15, p. 165, Problem 7, p. 173 (parts (a), (b), and (c) only) of Stein and Shakarchi, and this problem. Homework 8 solutions.
Homework #9 (due 04-25-07) #1, #4, p. 207-208, #12, p. 211 (Do it for the RT on R^2 as we defined in class, rather than for R^3 as in the exercise. It is easier in R^2), Problem 6, p. 216of Stein and Shakarchi Homework 9 solutions.
MATLAB demos:
Useful references:
Fourier Analysis: An Introduction, Elias M. Stein and Rami Shakarchi, Princeton U. Press (2003), ISBN 0-691-11384-X
The Fourier Transform and its Applications, Ronald Bracewell, McGraw-Hill 2000. ISBN 0-07-303938-1.
Fourier Analysis and Boundary Value Problems, James Brown and Ruel Churchill (6th edition), McGraw-Hill 2000. ISBN 0-07-232570-4.
Fourier Analysis, James Walker, Oxford University Press 1988. ISBN 0-19-504300-6.
Fourier Analysis, T. W. Korner, Cambridge University Press 1988. ISBN 0-521-38991-7.
Exercises for Fourier Analysis, T. W. Korner, Cambridge University Press 1993. ISBN 0-521-43849-7.
Harmonic Analysis and Applications, John Benedetto, CRC Press 1996. ISBN 0-8493-7879-6.
Fourier Analysis and its Applications, G. B. Folland, Brooks/Cole 1992.
A First Course in Fourier Analysis, D. Kammler, Prentice Hall 2000
Useful links:
David Kammler's webpage.
Some help with Matlab.
To contact me, send email to dwalnut@gmu.edu