Syllabus

Topics. The basic theory of Fourier series and Fourier integrals including different types of convergence. Applications to certain differential equations.
Discrete Fourier transforms, including fast implementations and some finite fields. Applications to signal processing and error correcting codes.

Prerequisites. Math 233 (Calculus III) and Math 309 (Matrix Algebra).

Time. Classes meet Mondays, Wednesdays, and Fridays, 10:00 am to 11:00 am, in Eads Hall, room 208.

Text. The lectures will follow Hugh L. Montgomery's textbook Early Fourier Analysis, first edition, ISBN 978-1-4704-1560-0, American Mathematical Society, 2015.

Homework. You are encouraged to collaborate on homework and to work additional exercises from the indicated problem sections, although the homework grade will be based only on the exercises listed below. Please return your solutions to the instructor by the end of class. Problem sets will be assigned as follows:

HW #1, due Fri, Sep 8 (Page images: ss.1.1, ss.1.2, ss.1.3, ss.1.4ex1, ss.1.4ex5, ss.1.4ex7) HW #2, due Fri, Sep 15 HW #3, due Fri, Sep 22 HW #4, due Fri, Sep 29 HW #5, due Fri, Oct 6 HW #6, due Fri, Oct 13	HW #7, due Fri, Oct 27 HW #8, due Fri, Nov 3 HW #9, due Fri, Nov 10 HW #10, due Fri, Nov 17 HW #11, due Fri, Dec 1 HW #12, due Fri, Dec 8 (last class)

Solutions are due at the end of class on the due date. Late homework will not be accepted. The problems will often require a complete proof. The homework will be judged for correctness and clarity. If you use a computer for solution, please include your well-documented computer code which will be judged in part for its understandability. Please print and submit: (i) the code, with a comment for every line, (ii) the input you gave it, and (iii) the output it produced, for at least one example run.

Tests. There will be one midterm examination in class on Friday, October 20th, 2017. There will be one cumulative take-home final examination emphasizing the remaining material, due on Monday, December 18th, 2017 by 1:00 pm in my office, room 105a, Cupples I Hall.

Grading. One score will be assigned for homework, one for the midterm examination, and one for the final examination. These three will contribute in respective shares of HW 50%, MT 20%, and FE 30% to the course score. Letter grades, computed from the course score class average and standard deviation, will be at least the following:

Computing. Students are encouraged to use computers for both symbolic and numerical computations.

Office Hours. See me in Cupples I, room 105a, Mondays and Wednesdays, 11am-noon, or by appointment.