Fourier Series and Boundary Value Problems
Fall 2008, Math 136 (http://www.math.hmc.edu/math136) (Muddshots)
TTh 2:45-4:00 pm, Beckman B134
Prof. Darryl Yong (dyong@hmc.edu), Olin 1265, x72844
Office Hours: Th 9:30-11am, 1-2:30pm (open door policy)
Grader: Jason Wyman

Course description

Objective: By the end of this course, I hope that you will

Topics covered (tentative): Complex arithmetic, complex functions, multi-valued functions and branch cuts, Cauchy-Riemann equations, Cauchy's theorem, analytic functions, singularities, residue calculus, principle value integrals, Liouville's Theorem, Picard's Theorem, conformal mapping, integral transforms (including Laplace transforms), analytic continuation, asymptotic evaluation of integrals, Riemann-Hilbert problems.

Course Materials

Lecture notes are available to students in this class accessing this web site using a computer on the Claremont Colleges.

Week Tue Thu Fri
1 9/2
Complex Arithmetic (group work)		 9/4
Complex functions
Exponential, Logarithm fn		 9/5
Problem Set 1 due
(solutions)
2 9/9
 9/11
 9/12
Problem Set 2 due
3 9/16
 9/18
 9/19
4 9/23
 9/25
 9/26
5 9/30
 10/2
 10/3
6 10/7
 10/9
 10/10
7 10/14
 10/16
 10/17
8 10/21
(Fall Break)		 10/23
 10/24
9 10/28
 10/30
 10/31
10 11/4
 11/6
 11/7
11 11/11
 11/13
 11/14
12 11/18
 11/20
(Thanksgiving)		 11/21
(Thanksgiving)
13 11/25
 11/27
 11/28
14 12/2
 12/4
 12/5
15 12/9
 12/11
 12/12

There is no required textbook for this course, but you may find some of these materials helpful. I own these and many more textbooks and am happy to recommend some to you based on your preferences.

Other interesting links to material related to complex variables on the internet:

Grading

Class presentation 15%
Final Exam 35%
Homework 50%

Coursework

Most of your learning will occur while completing your homework assignments, so take them seriously, and complete them thoroughly. Your homework should show clearly your solution processes. I encourage you to describe your solution process in words. Poor presentation may result in loss of credit.

No late homeworks asignments will be accepted except for family or medical emergencies. Your lowest homework grade will be dropped.

You are encouraged to work cooperatively on your homework assignments with your classmates. However, every student MUST write up his/her own homework separately. In addition, you must cite any sources of help that you use. If you work with one of your classmates on a problem, be sure to acknowledge that person in your homework write-up; if you use any textbooks or websites, acknowledge that too. Harvey Mudd's honor code is in effect for all students in this course.

I encourage you to use a computer algebra system (CAS) such as Mathematica on your homework, when it is appropriate. The Claremont Consortium has a site-wide license for Mathematica. To install it on your personal computer, look in the Dist-Software directory on charlie.hmc.edu. Try this Google search to look for Mathematica tutorials.

In addition to the homework assignments and exams that you will turn in for this course, you will also be responsible for presenting some topic in complex analysis to the class. You and a partner will be able to choose from a list of potential topics. I will work with you to prepare your presentation.

<dyong@hmc.edu> Last modified: Thu Sep 04 18:13:26 Pacific Daylight Time 2008