APPM 5430

Methods in Applied Mathematics — Applications of Complex Variables

Course Webpage

Go to https://sites.google.com/site/appm5430/ for the latest course info.

Course info

Instructor: M. J. Ablowitz
Email: mark.ablowitz (at) colorado.edu
Office: ECCR 255
Phone: 2-5502
Office Hours: MW 3:30–4:30 pm or by appointment
Class: MW 4:30–5:45pm in ECCR 110
Text: Complex Variables: Introduction and Applications by M. J. Ablowitz and A. S. Fokas, Cambridge University Press, 2nd ed., 2003. Check errata for typos/corrections on MJA's web page.
Syllabus: PDF

Homeworks

There will be homework assignments due about every two weeks. The homeworks must be placed in MJA's mailbox by 5pm on the day they're due.

Homework #1 — Due Friday, September 3, 2010 — PDF
Note: In the additional problem part (b), ?₂ should be between p/2 and -3p/2.

Homework #2 — Due Monday, September 20, 2010 — PDF

Homework #3 — Due Monday, October 4, 2010 — PDF

Homework #4 — Due Monday, October 25, 2010 — PDF – Revised

Homework #5 — Due Wednesday, November 10, 2010 — PDF

Homework #6 — Due Friday, December 3, 2010 by 5pm (no late HW will be accepted) — PDF

Course lecture

The undergrad. students will each give a 15 min. portion of a course lecture early in the semester and the grad. students will each give a 20 min. portion of three course lectures later in the semester. These lectures will occur during the semester and will be 'woven' into the course lectures. The instructor will likely make clarifying comments during the lecture.

Schedule

Wednesday, Oct 13
Section 4.2: Jordan's lemma (prove one case and discuss all cases)
Examples 4.2.3 (or equivalent type of example), 4.2.5, 4.2.8, and 4.2.9
Betrand, Carpenter, Crawford, and Zhang — 15 min each = 60 min

Monday, Oct 18 — Section 4.3 — DB
Wednesday, Oct 20 — No Class

Monday, Oct 25
Section 4.4 and begin 4.5: Introduction to Fourier transform
Davis, Guinn, Hao, and Larremore — 20 min each = 80 min

Wednesday Oct 27
Sections 4.5–4.6 (start where previous students left off): Fourier and Laplace transforms, their properties and applications
Ashsar, Lenzini, Rose — 25 min each = 75 min

Monday Nov 8
Section 5.6: Schwarz–Chrostoffel transform
Satkaukas, Schauf, Schmidt, Sen — 20 min each = 80 min

Project

A project will be required on a topic relevant to the course. The project will consist of a written report and a 30 min. talk plus 5 min. of questions. The projects will be presented at the end of the course. At a mid-point of the semester a one page description of the topic you plan to study will be required.

List of potential projects (PDF).
Template for the Project Report (PDF)

Please turn in a 1-page project proposal by Oct. 18. If you're an undergrad, then you can do the project as a group of 2 or 3 undergrads.

Graders

Douglas Baldwin — douglas.baldwin (at) colorado.edu
Sean Nixon — sean.nixon (at) colorado.edu

Douglas and Sean may be willing to give 'hints' on the HWs.
Douglas's office hours are in ECCR 251 whenever he's in the office — the best times are 3pm to 6pm and 10am to 1pm.
Sean's office hours are also in ECCR 251 and are on Tuesdays between noon and 3pm or anytime after 3pm that Sean's in the office.