Methods in Applied Mathematics — Fourier Series and Boundary Value Problems

Course Webpage

We keep a mirror of this page at http://amath.colorado.edu/courses/4350/2011fall/index.html in case of server issues.

Course info

General info

Instructor: M. J. Ablowitz
Email: mark.ablowitz (at) colorado.edu
Office: ECCR 255
Phone: 2-5502
Office Hours: MWF 2–3 pm or by appointment
Classroom: ECCR 155
Text: Applied Partial Differential Equations by R. Haberman, Pearson/Prentice Hall, 4th ed., 2004.
Syllabus: (PDF)

Homework help sessions

Every Thursday from 6 to 7:30 pm in ECCR 1B51.

You can also come to any of the following office hours:

Office Hour Times
  Monday Tuesday Wednesday Thursday Friday
8:30–9:30am Strudevant
(STAD 152)
  Strudevant
(STAD 152)
  Strudevant
(STAD 152)
11am–12pm Baldwin
(ECCR 251)
  Baldwin
(ECCR 251)
  Baldwin
(ECCR 251)
2–3pm Ablowitz
(ECCR 255)
  Ablowitz
(ECCR 255)
  Ablowitz
(ECCR 255)
6–7:30pm       Baldwin
(ECCR 1B51)
 

Graduate teaching assistant

Douglas Baldwin <douglas.baldwin (at) colorado.edu> is responsible for the help sessions, projects, webpage, etc.

Office hours for Douglas are MWF 11am–12pm in ECCR 251.

Benjamin Sturdevant grades homeworks and has office hours MWF 8:30–9:30am in STAD 152.

Graders

Kristina Callaghan and Stetson Zirkelbach.

Grade determination

Exams: 50%; homework: 25%; final report and talk: 25%. (The instructor reserves the right to modify grade distribution for various reasons — such as if it becomes clear that a student has not worked with sufficient independence.)

Homeworks

There will be homework assignments due about every two weeks, usually on Mondays.

You must do the homework regularly. Doing and understanding the homework is extremely important in this class. They are challenging. Do not wait until the last minute!

Homework #1 (PDF) — Solutions (PDF)

Homework #2 (PDF) — Solutions (PDF)

Homework #3 (PDF) — Due October 1, 2012 by 5pm

Exams

Two exams will be given in the evening. The expected dates and times for these evening exams are:

  1. Thursday, October 6, 2011 from 5:30pm to 7pm — Solutions (PDF) — and
  2. Thursday, December 8, 2011 from 5pm to 7pm.

Bring one blue book for Exam 1 and up to three pages of notes. Bring two blue books and up to four pages of notes for Exam 2.

Note that the second exam is not cumulative.

Review

The exam reviews are

  1. Wednesday, 5 October 2011 from 5pm to 6:30pm in ECCR 245 and
  2. Wednesday, 7 December 2011 from 5pm to 6:30pm in ECCR 150.

Project

A written report and talk will be required on a topic relevant to the course.

Experiments

Most projects have experiments that need to be done in the ITLL. All the experiments in the ITLL use equipment that is only available during public hours (8am–5pm, M–F). If you arrange your experiments during Douglas's office hours (11am–noon, MWF), then he may be able to go to the ITLL to give you some suggestions. Douglas will also be available to help with the experiments in the ITLL from 11am to noon on Thursdays (27 October, 3 November, and 10 November 2011) — check the “Media Shack” in the basement of the ITLL if you don't see him.

Report

Please follow this template for the report.

Presentation

Your group will speak for 15 minutes — 5 minutes each for groups of three and 7½ minutes each for groups of two. There are stiff penalties for going over your 15 minutes, so practice your talk several times before you give it to us. We'll then ask you questions for about 5 minutes for a total of 20 minutes.

Be prompt and follow the schedule: there are extremely stiff penalties for showing up late. Wait outside the room until you're asked to speak. You're allowed to listen to any talk that isn't on your topic or that is after your talk.

Project Presentation Schedule
  Monday, 14 November 2011 in ECCR 105
Drum & Guitar  
5:00–5:20pm E. Bergal, C. Bonfanti, A. Floriani
5:20–5:40pm A. Bromwell, A. Russell, B. Schneiders
5:40–6:00pm P. Musso, C. Vockrodt
Break 6:00–6:20pm
Heat Equation  
6:20–6:40pm A. Cullimore, E. Massey, K. Nasiatka
Vibrating Cantilevered Beam  
6:40–7:00pm M. Cullen, N. Husefest, W. Qiu
7:00–7:20pm E. James, D. Stewart, A. Zerr
  Tuesday, 15 November 2011 in ECCR 150
Water Waves  
5:00–5:20pm Y. Chen, T. Lynn, K. Thurimella
5:20–5:40pm K. Epple, C. Knauer, F. Ning
Chladni Patterns  
5:40–6:00pm C. Aicher, R. Young
Break 6:00–6:20pm
Financial Math  
6:20–6:40pm J. Baacke, C. Cookie, Z. Zhang
6:40–7:00pm R. Callahan, Z. Mullen, C. Ryan
7:00–7:20pm N. Look, T. Self, R. Viger
  Wednesday, 16 November 2011 in ECCR 105
Schrödinger’s Equation  
5:00–5:20pm J. Ballentine, E. Petrak, J. Yenzer
5:20–5:40pm M. Beale, B. Harter, S. Lawlor
5:40–6:00pm D. Costlow, T. Myers, N. Truesdale
6:00–6:20pm D. Dundhara, J. Erhard, J. Watson
Other  
6:20–6:40pm Satya
6:40–7:00pm P. Van Blerkom

Topics to be covered

  1. Introduction; review; physical discussion of the heat equation (Ch. 1 — 1 week). 
  2. Method of separation of variables in one-dimension (Ch. 2 — 2 weeks). 
  3. Fourier Series (Ch. 3 — 2 weeks).
  4. Applications (Ch. 4 — 1 week).
  5. Generalized Sturm-Liouville BVPs (Ch. 5 — 3 weeks).
  6. Multi-dimensional BVPs (Ch. 7 — 4 weeks)
  7. Non-homogeneous problems; BVPs in infinite space; Fourier transforms (Ch. 8 & 10 — 2 weeks)

Time periods are approximate.