MATH 328: Introduction to Partial Differential Equations

Spring 2006

Description and goals: This is an introductory course in partial differential equations with emphasis on the role of Fourier series and integrals in solving boundary value problems of mathematical physics. The primary goal here is to introduce students to a number of useful techniques for solving classical partial differential equations. However, the course will be far from a "handbook" approach to the subject. Theoretical aspects and relevant mathematical ideas will be discussed when appropriate.

Texts

Syllabus

Homework

A quick Maple tutorial

Announcements:

• 5/31: Check your COURSE GRADE.

• 5/23: Final Exam. Make sure you return your work to Kiely 421 (our lecture room) on Friday 5/26 at 1:15. Be there on time.

• 4/11: Here are suggestions for the short project.

• 3/25: You can now check your grades as of today.

• 3/24: Midterm Solutions.

• 3/21: Midterm Problems.

• 3/6: Check out the following maple animations which illustrate the solutions of the 1-dimensional heat equation along a finite rod, with three different boundary conditions. Click on your browser's stop button to freeze the frame; refresh the page to start over.
  Example 1, Example 2, Example 3, Example 4.

• 2/14: Here is a copy of the Fourier series Maple worksheet that was used in today's lecture. Feel free to download and experiment with.

• 2/7: The example of half-range expansions we discussed in today's lecture: An even extension giving a cosine series, and an odd extension giving a sine series.

• 2/6: The recommended text is now available at the bookstore.

• 2/2: The two examples of Fourier series we discussed in today's lecture: A rectangular pulse and a triangular pulse.

• 1/26: Welcome!

General Information and Ground Rules:

• Class lecture meetings are Tuesdays and Thursdays 1:40 - 2:55 in Kiely 421.

• Homework is posted here every Friday and is due at the next Thursday lecture. Doing homework is an absolutely essential part of this course. You are encouraged to work in groups and discuss the problems with each other, but the work that you hand in must be your own write up. Please note that late homework will never be accepted.
  
  You will be encouraged to use packages such as Maple or Mathematica. I will give you instructions on what to do when the time comes.

• A Project is another requirement for this course. You will be given a list of topics and supplementary reading material for the project. Presentations are not required, but you are expected to write a short expository paper (up to 5 pages) on the topic of your choice.

• The course grade will be based on the following scheme:
  
  

  Project	Homework	Midterm	Final
  10%	20%	30%	40%

• The exams are scheduled as follows:
  
  

  Midterm	Final
  Thursday March 23	Friday May 26

• The prerequisite for this course is MATH 223. If you have not taken MATH 223 or have not passed it successfully, you should not be enrolled in this class. Please go to the Math Department office (Kiely 237) and seek advice.

• If the midterm is missed because of a documented illness or valid emergency, the course grade will be determined on the basis of the other work done during the semester. A midterm missed for other reasons will count as a failure.

• At the end of the semester, everyone who has not withdrawn from the class will receive a grade. Incompletes will never be given to avoid F's.

Saeed Zakeri