Course:
Partial Differential Equations
MATH 302
MWF 3:00-3:50 Thompson 316
Tu 3:30-4:20 Thompson 228
Fall 2002

Instructor:
Martin Jackson
Office: Thompson 325
Phone: 879-3567
E-mail: martinj@ups.edu

Course Web Pages

Web pages for this course are located at

www.math.ups.edu/~martinj/courses/fall2002/m302/m302.html

You can get to this page by following links at www.math.ups.edu/~martinj. Assignments will be listed and class handouts will be available to download as PDF files. Scores for assignments and exams will be posted by code name for those who wish. If you want your scores to be posted, send me an e-mail with the code name you want to use.

Course Overview and Text

The central theme for this course is analyzing partial differential equations, especially those which arise in modeling physical phenomena. After successfully completing this course, a student should be able to

• compute a Fourier series for a function and analyze the convergence issues for that Fourier series;
• solve partial differential equation problems using separation of variables and Fourier series;
• understand the physical relevance of the prototypical partial differential equations: the heat equation, the wave equation, and Laplace's equation; and
• formulate, solve, and interpret partial differential equations problems that model a variety of physical phenomena.

Grading, Coursework, and Policies

In class, we will discuss new material, respond to questions from reading the text, and work through assigned problems on which there are difficulties. When we discuss new material, the focus will be on ``the big picture.'' That is, we will look at new ideas in their simplest form and how these ideas fit together. Often, we will not consider details and variations in depth during a first pass through new material. Your mastery of the details will begin outside of class with a careful reading of the text and work on the assigned problems. We will address the details by responding to questions on the reading and problems that you bring to class. You are expected to participate in class by being present (and alert), by responding to questions I pose, and by asking the questions that you have.

Outside of class, you should read the relevant sections of the text carefully. This will generally include working through the reasoning of arguments and filling in steps that are omitted in calculations. You should keep a list of specific questions from the reading and find answers to those questions either in class, with me outside of class, or with study partners.

The text is also a source of problems that are essential in building understanding and skill. I will assign homework problems from the textbook on which I expect you to spend considerable time and effort. I will also designate problems to be collected and evaluated. For these problems, you should write up careful solutions using the standards of proper technical writing. You should not get in the habit of focusing only on the problems designated to be turned in. You will need to do many more problems in order to become facile with the concepts, techniques, and applications.

Solving a typical partial differential equation problem generally involves breaking the problem down into several smaller problems, solving each of the smaller problems, and then putting the pieces together to get a full solution to the original problem. Some of the smaller problems involve detailed analysis. You will need to learn how to organize your work and you will need to take care of the details. Because any one problem can be quite long, you will need to learn more from each problem.

Many partial differential equations problems arise in the context of modeling physical phenomena. An important part of the modeling process is interpreting solutions in terms of the physical phenomena. To do so, it is often useful to use appropriate graphing tools. I will introduce you to Mathematica but you are welcome to use any graphing tool with equivalent capabilities.

We will have three exams during the semester. These will be a combination of in-class and take-home. I will give you at least one week notice before any in-class exam. The final exam is scheduled for Tuesday, December 17 from 8:00-10:00 am. The final exam may also include a take-home component.

To determine course grades, I calculate a total course score with homework problems weighted at 40% and exams (including the final) weighted at 60%. I assign a preliminary course grade based on an objective standard (ususally 93.0-100% for an A, 90.0-92.9% for an A-, 87.0-89.9% for a B+, 83.0-86.9% for a B, etc.). I then look at each student's performance subjectively. Occasionally I will assign a course grade that is higher than the objective standard. For example, if a student has a grade of B according to the objective standard but has shown steady improvement, I might assign a course grade of B+.

Office Hours

I am available in my office for help several hours each day. I am often in my office during the day in hours at which I do not have a scheduled class, meeting, or other activity. My schedule is available here.. To be (almost) guaranteed that I will be in, come during one of the hours labeled as an ``office hour.'' You can also call, send e-mail, or stop me after class to schedule an appointment for a specific time.