Partial Differential Equations

Welcome to PDEs! Here we use the tools you’ve learned through years of studying Calculus to studying fascinating phenomena which require more than a single variable:

• How does a string vibrate if you pluck it? (one space variable and one time variable)
• If you leave the metal poker in the fire, how long before the other end is too hot to touch? (one space variable, one time variable)
• How do waves propagate through water? Why do they break as they approach the shore? (2 space variables and one time variable)

These are the classical types of questions which intrigued mathematicians and physicists in the 19^th century. Understanding these phenomena required applying basic physics concepts – and then solving the resulting equations, which contained partial derivatives of the function in question. Hence the name PDEs. This semester, we will delve into the methods they used and the theory behind those methods.

Class Philosophy: One learns math by doing it, not by watching other people do it. Luckily in a class this small, we’ll all be able to do lots of math. You will be required to participate actively during class, and work very hard outside of it. For most class meetings, you’ll have a reading assignment. In class, we’ll discuss the readings, working through any difficulties you have. From time to time, we’ll also have a set of problems to do. Generally, you’ll be responsible for presenting those problems in class.

Text: Partial Differential Equations: An Introduction by Walter Strauss.

Office Hours:

Monday	2:40-3:40
Wednesday	10:40-11:40
Thursday	12:00-1:00

As you probably know, I’m around a lot at other times as well. If you’d like to meet, just drop by – or drop me an email.

My Contact Info:

Phone: x4433 Email: dtkung at smcm.edu Office: 175 Schaefer Hall

Grades: To some extent, we can decide as a class how each of you will earn your grade. There will be some sort of comprehensive examination at the end of the semester (either a take-home final or an oral exam). The rest of your grade will come from your semester project, class participation, a mid-term take-home exam, and anything else we decide on.

Semester Project: Everyone will be required to complete a substantial project this semester. This could take the form of studying an additional topic, writing up notes, and explaining that topic to the rest of the class. Or, you could use one of the computer mathematics systems to approximate a solution to a particularly nasty PDE. Choice of projects will be up to you – so keep your eyes peeled for ideas. I would be especially interested in projects which could be hung up in the Math hallway (across from the fishbowl).

Notebooks: You will need to get a notebook for this course. When you read the textbook, do so with your notebook open. When he does an example, do the example - making sure you write down the steps he skips. When there are things you don't understand, write them in your notebook and bring it to class. By the end of the semester, you will have a great deal of knowledge of PDEs in your notebook and, more importantly, in your head.