Math 316: Partial Differential Equations

Block 5, 2012-2013

Professor: David Brown

Office: TSC 206E

Office Phone: 227-8215

The class will meet each morning in Palmer 125.

I will have office hours or a problem session M-F 1:30 – 3:00 pm.

The textbook is:
Partial Differential Equations with Fourier Series and Boundary Value Problems (2nd ed.),
by Nakhle Asmar.
A student's solutions manual is available on his website: http://www.math.missouri.edu/~nakhle

The course webpage is: http://faculty1.coloradocollege.edu/~dbrown/ma316/index.html

Course Overview

Partial differential equations are among the most widely used mathematical models, playing a central role in physics, biology, chemistry, economics, and many other fields. They are surpisingly difficult to solve, requiring much more mathematical "machinery" than ordinary differential equations. In this class we will learn to formulate and analyze simple PDEs, developing some of the most important techniques of classical mathematical analysis along the way.

         In this class, you will be required to do quite a lot of reading. Each day, I will assign some of the textbook to be read for the following day. Then, in class, I will set aside only 10-15 minutes to go over any questions that you had from the reading. After that, we will move on and I will present new material. You will be responsible for knowing the material covered in all of the assigned readings. At this point, you might have a couple of questions, such as:
        Q: "Why are you doing this to me?"
        A: Several reasons. Most importantly, it is meant to help you develop your ability to learn technical subjects independently. Of course, it is always easier to have someone explain things to us. But that won't always be possible, so the sooner you develop your independence, the better. Secondarily, your reading will allow us to have shorter class meetings; we will meet each morning for two hours instead of three.
        Q: "Seriously, you want me to read a math textbook?"
        A: Yes
        Q: "How?"
        A: Actively. You can't really read and understand mathematics with your feet up or your hands behind your head. You need to have a paper and pencil, take notes as if you were listening to a lecture, and try to fill in missing details. When you get stuck on something, spend five minutes wrestling with it - draw pictures, try examples, etc. If you are still stuck, move on. When you have finished reading the section, go back to the places you got stuck and re-read them. Maybe they will make sense now. If not, write down your questions and bring them to class. This will obviously take some time. I expect that you will be reading for an hour or two each day.
        Q: "What kinds of questions should I ask in class about the readings?"
        A: The more specific, the better. Keep in mind the 15 minute limit for discussing each reading. So, a question like "I didn't really get this whole section, now what?" is not very helpful. Try more focused questions, like "How did they get from equation 3 to equation 4?" or "Why doesn't pointwise convergence imply uniform convergence? Can I see an example?"

Grading

Homework will be due most days at 4:30 pm; please turn it in to the homework boxes in the lobby of the math department. Please make sure that your HW is stapled and that each problem is clearly labeled and readable. Some HW will require computer work (Mathematica). Please save your Mathematica files to your home space, then copy them to the appropriate folder on the course drive. Give your files obvious names like JaneDoeHW1.nb. The assignments will be posted on the class webpage.

There will be two open book take home tests, which will require a combination of pencil-and-paper and computer work. You will each give a 45 minute presentation on a topic we don't cover in class, on the last two days of the block. A list of possible topics is on the web page, and I will discuss this more in class. You will be expected to attend every class and participate actively.

Your grade will be based on the following breakdown: 25% homework, 25% each test, 20% presentation, and 5% class participation.

Honor Code: I expect you to adhere to the CC honor code. This means that you will neither give nor receive assistance on tests. I encourage you to work with others on homework, but when you put your name on something and turn it in, you are claiming to have complete understanding of it.