__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.