# Math 4163 (Intro. to Partial Differential Equations)

# Spring 2012

** Instructor: **

John Albert
Office: PHSC 1004, Ext. 5-3782.
Office hours: Tuesday 2:30-3:30; Thursday 10:30-11:30; Friday 1:30-2:30 (or by appointment)
E-mail: jalbert@ou.edu

## Information

## Homework

### Assignment 1 (due Mon, Jan 30)

2.3.2(a,d,e), 2.3.3(a,b), 2.3.6
### Assignment 2 (due Mon, Feb 6)

problems 3.2(a,b) and 3.4 from the supplementary problem set.
2.4.1(a), 2.5.1(a,b)
### Assignment 3 (due Wed, Feb 29)

problems 4.1, 4.3, and 4.4 from the supplementary problem set.
2.5.5(a,c)
### Assignment 4 (due Wed, Mar 7)

problems 1.5(a,b,c) from the supplementary problem set.
3.2.1(b,c,e,f)
### Assignment 5 (due Wed, Mar 15)

problems 6.3, 6.4, 6.6 from the supplementary problem set.
5.3.5, 5.3.6
### Assignment 6 (due Wed, Apr 11)

7.3.1(a), 7.3.2(b), 7.7.2(a), 7.7.9(c)
### Assignment 7 (due Fri, Apr 20)

problems 8.1, 8.2, 8.3, 8.4 from the supplementary problem set.
(The following is an informal assignment, nothing to turn in.) Go to the Wikipedia article on
"Vibrations of a Circular Drum" and look at
the animations at the bottom of the page. Explain to yourself why each vibration looks as it does. Based on what
you know about Bessel functions, and the formula for the separated solutions of the wave equation on a disk
you should be able to predict what the next modes look like: modes u_04 or u_31, for example.
### Assignment 8 (due Wed, May 2)

10.4.3(a), 10.4.4(a)

## Exams

### Exam 1: Fri., Feb. 17

### Exam 2: Fri., March 30

### Exam 3: Mon., April 30

### Final Exam: Friday, May 11 from 8:00 am to 10:00 am in PHSC 228

## Links

Here is a nice Java application that gives you an intuitive feel for how
Fourier series work. I found the "wave game" kind of hard to stop playing.
The Well-tempered Timpani is a website that gives a thorough introductory explanation
of the acoustic behavior of a circular drumhead. If you look at the section titled "Vibrating circular membrane" you'll find an account of
which of the basic modes (separated solutions) of the wave equation on a disk are most important for the sound of a timpani. Interestingly,
contrary to what happens with a string or a wind instrument, the mode with the lowest or fundamental frequency is not very important for the
sound; rather the sound is mainly comprised of a set of a few modes with higher frequencies.