Spring 2013

The following are

- The text by S. Farlow is a very inexpensive text from Dover (about $11), and is a slightly different take on the PDEs we cover in class.
- This is a text in numerical methods from Cleve Moler (a founder of Matlab), and he has a good chapter on Fourier analysis with a nice introductory example.

- Week 1: The homework for this week will be due at the beginning
of class on Wednesday, Jan 23 (No classes on Monday)
- Homework Set 1 (HW to turn in: Exercise 6 on the handout, and 1(a,b) in Section 1.2).
- Solutions to HW 1
- Homework Set 2 (HW to turn in: Exercise 2 on the handout and 1.3.3 in the text).
- Solutions to HW 2
- Homework Set 3: Section 1.4, 1.4.1(a-h), 1.4.2, 1.4.7, 1.4.11* (Not due on Wed, due with the set after that).

- Week 2: Homework from Set 1 and 2 (starred
problems) are due at the beginning of class on Wednesday this week.
- No classes.
- Wednesday class: Here is some review of vector calculus and the homework for today (The handout was updated on Friday, Jan 25 to correct a couple of typos and to clarify a bit).
- Homework Solutions, Section 1.5
- Section 2.2: 2.2.1-2.2.5 (Turn in only 2.2.2).
- Homework Solutions, Section 2.2

- Week 3
- Section 2.3, Day 1: 2.3.1
- Wednesday:
- Extra Practice Problems
- Solutions to Extra Practice
- Section 2.3, Day 2: 2.3.2(a,e*), 2.3.3(b,c), 2.3.4
- Homework Solutions, 2.3

- Friday: Finish 2.3, look at Maple, start 2.4. Example of Maple output

- Week 4
- Section 2.4: 1-4, 6(*). You should also work on the Extra Practice Problems
- Section 2.4, continued.
- Section 2.5: 1(a,f), 2, 3, 5(a), 7(a), 10.

- Week 5
- Finish up 2.5 (See Friday's link for solutions).
- Catch up/Review
- Exam 1 (Feb 15)

- Week 6: Chapter 3 (Fourier Series)
- Wednesday:
- How does a cochlear implant work? (Optional)
- Overhead slide for Section 3.1
- Homework Assignment, 3.1-3.2. The starred problems are due on Wednesday, Feb 27.

- Friday:
- Homework assigned today: Section 3.3: 1(a,c,d), 2(c), 5, 8, 18*
- Overhead slide, Gibbs

- Wednesday:
- Week 7
- Monday: Finished 3.3, discussed Gibbs. Nothing new assigned.
- Wednesday: Sections 3.4-3.6.

Homework handout.

Solving a non-homogeneous PDE using Eigenfunctions (finishes the example from class). - Friday: Discrete Fourier Transforms.
- Notes about the Complex and Discrete Fourier Series
- Matlab output for discretization problem.
- Matlab output for analyzing a known signal
- Matlab output for analyzing sunspot data
- Introduction to Matlab
- HOMEWORK: Log into the Math computer lab, find the
program Matlab, and work through the introduction.

Here is a video series produced by Matlab to get you started. - Example Matlab script 1 (Discretization)
- Example Matlab script 2 (Analyzing a known function)
- Example Matlab script 3 (sunspot data)

- Week 8
- Monday: Sections 4.1-4.2, Exercise 4.2.1(*), 4.2.5.

Overhead slide for Wave Equation setup - Wednesday: Sections 4.4-4.5.

Homework:- 4.4: 1(*), 5, 7

Here is the website with nice Java applets, go to "Loaded String Applet" to play with the normal modes.

- 4.4: 1(*), 5, 7
- Friday: 4.4, continued. For HW, see the Maple Lab.
- Worked Exercises and Maple Scripts
- Maple Lab:
- Maple Lab for Ch 4 (with Homework Questions)
- Example Maple File for last exercise. This solves Exercise 4.4.7.

- Monday: Sections 4.1-4.2, Exercise 4.2.1(*), 4.2.5.
- Week 9 after break. We're a couple
of days behind in the schedule.
- Monday, 3/25: Sections 5.1-5.3.

Homework: Add 4.4.7, 8, 9. In Section 5.3, do 2, 3, 5, 7*, 8*, 9. - Wednesday, 3/27: Turn in HW from 4.2, 4.4.

Read sections 5.3, 5.4, start 5.5.

Homework: Work on the Maple lab from before break. (Due: Monday, but do try to do it earlier so you have time for questions).

Homework for Section 5.4: 5.4.1, 2, 3, 5* - Friday, 3/29: Sections 5.4, 5.5

Homework for Section 5.5: 1(b,c), 7*, 8

- Monday, 3/25: Sections 5.1-5.3.
- Week 10: April 1-5
- Monday: Finish 5.5/5.6

Homework: 5.6, 1 and 2 (NOTE: For 5.6.2, do not use trial functions). - Wednesday: Sections 5.7/5.8

Homework: 5.7, 1 and 5.8: 3, 5 - Friday: Review/Catch up

- Monday: Finish 5.5/5.6
- Week 11: April 8-12
- Monday: Exam 2
- Wednesday: Sections 5.8 and 7.3. Homework:

5.8: 3, 7*, 9, 11

7.3: 1(b)*, 2, 3, 5, 7(a) - Friday: Sections 7.3-7.4

Maple file to illustrate some interesting phenomena with two dimensional eigenfunctions on a rectangular domain.

Homework: 7.4 1(a,b), 2.

Extra Practice problems (Also do these for next Wed)

- Week 12: April 15-19
- Monday: Sections 7.5-7.6

Homework: 7.5: 4*, 8 and 7.6: 1, 2(a), 4* (Not due this week) - Wed: Section 7.6, continued.

Vibrational Modes of a Circular Membrane - Fri: Section 7.7

Homework: 1, 3, 7*, 12

Animated GIFs:

- Monday: Sections 7.5-7.6
- Week 13: April 22-26
- Monday: Sections 7.8-7.9
- Homework problems
- Sect07_8Basis.mw This file illustrates the use of the Bessel functions as a series.
- Sect07_8LargeAndSmallApp.mw This file illustrates the large and small value approximations for the Bessel function.
- Sect07_8Zeros.mw Short script file looking at the approximate zeros of the Bessel function.
- Sect07_8nodalcurves.mw This file illustrates how to find and plot nodal curves (Compare to Fig 7.8.3).
- Sect07_8Modes.mw Short animation file.

- Wed: Homework: 7.8: 1, 2, 5(d,f), 7. 7.9: 1(a,b), 2(a,b), 5*
- Fri: Homework: 8.2: 1(a,d,e), 2(b), 3*. 8.3: 1(c), 2, 3. Handout below.

Extra practice, Ch 8 (nothing due here, but you should work through it)

Worked Examples for 8.1-8.3

- Monday: Sections 7.8-7.9
- Week 14: April 29-May 3
- Monday: Section 10.2, 1
- Wednesday: Section 10.3: See HW sheet from Friday.
- Friday: Section 10.4

- Exam 1 Materials
- Exam 1 Review Problems Added Feb 14: You can skip 1(d).
- Solutions to the Review Problems
- Extra Practice Problem: Solve Laplace's Equation on an Annulus (with the full solution).
- Exam 2 Materials
- Homework Solutions:
- Overview of the material we've covered
- Exam Review Sheet
- Exam Review Solutions
- Final Exam Materials
- Homework Solutions:
- Section 5.8
- Sections 7.3 and 7.4
- Extra Practice (turned in, for solutions see HW set 8)
- Homework Set 8
- Section 7.5 and 7.6
- Section 7.7
- Extra Practice (Maple)
- Homework Set 9
- Sections 7.8 and 7.9
- Sections 8.2 and 8.3
- Homework Set 10
- Extra Practice, Chapter 8 handout solutions (Updated to correct 1(d))
- Sections 10.1-10.4 (on handout)

- New Table for Exam
- Topics for the exam
- Review Questions: Typos, Problem 3 (PDE should have +x instead of +u), and Problem 8 (Last two BCs should be derivatives in z). The review doesn't touch that much in Chapter 10, so be sure to look over the homework for Ch 10 as well!
- Solutions to the Review.