Office Hours:
Tuesday 1:00-3:00, Thursday 1:00-3:00

Lecture:
TTh: 9:00-10:20, Rockefeller Library A9

**Textbooks: ***Introduction to Pertrubation Methods*, Mark H. Holmes, 2013

Course Handouts and Useful
Websites:

1. Syllabus: (.pdf)

2. Homework Policy (.pdf)

3.** Latex Templates**

Lecture Notes:

1. Notes 1 (.pdf)

2. Notes 2 (.pdf)

3. Notes 3 (.pdf)

4. Notes 4 (.pdf)

5. Notes 5 (.pdf)

6. Notes 6 (.pdf)

7. Notes 7 (.pdf)

Mathematica Notebooks:

1. Examples from Lecture 1.

2. Example of matched asymptotic expansion.

3. Method of multiple scales.

Homework Assignments:

1. Homework Assignment #1 (.pdf) (Due 9/12/14)

2. Homework Assignment #2 (.pdf) (Due 9/19/14)

3. Homework Assignment #3 (.pdf) (Due 10/09/14)

4. Homework Assignment #4 (.pdf) (Due 10/24/14)

5. Homework Assignment #5 (.pdf) (Due 11/20/14)

Potential Projects:

There are two types of recomended projects: extensions of book problems and general term papers on canonical partial differential equations. Below is a list of interesting book problems that could form the starting point of a project.

Book Projects:

1. Quantum jumps in ion trapping experiments: pg. 148 #3.8

2. Population growth and the logistic equation: pg. 157 #3.15

3. Relativistic motion of planets (i.e. how Einsteain proved he is correct): pg. 163 #3.18

4. Collective motion: pg. 205 #3.60

5. Sound propagation in fluid (i.e. how waves communicate): pg. 206 #3.63

6. Wave propagation in the spine: pg. 207 #3.67

7. Time independent Shrodinger equation: pg. 246 #4.18

8. Quantum tunneling: pg. 247 #4.19

9. Motion of planetary rings: pg. 248 #4.2

10. Diffusion of a disease: pg. 315 #5.10

11. Explosions: pg. 105 #2.41

12. Steady state air flow over a wing: pg. 130 #2.62

If you would like to do a broader term paper on canonical partial differential equations the
below list of equations would make for excellent projects. Good starting points are of course Wikepedia but also the books Applied Asymptotic Analysis by Peter Miller and Pattern Formation and Dynamics in Nonequilibrium Systems by Cross and Greenside are excellent references. Also, talke to me and I can help point you in the right direction.

Canonical PDE Projects:

1. Korteweg - de Vries (shallow water wave equations)

2. Nonlinear Schrodinger equation (nonlinear optics)

3. sine-Gordon equation (coupled oscillators and Josephson junctions)

4. Ginzberg - Landau equation (superconductivity)

5. Swift-Hohenberg equation (pattern forming systems, like zebras)

6. Boussinesq equation (long water waves)

7. Fisher's equation (gene propagation)

8. FitzHugh - Nagumo equation (activation spikes in neurons)