226 Gray Hall

michaelr at american {dot} edu

Office hours: Monday, Tuesday, Thursday 10am-noon, or by appointment (please contact me 24 hours in advance to make arrangements)

My research website http://www.drmichaelrobinson.net/

Feel free to contact me with any questions (course-related or not)

Homework assignments

Course schedule

Concerning programming in this course

Information about exams

Some useful links

Course policies

Prerequisite: MATH-321

The course textbook is *Elementary Applied Partial Differential Equations*, by Richard Haberman, Prentice Hall. I'm teaching out of the Third Edition, but you can get any version you like.

In this course, students will

- Learn to solve the transport equation, heat equation, wave equation, and Laplace's equation
- Explain elementary physical derivations of each of these equations
- Interpret the solutions to these equations in terms of measureable, physical implications
- Describe the kinds of boundary conditions that typically arise, and their meanings

Homework 1 due January 28

Homework 2 due February 11

Homework 3 due March 7

Homework 4 due March 25

Homework 5 due April 11

Homework 6 due April 25

Homework 7 due at beginning of the final

- Explain the physical meaning of the heat equation, its boundary conditions, and its solutions
- Solve the heat equation using the method of separation of variables

January 14: 12.2.2: The transport equation

January 17: 1.2: Derivation of the heat equation

January 24: 1.3: Boundary conditions for the heat equation

January 28: 1.4: Equilibrium temperature distributions

January 31: 1.5: Heat conduction in higher dimensions

February 4: 2.1-2.3.2: Separation of variables on the heat equation

February 7: 2.3.3-2.3.8: Solving the heat equation

February 11: 2.4: Other boundary conditions

February 14: Review for exam 1

February 18: Exam 1 (in class)

- Explain how to derive Laplace's equation, and where it can be used
- Explain the physical meaning of the wave equation, its boundary conditions, and its solutions
- Solve Laplace's equation and the wave equation on rectangular domains
- Explain the meaning of the Fourier series representation of a function

February 21: 2.5.1: Solving Laplace's equation on a rectangle

February 25: 2.5.2: Solving Laplace's equation on a disk

February 28: 3.1-3.2: Introduction to Fourier series

March 4: Dr. Robinson on travel

March 7: 3.3, 3.6: Fourier series coefficients

March 18: 3.4-3.5: Calculus with Fourier series

March 21: 4.1-4.3: The wave equation

March 25: 4.4: Solving the wave equation

March 28: Review for Exam 2

April 1: Exam 2 (in class)

- Compute scattering angles for waves incident on a planar boundary
- Model the solution to the one-dimensional wave equation as a superposition of traveling pulses
- Explain how traveling wave expansions can be used to model wave propagation in complicated, higher-dimensional environments

April 4: 4.5: Wave equation in higher dimensions

April 8: 4.6: Snell's law

April 11: 12.1-12.2: Method of characteristics

April 15: 12.3: Solving the wave equation, infinite string

April 18: 12.4: Reflections

April 22: 12.5: Solving the wave equation on a finite string

April 25: 12.6-12.7: Characteristics and quasi-linear PDE

April 29: Review for final

**Final exam: May 6, 2:35pm-5:05pm**

25% Homework

25% Exam 1

25% Exam 2

25% Final exam

Late homeworks will not be accepted, unless there is an official (University-approved) reason for doing so.