APMA 1940R: Linear and Nonlinear Waves (Spring 2012)

Class information

Instructor	Björn Sandstede
Office	Room 105 in 182 George Street
Phone	863-2815
Email	bjorn_sandstede@brown.edu
Office Hours	Mondays noon-2pm, or by appointment
Class meetings	Wednesdays 3:00-5:20 pm in BH 163
Syllabus	[PDF]

Overview

From sound and light waves to water waves and traffic jams, wave phenomena are everywhere around us. In this senior seminar, we will explore linear and nonlinear waves. Among the tools we will learn about are numerical simulations in Matlab and analytical techniques from ordinary and partial differential equations. We will also study applications in nonlinear optics and to traffic flow problems. The class format will be as follows: I will lecture for the first few weeks; afterwards, some of the lectures will be given by participants and also include class discussions.

Prerequisites: MATH 0180, and APMA 0330-0340 or APMA 0350-0360. No background in partial differential equations is required.

Grade

The grade will be determined as follows:

Homework	40%
In-class presentation	10%
Project	30%
Oral final exam	20%

Homework assignments will be handed out every week and are due a week later. You can work together on homework problems, but you need to write up your solutions individually.

Class materials

No textbook is required but much of the initial material will come from the following book:

Roger Knobel: An introduction to the mathematical theory of waves, American Mathematical Society.