## Fourier Analysis and Partial Differential Equations

SLN 10210
THO 125, MWF 10:30-11:20am
Prereqs: Amath 351 or Math 307

### Instructor: Bernard Deconinck

Lewis 313
bernard@amath.washington.edu
Tel: 206-543-6069
Office Hours: M9-10, T9-11
TA:

#### Course Description

Heat equation, wave equation, and Laplace's equation. Separation of variables. Fourier series in context of solving heat equation. Fourier sine and cosine series; complete Fourier series. Fourier and Laplace transforms. Solution of partial differential equations on infinite domains. D' Alembert's solution for wave equation.

#### Textbook

The textbook for this course is Roger Knobel's "An introduction to the mathematical theory of waves", American Mathematical Society 1999, Student Mathematical Library Vol 3. This is a reasonably priced monograph which we will completely cover. Some material on separation of variables will be gotten from other sources, see below. Some homework problems will come from this text, but most will come from other sources.

Other useful books from which on occasion material may be used are:
• Stanley Farlow, "Partial Differential Equations for Scientists and Engineers", Dover 1993
• Richard Haberman, "Applied Partial Differential Equations", Pearson 2012
• Peter Olver, "Introduction to Partial Differential Equations", Springer 2014

#### Course Canvas Page

I will use Canvas to post homework sets, link to the class message board, etc. You will need a UW account and be enrolled in the course to access this page

#### Syllabus

The following topics will be covered, time permitting, in some order to be decided.
• Traveling waves of linear equations
• Dispersion relations
• Stability
• Superposition and Fourier analysis
• d' Alembert solution
• Standing waves
• Vibrations and separation of variables
• Traveling waves of nonlinear equations
• Conservation laws
• Characteristics
• Breaking
• Shocks
• Rarefaction