Fourier Analysis and Partial Differential Equations
THO 125, MWF 10:30-11:20am
Prereqs: Amath 351 or Math 307
Instructor: Bernard Deconinck
Office Hours: M9-10, T9-11
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.
TextbookThe 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.
The following topics will be covered, time permitting, in some order to be decided.
- Traveling waves of linear equations
- Dispersion relations
- Superposition and Fourier analysis
- d' Alembert solution
- Standing waves
- Vibrations and separation of variables
- Traveling waves of nonlinear equations
- Conservation laws
Homework sets are assigned weekly. Homework is due at the beginning of class on its due date. Late homework is not accepted. Every homework set you hand in should have a header containing your name, student number, due date, course, and the homework number as a title. Your homework should be neat and readable. Your homework score may reflect the presentation of your homework set. Your course grade will be calculated by weighing your homework, midterm, and final exam scores in the proportions 50%, 15%, and 35%, respectively.