Advanced Methods for Partial Differential Equations
LOW 101, MWF 13:30-14:20pm
Prereqs: A previous course in PDEs or instructor permission
Instructor: Bernard Deconinck
Office Hours: M16:30-17:30pm, T13:30-15:30pm
Analytical solution techniques for linear partial differential equations. Discussion of how these arise in science and engineering. Transform and Green's function methods. Classification of second-order equations, characteristics. Conservation laws, shocks.
TextbookThe textbook for this course is Ron Gunther and John Lee's "Partial Differential Equations of Mathematical Physics and Integral Equations", Dover 2012. This is a very reasonably priced monograph which we will cover to some extent.
Other useful books from which on occasion material may be used are:
- Lawrence Evans, "Partial Differential Equations", American Mathematical Society 2010
- 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.
- First order equations (characteristics, shocks, rarefaction, Rankine-Hugoniot conditions)
- Classification of second order equations (hyperbolic, parabolic, elliptic)
- Fourier analysis
- Separation of variables and superposition
- Maximum principles
- Green's functions
- Sturm-Liouville problems and completeness
Homework sets are assigned biweekly. 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 and final exam scores in the proportions 60% and 40%, respectively.