Math 7006: Partial Differential Equations

This is a graduate course on the qualitative study of partial differential equations posed on subsets of $n$-dimensional space. We first study four important linear partial differential equations in detail: the transport equation, Laplace’s equation, the heat equation, and the wave equation. Then we move on to the covering first order nonlinear partial differential equations, and various techniques to obtain and methods to represent solutions of the partial differential equations under investigation in the entire course. The techniques for solving the second-order equations will include finding fundamental solutions, Green’s functions, maximum principles, and energy methods. This plan amounts to covering the material from Chapters 1–4 of the text book.

Textbook

Partial Differential Equations, by Lawrence C. Evans, 2010 (2nd Edition), American Mathematical Society, ISBN-13:978-0821849743.

Syllabus

Please read the syllabus for the organizational information about this course.

Canvas

All the assignments are on Canvas course website.

Advice for Students

Questions are highly encouraged — if something is unclear during class, please ask, ask, ask, ask. This course is for you. Review your the notes after each class and make a list of points that are unclear. Ask me about these points either in class or office hours. Do not postpone understanding something.

Homework Assignments

These assignments are also provided at the end of relevant lecture notes posted on this website (see the menu in the left pane).

More homework will be posted here as the course progresses in Spring 2021.