University of Oxford                

EPSRC - Engineering and Physical Sciences Research Council


EPSRC Centre for Doctoral Training

In Partial Differential Equations: Analysis and Applications

Introduction to Partial Partial Differential Equations

October  2017,   Prof. Gui-Qiang G. Chen


This is an introductory course on PDEs that are central to the other CDT courses. The course emphasizes rigorous treatment and analysis of PDEs through examples, representation formulas, and properties that can be understood by using relatively elementary mathematical tools and techniques.

Topics will include: The transport equation, Laplace's equation, the heat equation, the wave equation, conservation laws, and Hamilton-Jacobi equations.

Methods introduced through these topics will include:  Method of characteristics, mean-value formulas, fundamental solutions, Green's functions, energy methods, maximum principles, separation of variables, Duhamel's principle, spherical means,  Hadamard’s  method of descent, transform methods, asymptotics, numerical methods, and many more.

Recommended prerequisites include undergraduate-level advanced calculus, linear algebra, and ODE, and some exposure to complex analysis. Though this is an introductory course, it will move quickly and require considerable mathematical maturity.


Learning Outcomes:  Students will learn basic rigorous treatment and analysis of partial differential equations with emphasis on prototypical linear/nonlinear PDEs, as well as various techniques to represent solutions of these PDEs.  



Lecture Notes:

Lecture 0
Lecture 1
Lecture 2
Lecture 3


Lecture 4




Set of Problems


Topics & References:  See  Syllabus