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’smethod 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.