Math 6160 Partial differential equations
This course is an introduction to the theory of partial differential equations (PDE). It shoud be of interest to students working on applied mathematics, differential geometry, mathematical physics, fluid mechanics, mathematical biology, probability, harmonic analysis, dynamical systems, and other areas, as well as to PDE/analysis-focused students.
This course aims to teach the basics of Partial differential equations, a subject that touches on many branches of pure mathematics, applied mathematics, as well as physics and applied science. Partial differential equations are a very rich subject; so much so that at a research level most workers in the field specialize in one of the many sub-fields. The aim of this one-semester course is both to give an overview of the subject as much as possible, and introduce some tools that are used throughout.
Although there are not formal pre-requisites, it is expected that students are familiar with basic real analysis, primarily Lebesgue measure and Lp spaces, the basics of the Fourier transform on Rn and some functional analysis, along with multivariable calculus (Stokes’ theorem). Familiarity with the general theory of ordinary differential equations is desirable also an undergraduate-level PDE course will be an asset.
The main textbook will be Partial Differential Equations by L. C. Evans, (American Math Society, 2010). This will be complemented by further materials, either notes from the instructor, or referrals to other textbooks.