Partial Differential Equations

This course is an introduction to partial differential equations (PDEs) and Fourier analysis.

  1. We will study the classical PDEs of mathematical physics: the heat equation, the wave equation, and Laplace’s equation.
  2. We will learn how to solve these equations using separation of variables and Fourier series.
  3. Complex variables will be introduced as tools to help us understand Fourier series.
  4. Properties of complex exponentials, sines, and cosines will be generalized to abstract properties of functions in \(L^2\) spaces. Accordingly, will will study the notion of Hilbert spaces.
  5. An introduction to Sturm-Liouville theory will be given, including eigenvalue problems and orthogonal functions.
  6. If time permits, we will study additional topics such as Fourier and Laplace transforms.

Course information

Instructor: John Myers
Office: Marano 175
Office hours: To be determined
Syllabus: link

Schedule, slides, exercises, and info

week date topics slides exercises info
02 02.02 mon ↓ ↓ ↓
01.30 fri 01 An introduction to PDEs slides ↓
01.28 wed Another “remote day”: Watch the videos below if you haven’t already, continue working on Exercises 1-8. ↓
01 01.26 mon “Remote day”: Watch the videos here, here, and here. Begin working on Exercises 1-8 (see link to the right). exercises