Partial Differential Equations

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

We will study the classical PDEs of mathematical physics: the heat equation, the wave equation, and Laplace’s equation.
We will learn how to solve these equations using separation of variables and Fourier series.
Complex variables will be introduced as tools to help us understand Fourier series.
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.
An introduction to Sturm-Liouville theory will be given, including eigenvalue problems and orthogonal functions.
If time permits, we will study additional topics such as Fourier and Laplace transforms.

Course information

week	date	topics	slides	exercises	info
Week 4	02.20 fri				Quiz on Sec 4 and 5
	02.18 wed	Sec 6: A first look at Fourier series, part 2	Sec 6 Slides	Sec 6 Exercises
	02.16 mon	Sec 5: A first look at Fourier series, part 1	Sec 5 Slides	Sec 5 Exercises
Week 3	02.13 fri	Same as below ↓	Same as below ↓	Same as below ↓	Quiz on Sec 2 and 3
	02.11 wed	Sec 4: General PDEs and boundary conditions	Sec 4 Slides	Sec 4 Exercises
	02.09 mon	Sec 3: The Laplacian and Laplace’s equation	Sec 3 Slides	Sec 3 Exercises
Week 2	02.06 fri	Same as below ↓	Same as below ↓	Same as below ↓	Quiz on Sec 1
	02.04 wed	Sec 2: Separation of variables	Sec 2 Slides	Sec 2 Exercises
	02.02 mon	Same as below ↓	Same as below ↓	Same as below ↓
Week 1	01.30 fri	Sec 1: An introduction to PDEs	Sec 1 Slides	Same as below ↓
	01.28 wed	Another “remote day”: Watch the videos below if you haven’t already, continue working on Exercises 1-8.		Same as below ↓
	01.26 mon	“Remote day”: Watch the videos here, here, and here. Begin working on Exercises 1-8 (see link to the right).		Sec 1 Exercises