**Instructor:** Maciej Zworski

**Lectures:** TuTh 11 AM-12:30 PM, Room Evans 740

**Course Control Number:** 23551

**Office:** 801 Evans

**Office Hours:** Wed 1-3 PM, or by appointment

**Prerequisites:** Math 53, Math 54

**Website:** bcourses

**Text: ** David Borthwick Introduction to Partial Differential Equations (available via UC Berkeley Library Proxy)

**Syllabus:** The course provides a broad introduction to partial differential equations
emphasizing physical origins of the problems.
Topics will include:

1. Introduction; review of calculus and ordinary differential equations

2. First order equations; method of characteristics.

3. Wave equation: analysis in one and three space dimensions

4. Wave equation: energy methods

5. Separation of variables for the wave equation and Laplace's equation

6. Heat equation: one space dimension and then higher dimensions.

7. Linear algebra in infinite dimensions: function spaces

7. Fourier series with applications to solving wave and heat equations

8. More on Laplace's equation: the maximum principle

9. Calculus of variations in one variable; ordinary differential equations revisited

10. Calculus of variations in higher dimensions; eigenvalues of the Laplacian.

**Grading:** The grade will be based on bi-weekly homework assignments (40%),
a midterm exam (20%) and the final exam (40%).