Math 126: Introduction to Partial Differential Equations

Instructor: Maciej Zworski

Lectures: TuTh 3:40-5PM, Room 3111 Etcheverry

Course Control Number: 26617

Office: 801 Evans

Office Hours: Tu 1:30-3:30 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%).