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
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%).