# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 218A: Partial Differential Equations

**Approved:**2001-10-12, S. Shkoller

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Course Description:**

- Laplace's and linear heat equation.
- Fundamental solution.
- Mean-value formula.
- Green's function.
- Energy methods.
- Linear wave equation.
- Representation of solutions and energy methods.
- Transform methods.
- Fourier, Laplace and Similarity transforms.
- Linear Elliptic and Evolution equations.
- Distribution theory and weak solutions.
- Sobolev spaces.
- Weak derivatives and approximation of smooth function spaces.
- Extension and trace theorems.
- Basic inequalities.
- Gagliardo-Nirenberg.
- Sobolev Embedding Theorem.
- Second Order Elliptic Boundary Value Problems.
- Weak Solutions, Elliptic Regularity, and Maximum Principles.
- Eigenvalue Problems.