## Lecture Notes

## Lecture Notes: By Chapter

- Contents
- Chapter 1: Preliminaries
- Chapter 2: Laplace's equation
- Chapter 3: Sobolev spaces
- Appendix: Functions of one variable
- Chapter 4: Elliptic PDEs
- Appendix: Heat flow
- Chapter 5: The heat equation
- Appendix: The Fourier transform
- Chapter 6: Parabolic equations
- Appendix: Vector-valued functions
- Chapter 7: Hyperbolic equations
- Chapter 8: Friedrich symmetric systems
- Bibliography