PDE course.

1. Chapter 3. Fourier analysis, distribution theory, and constant coefficient linear PDE

2. Appendix A. Outline of functional analysis

3. Measure Theory and Integration, Appendix G, Integration of Differential Forms

4. The heat kernel and the wave kernel

5. Waves in Even Dimensions — the Method of Descent

6. Functions of the Laplace Operator and the Wave Equation

7. Chapter 8. Spectral theory

8. Bessel Functions and Hankel Transforms

9. The Schrodinger equation and Gauss sums

10. Chapter 10 (Measure Theory and Integration). Lp Sobolev Spaces

11. Chapter 4. Sobolev spaces

12. Chapter 13. Function space and operator theory for nonlinear analysis

13. Chapter 7. Pseudodifferential Operators

14. Appendix C. Connections and curvature

15. Curvature and Uniformization (with R. Mazzeo)

16. The Work of Lars Hormander

17. The Schrodinger equation and the Fresnel integral

18. Harmonic functions on domains in Rn

19. Local regularity of solutions to Lu=f

20. Dirichlet problem for wave equations