 ## APM346 Partial Differential Equations

### Lecture notes:

##### Current version: http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook
1. PDE: Motivations and Context
2. First order differential equations
3. 1D wave equation
4. 1D Wave equation reloaded: characteristc coordinates
5. 1D Wave equation reloaded (continued)
6. 1D Wave equation reloaded: discussion and examples
7. 1D Wave equation: IVBP
8. 1D Wave equation: Misc
9. 1D Diffusion Equation: Introduction--Slide presentation, press "Space" or "->" for the next slide and "<-" for the previous one.
10. 1D Heat equation: method of self-similar solutions
11. 1D Heat equation: Misc
12. 1D Heat equation: Misc. II
13. Separation of Variables: Introduction--Slide presentation
14. Separation of variables: 1D wave equation
15. Eigenvalue problems (examples)
16. Ortogonal systems
17. Fourier Series: Overview Slide Presentation
18. Ortogonal systems and Fourier series
19. Other Fourier series
20. Fourier transform, Fourier integral
21. Properties of Fourier transform
22. Applications of Fourier transform to PDEs
23. Separation of variables: heat equation
24. Separation of variables: Misc equations
25. Laplacian in polar and spherical coordinates
26. Laplacian: separation of variables in polar coordinates
27. Laplacian: separation of variables in polar coordinates. II
28. General properties of Laplace equation
29. Potential theory and around
30. Green function
31. Wave equation--solution
32. Wave equation: energy method
33. Separation of variables in spherical coordinates

#### Appendices

1. Some classes of PDEs
2. Appendix B to Lecture 13--counting the number of negative eigenvalues by applying variational principles
3. Appendix C to Lecture 13--direct counting the number of negative eigenvalues
4. Exploded (Incomplete) View of APM346