MAT394 Partial Differential Equations (TOC)

Week 1

1. Introduction (external link)
2. First order PDEs
   • Fully nonlinear first order PDEs (advanced topic)
3. Homogeneous 1D wave equation
   • Extras. For the 1-st week look at 2011F home assignment 1 (solutions are discussed on Forum 2011#6.0)
   • Home Assignment 1, deadline: Fri October 4

   Week 2

4. 1D Wave equation reloaded: characteristic coordinates
5. Wave equation reloaded (continued)
6. 1D Wave equation reloaded: discussion and examples
   • Extras. For the 1-st week look at 2011F home assignment 2 (solutions are discussed on Forum 2011#8.0)
   • Home Assignment 2, deadline: Fri October 11

   Week 3

7. 1D Wave equation: IBVP, 1D Wave equation: Misc, and Hyperbolic first order systems with one spatial variable
8. Energy integral
9. Relax!

Week 4

9. 1D Heat equation: method of self-similar solutions
10. 1D Heat equation: Misc--Coming
11. 1D Heat equation: Misc. II--Coming
    • Extras. For the 3-rd and 4-th weeks look at 2011F home assignment 3 (solutions are discussed on Forum 2011#9.0)
    • Extras. 1D Diffusion Equation: Introduction--(external link) Slide presentation, press "Space" or "->" for the next slide and "<-" for the previous one.
    • Home Assignment 3, deadline: Fri October 18

    Week 5

12. Separation of variables: 1D wave equation
13. Eigenvalue problems (examples)
14. Ortogonal systems
• Extras. Separation of Variables: Introduction--Slide presentation
• Home Assignment 4, deadline: Fri October 25

Week 6

15. Ortogonal systems and Fourier series
16. Other Fourier series
    • Extras. Separation of Variables: Introduction--Slide presentation
    • Home Assignment 5.

Week 7

17. Fourier transform, Fourier integral
18. Properties of Fourier transform
19. Applications of Fourier transform to PDEs
    • Home Assignment 6.

Week 8

20. Separation of variables: heat equation
21. Separation of variables: Misc equations
22. Laplacian in polar and spherical coordinates
23. Laplacian: separation of variables in polar coordinates
    • Home Assignment 7.

Week 9

24. Laplacian: separation of variables in polar coordinates. II
25. General properties of Laplace equation
26. Potential theory and around
27. Green function
    • Home Assignment 8.
Week 10
28. Wave equation--solution
29. Wave equation: energy method
30. Separation of variables in spherical coordinates
    • Home Assignment 8.

Week 11

31. Reserve

Week 12

32. Project 1
    • Random walks and PDEs--done!
33. Project 2
    • Hydrogen Atom--done!

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. Appendix D to Week 1--analyzing traffic flow
5. Appendix E Eigenvalues of Laplacian in the disk and a ball
6. Exploded (Incomplete) View of APM346