- Introduction (external link)
- First order PDEs
- Fully nonlinear first order PDEs (advanced topic)

- 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

- 1D Wave equation reloaded: characteristic coordinates
- Wave equation reloaded (continued)
- 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

- 1D Wave equation: IBVP, 1D Wave equation: Misc, and Hyperbolic first order systems with one spatial variable
- Energy integral
- Relax!
- 1D Heat equation: method of self-similar solutions
- 1D Heat equation: Misc--Coming
- 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

- Separation of variables: 1D wave equation
- Eigenvalue problems (examples)
- Ortogonal systems
*Extras.*Separation of Variables: Introduction--Slide presentation- Home Assignment 4, deadline: Fri October 25
- Ortogonal systems and Fourier series
- Other Fourier series
*Extras.*Separation of Variables: Introduction--Slide presentation- Home Assignment 5.

- Fourier transform, Fourier integral
- Properties of Fourier transform
- Applications of Fourier transform to PDEs
- Separation of variables: heat equation
- Separation of variables: Misc equations
- Laplacian in polar and spherical coordinates
- Laplacian: separation of variables in polar coordinates
- Laplacian: separation of variables in polar coordinates. II
- General properties of Laplace equation
- Potential theory and around
- Green function Week 10
- Wave equation--solution
- Wave equation: energy method
- Separation of variables in spherical coordinates
- Reserve
- Project 1
- Random walks and PDEs--done!

- Project 2
- Hydrogen Atom--done!

- Some classes of PDEs
- Appendix B to Lecture 13--counting the number of negative eigenvalues by applying variational principles
- Appendix C to Lecture 13--direct counting the number of negative eigenvalues
- Appendix D to Week 1--analyzing traffic flow
- Appendix E Eigenvalues of Laplacian in the disk and a ball
- Exploded (Incomplete) View of APM346