- PDE: Motivations and Context
- First order differential equations
- 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, PDF file--due Mon September 24

- 1D Wave equation reloaded: characteristc coordinates
- 1D Wave equation reloaded (continued)
- 1D Wave equation reloaded: discussion and examples
*Extras.*For the 2-nd week look at 2011F home assignment 2 (solutions are discussed on Forum 2011#8.0)- Home Assignment 2, PDF file--due Mon October 1

- 1D Wave equation: IVBP
- 1D Wave equation: Misc
- 1D Diffusion Equation: Introduction--Slide presentation, press "Space" or "->" for the next slide and "<-" for the previous one.
- 1D Heat equation: method of self-similar solutions
*Extras.*For the 3-nd week look at 2011F home assignment 3 (solutions are discussed on Forum 2011#9.0)- Home Assignment 3, PDF file--due Wed October 10

- 1D Heat equation: Misc
- 1D Heat equation: Misc. II
- Separation of Variables: Introduction--Slide presentation
- Separation of variables: 1D wave equation
*Extras.*For the 4-th week look at 2011F home assignment 4 (solutions are discussed on Forum 2011#10.0)- Last year TT1 discussed on Forum 2011#11.0
- Home Assignment X, PDF file--Not graded, recommended as a preparation to Term Test 1

- Eigenvalue problems (examples)
- Ortogonal systems
- Fourier Series: Overview Slide Presentation
- Ortogonal systems and Fourier series
*Extras.*For the 5-th week look at 2011F home assignment 5 (solutions are discussed on Forum 2011#15.0)- Home Assignment 4, PDF file--due Wed October 24

- Other Fourier series
- Fourier transform, Fourier integral
- Properties of Fourier transform
*Extras.*For the 6-th week look at 2011F home assignment 7 (solutions are discussed on Forum 2011#17.0) and
2011F home assignment 8
(solutions are discussed on Forum 2011#18.0)
- Home Assignment 5, PDF file, due Wed October 31

- Applications of Fourier transform to PDEs
- Separation of variables: heat equation
- Separation of variables: Misc equations
- Last year TT2 discussed on Forum 2011#12.0--this year scope will be slightly different (Fourier transform included)
- Home Assignment 6, PDF file, due Wed November 7

- Laplacian in polar and spherical coordinates
- Laplacian: separation of variables in polar coordinates
- Laplacian: separation of variables in polar coordinates. II
- Home Assignment 7, PDF file, due Mon November 19
- Home Assignment Y, PDF file--Not graded, recommended as a preparation to Term Test 2

- General properties of Laplace equation
- Potential theory and around
- Green function
- Home Assignment 8, PDF file, due Wed November 28

- Wave equation--solution
- Wave equation: energy method
- Separation of variables in spherical coordinates
- Home Assignment 9, PDF file, due Wed December 5

- 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
- Exploded (Incomplete) View of APM346

- Last year Final Exam discussed on Forum 2011#13.0