Department of Mathematics

University of Toronto

APM346 Partial Differential Equations

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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
   • 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
4. 1D Wave equation reloaded: characteristc coordinates
5. 1D Wave equation reloaded (continued)
6. 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
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.
9. 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
10. 1D Heat equation: Misc
11. 1D Heat equation: Misc. II
12. Separation of Variables: Introduction--Slide presentation
12. 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
13. Eigenvalue problems (examples)
14. Ortogonal systems
15. Fourier Series: Overview Slide Presentation
15. 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
16. Other Fourier series
17. Fourier transform, Fourier integral
18. 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
19. Applications of Fourier transform to PDEs
20. Separation of variables: heat equation
21. 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
22. Laplacian in polar and spherical coordinates
23. Laplacian: separation of variables in polar coordinates
24. 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
25. General properties of Laplace equation
26. Potential theory and around
27. Green function
    • Home Assignment 8, PDF file, due Wed November 28
28. Wave equation--solution
29. Wave equation: energy method
30. Separation of variables in spherical coordinates
    • Home Assignment 9, PDF file, due Wed December 5

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

• Last year Final Exam discussed on Forum 2011#13.0