Department of Mathematics

University of Toronto

APM346 Partial Differential Equations


Lecture notes:

Current version:
  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


  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