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Course Outline

  • First-order non-linear pdes: characteristics, fans, shocks and applications
  • Classification of linear second order pdes in two variables, canonical forms, initial and boundary conditions
  • The wave equation and d'Alembert's solution
  • Laplace's equation, Poisson's equation, harmonic functions, maximum and minimum principles
  • The heat equation, convective diffusion equation, Burgers' equation and the Hopf-Cole transformation
  • Sturm-Liouville equation, properties of eigenfunctions and eigenvalues
  • Series solutions of odes, ordinary points, regular singular points, Bessel and Legendre functions
  • Green functions

Generic skills:

In addition to learning specific technical skills that will assist you in your future careers in science, engineering, commerce, education or elsewhere, you will have the opportunity to develop in this subject, generic skills that will assist you whatever your future career path:

  • you will develop problem-solving skills including engaging with unfamiliar problems and identifying relevant strategies;
  • you will develop analytical skills - the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of the analysis;
  • through practice classes and other interactions with fellow students, you will develop the ability to work in a team. The department distinguishes between ethical collaboration which is strongly encouraged and plagiarism, which is prohibited.

(From the Department's generic statement.)

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