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MATH 436  Partial Differential Equations  Units: 3.00  
Well-posedness and representation formulae for solutions to the transport equation, Laplace equation, heat equation, and wave equation. Fundamental solutions. Properties of harmonic functions. Green's function. Mean value formulae. Energy methods. Maximum principles. Method of characteristics for quasilinear equations. Burgers' equation. Shocks formation and entropy condition. Applications to fluid dynamics, elasticity problems and/or optimization problems.
Learning Hours: 132 (36 Lecture, 96 Private Study)  
Requirements: Prerequisite MATH 231/3.0 and MATH 280/3.0.  
Offering Faculty: Faculty of Arts and Science  

Course Learning Outcomes:

  1. Solve and analyze the partial differential equations modeling transport phenomena.
  2. Solve and analyze the partial differential equations modeling diffusion phenomena.
  3. Solve and analyze the initial-boundary value problems involving Laplace equation and Poisson equation.
  4. Solve and analyze the partial differential equations modeling waves and vibrations.
  5. Use the method of characteristics to solve first-order quasilinear equations.
  6. Apply analytical tools to solve nonlinear partial differential equations.