Offered every winter and spring term.
Brief description:
Mathematical models based on Partial Differential Equations (PDEs) are ubiquitous these days, arising in all areas of science and engineering, and also in finance and economics. This course is an introduction to this fundamental field of applied mathematics. The emphasis is on linear PDEs, in particular the three key prototypes, the diffusion equation, the wave equation and Laplace's equation, each of which describes a class of systems that behave in completely different ways. One section of the course, however, is devoted to nonlinear PDEs, which provides a glimpse of the complexities that nonlinearity can lead to.
Prerequisites:
AMATH 231 (Calculus 4) and AMATH 250 (Introduction to ODEs), or consent of the instructor.
Intended audience:
- AMATH 353 is a required course for all Applied Mathematics programs and for the Mathematical Physics program.
- PDEs play an important role in continuum mechanics (AMATH 361) -- the basis for fluid mechanics, elasticity and biomechanics, with current applications to geophysics, the environment and medicine.
- AMATH 353 will benefit students who are interested in the mathematics of finance, since PDEs are being applied in this area.
- In complex mathematical models the PDEs are invariably nonlinear, which usually means that detailed information about the solutions can only be obtained by using computer software based on a numerical method. AMATH 353 thus provides the foundation for AMATH 442, (Numerical Solution of Partial Differential Equations).