Partial Differential Equations

Catalog description

Many laws of physics are formulated as partial differential equations, including the propagation of sound waves, the diffusion of a gas, and the flow of a fluid. This course discusses the simplest examples of such laws as embodied in the wave equation, the diffusion equation, and Laplace's equation. The course also discusses nonlinear conservation laws and the theory of shock waves. Applications to physics, chemistry, biology, and population dynamics are discussed.