JFM 504E - Advanced Differential Equat.

Course Objectives

Starting from physical problems, demonstrate the construction of mathematical models described by partial differential equations

To Emphasize the importance of making appropriate assumptions and approximations based on the physical nature of the problem

To demonstrate how the solution of partial differential equations are obtained based on initial and/or boundary conditions specific to the problem

To give insight as to how problems without exact (analytical) solutions can be solved by numerical approximations.

Course Description

Construction and solution of parabolic (diffusion equation)

Hyperbolic (wave equation) type initial-boundary-value problems

Elliptic type (Laplace’s and Poisson’s equations) initial-value problems using the methods of separation of variables,

Integral transforms (Fourier series, Fourier transform, Laplace transform),

Eigenfunction expansion,

Green’s function (impulse-response),

Change of coordinates and

Finite differences.