UZB 218E - Int.to Partial Diff.Eq. in Eng_2016

Course Objectives

Students are introduced with linear partial differential equations through simple models, namely, the heat and wave equations, which describe a broad range of scientific phenomenon. Equations are formulated carefully from physical principles, motivating the mathematical solution techniques. Only exact solution methods are discussed.

Course Description

Review of ordinary differential equations. Boundary value problems. Heat Equation. Method of separation of variables: One dimensional heat equation. Laplace's equation in Cartesian and polar coordinates. Fourier series, Fourier sine and cosine series. Complex form of Fourier series. Vibrating strings and membranes. Sturm-Liouville eigenvalue problems. Rayleigh quotient. Vibrating circular membrane. Bessel functions. Laplace’s equation in a circular cylinder. Non-homogeneous problems. Eigenfunction expansions. Poisson's equation. A brief introduction to Laplace transforms