Differential Equations

(3-5 Credit Hours) · Undergraduate

Students are able to (1) understand and employ the fundamental theorems of multivariable calculus; (2) understand and apply Green's theorem, Stokes' theorem and the Divergence theorem; (3) understand and employ complex analysis, particularly the method of residues; (4) understand and employ techniques of Fourier series; (5) employ methods of solution of both ordinary and partial differential equations; and (6) understand any apply Sturm-Liouville theory. The object of this module is to provide a broad introduction to analytical methods for solving ordinary and partial differential equations and to develop students' understanding and technical skills in this area. This module is a prerequisite for several other Honours options. The syllabus includes: existence and uniqueness of solutions to initial-value problems; non-linear ODE's; Green's functions for ODE's; Sturm-Liouville problems; first order PDE's; method of characteristics; classification of second order linear PDE's; method of separation of variables; characteristics and reduction to canonical form.