MAT 232 - Differential Equations

Course Objectives

1. To introduce the basic concepts required to understand, construct, solve and interpret differential equations.
2. To teach methods to solve differential equations of various types.
3. To give an ability to apply knowledge of mathematics on engineering problems.

Course Description

Classification of Differential Equations, First order equations; Linear equations, Separable equations, Change of variable and integrating factor, Existence and uniqueness theorems, applications. Second order linear equations; Linear equations with constant coefficients, Homogeneous equations, The method of reduction of order, Nonhomogeneous Equations, The method of undetermined coefficients, The method of variation of parameters, Higher order linear equations. Euler-Cauchy equation. Power series method; Solutions around ordinary and regular-singular points. Laplace transformation; basic definition and theorems, Solutions of initial value problems, Convolution, Delta function, Transfer function. Systems of linear differential equations; Fundamental theorems, Solutions of homogeneous and nonhomogeneous system of differential equations, Solutions using Laplace transformation.