EEF 210 - Differential Equations

Course Objectives

First Order Differential Equations, Second Order Linear Differential Equations, Higher Order Linear Differential Equations, Laplace Transforms, Systems of First Order Linear Equations, Series Solutions of Second Order Linear Equations

Course Description

1 Introduction. First Order Differential Equations (Basic Concepts, A Simple DE Example, Clasification of DEs) I - II
2 First Order Differential Equations (Linear Eqns, Separable Eqns, Existence and Uniqueness Thm) II-III
3 First Order Differential Equations (Exact Eqns, Homogeneous Eqns, Riccati Eqn) II - III
4 Second Order Differential Equations (Constant Coefficient, Homogeneous,Linear DE, Basic Theorems and the Wronskian, Complex Roots of the Characteristic Eqn) III - IV
5 Second Order Differential Equations (Repeated Roots of the Characteristic Eqn, Reduction of Order, Nonhomogeneous Eqns, Method of Undetermined Coefficients, Variation of Parameters) IV
6 Second Order Differential Equations (Mechanical and Electrical Vibrations, Forced Vibrations), Higher Order Differential Equations (General Theory of nth Order Linear Equations) III - IV
7 Higher Order Differential Equations (Homogeneous Eqns with Constant Coefficients, Method of Undetermined Coefficients, Method of Variation of Parameters) IV
8 The Laplace Transform (Definition of Laplace Transform, Initial Value Problems, Step Functions) V
9 The Laplace Transform (DE with Discontinuous Forcing Functions, Impulse Function, Convolution Integral) V
10 Systems of First Order Linear Equations (Introduction, Basic Theory of Systems of First Order Linear Equations) VI
11 Systems of First Order Linear Equations (Homogeneous Linear Systems with Constant Coefficients, Complex Eigenvalues, Fundamental Matrices) VI
12 Systems of First Order Linear Equations (Repeated Eigenvalues, Nonhomogeneous Linear Systems) VI
13 Series Solutions of Second Order Linear Equations (Series Solutions Near an Ordinary Point, Euler Equations, Regular Singular Points) VII
14 Series Solutions of Second Order Linear Equations (Series Solutions Near a Regular SingularPoint) VII