EEF 210E - Differential Equations

Course Objectives

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

Course Description

Introduction: First-Order Differential Equations (Basic Concepts, Simple DE Example, Classification of DEs) I - II
First-Order Differential Equations: (Linear Equations, Separable Equations, Existence and Uniqueness Theorem) II - III
First-Order Differential Equations: (Exact Equations, Homogeneous Equations, Riccati Equation) II - III
Second-Order Differential Equations: (Homogeneous Linear Equations with Constant Coefficients, Fundamental Theorems, Wronskian, Complex Roots of the Characteristic Equation) III - IV
Second-Order Differential Equations: (Repeated Roots of the Characteristic Equation, Reduction of Order Method, Non-Homogeneous Equations, Method of Undetermined Coefficients, Variation of Parameters) IV
Second-Order Differential Equations: (Mechanical and Electrical Oscillations, Forced Oscillations)
Higher-Order Differential Equations: (General Theory of n-th Order Linear Equations) III - IV
Higher-Order Differential Equations: (Linear Equations with Constant Coefficients, Method of Undetermined Coefficients, Variation of Parameters) IV
Laplace Transform: (Definition of the Laplace Transform, Initial Value Problems, Step Function) V
Laplace Transform: (Differential Equations with Discontinuous Forcing Functions, Impulse Function, Convolution Integral) V
First-Order Linear Systems of Equations: (Introduction, Fundamental Theory of First-Order Linear Systems) VI
First-Order Linear Systems of Equations: (Homogeneous Linear Systems with Constant Coefficients, Complex Eigenvalues, Fundamental Matrices) VI
First-Order Linear Systems of Equations: (Repeated Eigenvalues, Non-Homogeneous Linear Systems) VI
Series Solutions of Second-Order Differential Equations: (Series Solutions about an Ordinary Point, Euler Equations, Regular Singular Points) VII
Series Solutions of Second-Order Differential Equations: (Series Solutions about a Regular Singular Point) VII