Math& 238 ~ Differential Equations  
 
 
 

Course Description
An introductory course in differential equations including first order equations, second order and higher order equations, applications to physical and other systems.

Pre-requisite
Math 153 with a grade of C or higher.

Mode of Delivery (Modes)
Lecture

Offered
Spring

Required for:


Course Content

Text: Elementary Differential Equations, 8th Ed., Boyce & Diprima, Wiley

Chapter 1 Introduction 1
1.1 Some Basic Mathematical Models; Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
1.4 Historical Remarks

Chapter 2 First Order Differential Equations
2.1 Linear Equations; Method of Integrating Factors
2.2 Separable Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Equations
2.5 Autonomous Equations and Population Dynamics
2.6 Exact Equations and Integrating Factors
2.7 Numerical Approximations: Euler’s Method
2.8 The Existence and Uniqueness Theorem
2.9 First Order Difference Equations

Chapter 3 Second Order Linear Equations
3.1 Homogeneous Equations with Constant Coefficients
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters
3.7 Mechanical and Electrical Vibrations
3.8 Forced Vibrations

Chapter 4 Higher Order Linear Equations
4.1 General Theory of nth Order Linear Equations
4.2 Homogeneous Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters

Chapter 6 The Laplace Transform
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
6.4 Differential Equations with Discontinuous Forcing Function
6.5 Impulse Functions