MATH 238 - Ordinary Differential Equations

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: An introductory course in differential equations. Topics include existence and uniqueness theorems, methods of solving first and second order differential equations, numerical methods, and Laplace Transforms. Graphing technology required.

Prerequisite: MATH& 153 with a C or higher.
Meets FQE Requirement: No
Elective Requirements: Fulfills Academic Electives
Integrative Experience Requirement: No

Student Learning Outcomes

Solve first and second order linear differential equations.
Solve second order equations with constant coefficients, and undetermined coefficients.
Graph and approximate the solution of an ordinary differential equation using numerical methods and technology.
Analyze and solve physical applications using ordinary differential equations.

Course Contents

First Order Differential Equations. Linear equations and integrating factors. Direction fields. Separable equations. Autonomous equations. Exact equations and integrating factors. Euler’s Method and Runge-Kutta Methods.
Second Order Linear Equations. Homogeneous equations with constant coefficients. Linear independence of solutions and the Wronskian. Complex roots of the characteristic equation. Repeated roots; reduction of order. Nonhomogeneous equations; method of undetermined coefficients. Variation of parameter.
Higher Order Linear Equations. Homogeneous equations with constant coefficients. The method of undetermined coefficients.
The Laplace Transform. Laplace transforms. Solution of initial value problems. Step functions. Discontinuous forcing functions (optional). Impulse functions (optional).
Numerical Methods. Euler’s Method. The Improved Euler Method. The Runge-Kutta Method.
Optional Topics. Systems of linear equations. Series solutions to second order equations.

Instructional Units: 5