Christian Brothers University 
Math 231 Differential Equations
Departmental Syllabus

Catalog Data  This course is an introduction to the concepts and methods of ordinary differential equations. Topics include: first-order equations, elementary numerical methods, qualitative analysis, second-order homogeneous linear equations, the methods of undetermined coefficients and variation of parameters for nonhomogeneous equations, Laplace transforms, and models in science and engineering.  Offered in Fall and Spring.
Three Credits. One semester. 
Prerequisite: MATH 132. 
Textbooks L. C. Becker, "Ordinary Differential Equations: Concepts, Methods and Models", CBU Press, 2002. 
Computer Use You must complete computer worksheets written with commercial software called Maple. 
Calculator Policy You must use a graphing calculator, such as the TI-89, on assignments and occasionally on tests. 
Prerequisites 1. Basic calculus
2. The definition of the derivative
3. The basic methods of integration 
Goals You will learn how to solve those ordinary differential equations that are typically encountered in undergraduate science and engineering courses; and, by discussing some simple applications, how to interpret some of these equations and their solutions in a physical setting. You should understand the rationale behind the various methods. 

Syllabus
Chapter Topic
1  Origins of Differential Equations and Solutions  
2  Separable Equations 
3  Direction Fields and Solution Curves
4  Numerical Methods for First-Order Equations
5  First-Order Linear Equations 
6  Modeling with First-Order Equations 
7  Modeling Abrupt Changes
8  Exact Equations
9  Homogeneous Linear Equations of Order Two
10  Nonhomogeneous Linear Equations of Order Two
11  Two-Dimensional Linear Systems with Constant Coefficients
12  Homogeneous Linear Equations / Companion Linear Systems
13  A First Look at the Laplace Transform 
14 
 A Second Look at the Laplace Transform 
Tests
Final Exam The final exam is departmental and comprehensive. 
Resources The Math Center located in Science 151 offers free tutoring in calculus. 
Coordinator Dr. L. Becker, Professor of Mathematics 
Estimated ABET Category Content Mathematics 100% or 3 Credits. 


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