# MATH250 Differential Equations

## Department of Science, Technology, Engineering & Mathematics: Mathematics

I. Course Number and Title
MATH250 Differential Equations
II. Number of Credits
3 credits
III. Number of Instructional Minutes
2250
IV. Prerequisites
MATH141 (C or better)
Corequisites
None
V. Other Pertinent Information
A minimum of three (3) tests and a Departmental Final Examination will be included in the course.
VI. Catalog Course Description
Topics for this course include first order and higher order ordinary differential equations; linear differential equations with constant coefficients; differential operators, non-homogenous differential equations and their solutions, special techniques for solving ordinary differential equations, and Laplace transforms.
VII. Required Course Content and Direction
1. ### Course Learning Goals

Students will:

1. recognize various types of differential equations;
2. solve differential equations by special techniques;
3. apply differential equations to solve problems involving mechanical vibrations; and
4. use Laplace Transform to solve differential equations.
2. ### Planned Sequence of Topics and/or Learning Activities

1. Direction fields and the approximation method of Euler
2. First order differential equations, including separable, exact, linear Homogenous equations and Bernoulli equations
3. Linear Differential Operators
4. Fundamental Solutions of Homogenous equations
5. Homogenous Linear equations with constant coefficients
6. Superposition and Nonhomogenous differential equations
7. Methods of Undetermined coefficients
8. Mechanical Vibrations and Simple Harmonic Motion
9. Damped Free Vibrations and Forced Vibrations
10. Definitions and properties of Laplace Transform
11. Inverse Laplace Transform
12. Solving initial value problems using Laplace Transform
13. Laplace Transforms and special functions
3. ### Assessment Methods for Course Learning Goals

The student applies mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment consists of open-ended questions reflecting theoretical and applied situations.
4. ### Reference, Resource, or Learning Materials to be used by Student:

Departmentally-selected textbook. Details provided by the instructor of each course section. See course syllabus.

Review/Approval Date - 9/98; New Core 8/2015