Course Description
Solution techniques for several types of ordinary differential equations are developed and applied to problems in physics, geometry, and other sciences. Topics include first order equations (separable, homogeneous, exact, and linear), higher-order linear equations with constant coefficients, the Laplace transform, systems of linear equations, and power series solutions. AAS: Mathematics elective.
Prerequisite(s)
MATH 2524 with a grade of C or better or equivalent
IAI Number
MTH 912
IAI Title
Differential Equations
Topical Outline
- Basic Definitions and Terminology
- Initial Value Problems
- Separable Variables
- Solutions by Substitution
- Exact Equations
- Linear Equations
- A Numerical Method
- Preliminary Theory
- Homogeneous Linear Equations with Constant Coefficients
- Undetermined Coefficients – Annihilator Approach
- Variation of Parameters
- Cauchy-Euler Equations
- Introductions to Systems of Differential Equations
- Linear Models
- Non-Linear Models
- Undamped Systems
- Free Damped
- External Forces
- LRC Circuits
- Solutions About Ordinary Points
- Definition of the Laplace Transform
- Inverse Transforms and Transforms of Derivatives
- First and Second Translation Theorems
- Operational Properties II, Convolutions, Periodic Functions
At the end of this course, students will be able to:
- Solve first and second order differential equations
- Apply first and second order differential equations to situations including, but not limited to electricity, engineering, physics, and chemistry.
- Solve a differential equation using the Laplace transform.
- Find a power series solution to a linear differential equation with variable coefficients and no singular point.
- Solve linear systems of differential equations by the methods of elimination and eigenvalues.