MTH 225 - Differential Equations
An introduction to ordinary differential equations and their applications. Analytical methods include: separation of variables, linear first order equations, substitution methods, second order linear equations with constant coefficients, undetermined coefficients, variation of parameters, autonomous systems of two first order equations, series solutions about ordinary points, and the Laplace Transform. In addition to analytical methods, quantitative and qualitative analysis will be employed through the use of Euler’s Method, phase lines, phase planes, and slope fields. Four class hours.
Prerequisite: MTH 211 with a grade of C or better.
Course Learning Outcomes
1. Classify a differential equation using appropriate mathematical terminology.
2. Solve a variety of differential equations using analytical methods.
3. Describe the qualitative behavior of the solutions of a differential equation.
4. Estimate the solutions of a differential equation using numerical and graphical methods.
5. Solve a differential equation using power series.
6. Solve an autonomous system of two first order differential equations.
7. Examine the qualitative behavior of the solutions of an autonomous system of two first order differential equations.
8. Solve initial value problems using the Laplace Transform.
9. Solve applied problems using differential equations.
Course Offered Fall and Spring