MATH 2210 - Differential Equations

1. Model using first- and second-order differential equations.
2. Draw and interpret slope fields.
3. Use approximation techniques for differential equations and systems of differential equations such as Euler’s method (with and without technology), Improved Euler’s method (with and without technology), and the Runge-Kutta method (with technology).
4. Understand existence and uniqueness theorems for differential equations.
5. Find equilibria and draw the phase line for autonomous first-order differential equations.
6. Use separation of variables to solve a separable first-order differential equation.
7. Use undetermined coefficients to solve a first-order linear differential equation.
8. Use an integrating factor to solve a first-order linear differential equation.
9. Use undetermined coefficients and/or integrating factors to solve a partially decoupled system of two linear differential equations.
10. Use eigenvalues (real, repeated, and complex) and eigenvectors to solve a system of two linear differential equations.
11. Solve constant-coefficient second-order linear differential equations (homogeneous and non-homogeneous).
12. Model the damped harmonic oscillator.
13. Model beating and resonance for a harmonic oscillator with an external forcing function.
14. Use Laplace Transforms to solve first- and second-order equations, including the Heaviside and the Dirac delta functions.

1. First order differential equations including uniqueness and existence theorems
2. Second order differential equations with undetermined coefficients and variation of parameters
3. Systems of linear differential equations
4. Higher order linear equations with constant coefficients
5. Laplace Transforms including convolution
6. Supplemental Topics (chosen from numerical approximation of solutions, series solutions, Fourier Series, and various applications)

1. The student should contact an instructor currently teaching or scheduled to teach the desired course.
2. The instructor will provide and schedule an exam date.
3. The student is to bring the Credit by Exam form to the scheduled exam.
4. The faculty member will notify the student and Records Office of the results.