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.
1. Basic Definitions and Terminology
2. Initial Value Problems
3. Separable Variables
4. Solutions by Substitution
5. Exact Equations
6. Linear Equations
7. A Numerical Method
8. Preliminary Theory
9. Homogeneous Linear Equations with Constant Coefficients
10. Undetermined Coefficients – Annihilator Approach
11. Variation of Parameters
12. Cauchy-Euler Equations
13. Introductions to Systems of Differential Equations
14. Linear Models
15. Non-Linear Models
16. Undamped Systems
17. Free Damped
18. External Forces
19. LRC Circuits
20. Solutions About Ordinary Points
21. Definition of the Laplace Transform
22. Inverse Transforms and Transforms of Derivatives
23. First and Second Translation Theorems
24. Operational Properties II, Convolutions, Periodic Functions