MATH 252 - Differential Equations

1. Model a mechanical oscillator.
2. Model a series or parallel electrical circuit of the RLC (resistor, inductor, capacitor) type.
3. Model one population in conditions of natural growth or decay, logistic growth, explosion, or extinction.
4. Model two populations in conditions of predation or competition.
5. Sketch graphical solutions of a first-order differential equation by hand using the slope field.
6. Determine the general solution of a simple first-order differential equation using such techniques as separation of variables, integrating factors, and substitution methods.
7. Compute the approximate solution of a first-order initial-value differential equation using a numerical method (Euler, Runge-Kutta, etc.) by hand or with a calculating device.
8. Determine the general solution of a homogeneous constant-coefficient linear differential equation by using the Characteristic Polynomial method.
9. Determine the general solution of a nonhomogeneous constant-coefficient linear differential equation by using the Undetermined Coefficients or Variation of Parameters method.
10. Determine the general solution of a system of linear differential equations by finding its real or complex eigenvalues and eigenvectors.
11. Identify graphically the location, type, and stability of all critical points in a given phase-plane diagram.
12. Determine analytically the location, type, and stability of all critical points by finding the eigenvalues of the linearized system.
13. Determine the Laplace transform of various simple functions by hand.
14. Determine the Laplace transform of various continuous, piecewise-continuous, or periodic functions with the aid of a table.
15. Determine the inverse Laplace transform of various functions with the aid of a table.
16. Solve differential equations by the Laplace transform method.
17. Determine power series solutions of a differential equation and their radii of convergence.