1. Recognize and solve separable, homogeneous, exact, and linear first order differential equations.
2. Construct and solve appropriate differential equations for applied problems involving mixtures, populations, and Newtonian Mechanics.
3. Calculate numerical solutions of differential equations.
4. Solve homogeneous, linear second and higher order differential equations with constant coefficients.
5. Solve non-homogeneous, linear second and higher order differential equations with constant coefficients by the Method of Undetermined Coefficients and the Method of Variation of Parameters.
6. Construct and solve applied problems involving mechanical vibrations, forced vibrations, and electric circuits.
7. Compute Laplace transforms of polynomials, exponential and trigonometric function.
8. Compute inverse Laplace transforms of rational functions and solve initial-value problems by Laplace Transform Method.
9. Find a power series solution to a given differential equation.
10. Solve a linear system by the Gauss-Jordan elimination method and by Matrix Methods.
11. Compute eigenvalues and eigenvectors of a given matrix.
12. Solve systems of 1st order linear differential equations by Matrix Methods