By the end of this course, a student will learn:

- basic classification of differential equations (first order, second order, linear, separable, etc.)
- standard solution methods for first order differential equations
- basic linear algebra needed to find eigenvalues and eigenvectors
- standard solution methods for systems of linear differential equations
- correspondence between linear second order differential equations and physical spring systems
- computation of Laplace transforms, and use to solve differential equations with discontinuous forcing functions
- applying separation of variables on partial differential equations
- computing Fourier series of functions; especially even and odd extensions
- deriving and writing the solution to the heat equation