1Learn the statement of the theorem of existence and uniqueness of solutions of first order differential equations and standard methods of solving linear, and some special non-linear, differential equations of first order.

2Interpret solutions qualitatively.

3Learn how to construct mathematical models.

4Learn the standard methods of solving linear homogenous differential equations of constant coefficients of arbitrary order.

5Learn methods to solve nonhomogeneous differential equations of constant coefficients of arbitrary order.

6Learn basic numerical methods for solving differential equations.

7Learn about the applications of differential equations to mechanical, physical, and biological models.

8Learn the theory of eigenvalues and eigenvectors and how they apply to systems of linear differential equations.

9Learn how to analyze systems of nonlinear differential equations (optional).

10Learn Laplace transforms and their applications to differential equations (optional).