# MATH 290 - Differential Equations

The following are the Student Learning Outcomes (SLOs) and Course Measurable Objectives (CMOs) for MATH 290. A Student Learning Outcome is a measurable outcome statement about what a student will think, know, or be able to do as a result of an educational experience. Course Measurable Objectives focus more on course content, and can be considered to be smaller pieces that build up to the SLOs.

## Student Learning Outcomes (SLOs)

- Students can solve the following ordinary differential equations (ODEs): separable, first order linear, homogeneous, Bernoulli, and exact.
- Students can solve linear ODEs of order n with constant coefficients.
- Students can solve linear initial value problems with constant coefficients using Laplace transform.

## Course Measurable Objectives (CMOs)

- Identify and solve the following ordinary differential equations (ODEs): separable, first-order, linear, homogeneous, Bernoulli, and exact.
- Set up and solve ODEs for the following applications: simple and logistic growth models, cooling, simple electric circuits, mixing, and orthogonal trajectories.
- Plot slope fields and numerically solve ODEs using a computer algebra system.
- Determine linear independence of functions using the Wronskian.
- Solve linear ODEs of order n with constant coefficients and Cauchy-Euler equations (homogeneous or non-homogeneous) using the method of undetermined coefficients and variation of parameters.
- Solve ODEs for the following applications: simple electric circuits and mass-spring systems.
- Solve linear systems of ODEs.
- Express higher order equations as first order systems.
- Solve non-linear systems numerically using numerical methods, including phase-plane analysis, using a computer algebra system.
- Solve systems of ODEs for the following applications: mass-spring systems and mixing problems.
- Apply LaPlace transform and its inverse, using basic rules of the LaPlace transform.
- Solve linear initial value problems with constant coefficients using LaPlace transform.
- Solve ODEs using infinite series.