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# Math 290 SLO and CMO

#### MATH 290 SLO

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

#### MATH 290 CMO

1. Identify and solve the following ordinary differential equations (ODEs): separable, first-order, linear, homogeneous, Bernoulli, and exact.
2. Set up and solve ODEs for the following applications: simple and logistic growth models, cooling, simple electric circuits, mixing, and orthogonal trajectories.
3. Plot slope fields and numerically solve ODEs using a computer algebra system.
4. Determine linear independence of functions using the Wronskian.
5. 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.
6. Solve ODEs for the following applications: simple electric circuits and mass-spring systems.
7. Solve linear systems of ODEs.
8. Express higher order equations as first order systems.
9. Solve non-linear systems numerically using numerical methods, including phase-plane analysis, using a computer algebra system.
10. Solve systems of ODEs for the following applications: mass-spring systems and mixing problems.
11. Apply LaPlace transform and its inverse, using basic rules of the LaPlace transform.
12. Solve linear initial value problems with constant coefficients using LaPlace transform.
13. Solve ODEs using infinite series.