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# Math 280 SLO and CMO

#### MATH 280 SLO

1. Students can analytically describe the physical states of objects with mass traveling in three dimensions.
2. Students can compute partial and directional derivatives for functions of several variables.
3. Students can apply partial derivatives to optimization problems.
4. Students can evaluate multiple integrals to compute volumes, surface areas, moments and centers of mass, flux, and work.

#### MATH 280 CMO

1. Plot points, graph cylinders and quadric surfaces, computer distances and give equations of lines and planes in three dimensional rectangular, cylindrical and spherical coordinate systems.
2. Perform vector operation, including linear combinations, dot and cross products and projections.
3. Plot and parameterize space curves, compute velocity and acceleration vectors, decompose acceleration vector into normal and tangential components, compute arc length and curvature.
4. Compute domain of functions of several variables, plot surfaces, level curves and level surfaces for functions of several variables.
5. Evaluate limits for functions of several variables and test for continuity.
6. Evaluate partial derivatives, including the use of Chain Rule.
7. Compute the total differential for a function of several variables, and apply this to error estimation.
8. Compute directional derivatives and the gradient vector, solve application problems using their properties.
9. Compute the equations for tangent planes and normal lines to surfaces.
10. Compute and classify extrema of functions of several variables, using the second partials test.
11. Compute and classify extrema with constraints using Lagrange multipliers.
12. Set up and evaluate double and triple integrals in rectangular, polar, cylindrical and spherical coordinates.
13. Set up and evaluate double and triple integrals for the following applications: plane area, volume, moments and centers of mass, moments of inertia.
14. Use the Jacobian to change coordinate systems and evaluate multiple integrals.
15. Set up and evaluate line integrals.
16. Plot vector fields, set up and evaluate line integrals for work, circulation, mass and center of mass.
17. Test vector fields for conservativeness and evaluate line integrals through conservative fields using potential functions and the Fundamental Theorem of Line Integrals.
18. Set up and evaluate line integrals by applying Green's Theorem.
19. Parametrize a variety of surfaces and compute surface area and flux using surface integrals.
20. Compute curl and divergence for a vector field.
21. Evaluate line integrals over closed paths using Stokes' Theorem.
22. Evaluate flux integrals over closed oriented surfaces using the Divergence Theorem.