# Math 280 SLO and CMO

**MATH 280 SLO**

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

**MATH 280 CMO**

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