Vector and Multivariable Calculus

Analyze functions of several variables and interpret their properties in various contexts.

Perform vector operations and recognize their applications.

Describe and visualize 3D lines, curves, planes, and fundamental surfaces and analyze geometrical properties of each.

Determine extrema of functions of several variables.

Depict and interpret vector fields and compute curl, divergence, and flux.

Model a written description of a physical situation graphically, numerically, analytically, or verbally using vectors, curves, surfaces, derivatives, and integrals in rectangular, polar, cylindrical, and spherical coordinate systems in R^2 and R^3.

State the Fundamental Theorem of Line Integrals, Green's Theorem, Stoke's Theorem, and the Divergence Theorem in their own words.

Compare and contrast several generalizations of the Fundamental Theorem of Calculus.

Illustrate multivariable concepts by hand and with appropriate technology.

Use technology to help solve problems and illustrate solutions.

Communicate concepts both orally and in well-written sentences and explain solutions to problems.