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|MA 27101 - Honors Multivariate Calculus|
Learning Outcomes: 1. Know techniques of vector algebra and be able to apply these to the geometry of space; in particular they will be able to find equations for lines and planes in space. 2. Find equations for standard surfaces in space. 3. Use vector methods to analyze motion in space, and calculate arc length and curvature. 4. Acquire a conceptual and computational knowledge of infinite series; in particular they will be able to test for convergence, and to do calculations with power series. 5. Understand the meaning of partial derivatives in various situations, and will be able to calculate with them. 6. Know the multivariable chain rule and its meaning, and will be able to apply it to calculate derivatives in various situations. 7. Know the meaning of directional derivatives and how to calculate them. 8. Find tangent planes. 9. Find and classify extreme values and saddle points and use the method of Lagrange multipliers. 10. Know the meaning of multiple integrals and how to calculate them. 11. Know the meaning of line integrals and surface integrals and how to calculate them. 12. Know Green's theorem, Stokes' theorem, and the divergence theorem and their applications.
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