Calculus 3 Learning Outcomes
LEARNING OUTCOMES: Upon completing Calculus 3 students should be able to:
1. Students will be able to use the concepts of continuity, differentiation, and integration of vector-valued functions to determine unit tangent and unit normal vectors in the process of modeling objects in three dimensions. Students will be able to parametrize piecewise-smooth curves using arc length. They will be able to compute the curvature of a space curve.
2. Students will be able to compute and sketch level curves and level surfaces for functions of several variables and sketch the graphs of functions of two variables. Analyzing limits, determining continuity, and computing partial derivatives of multivariate functions is also expected. Students will be able to use tangent planes, directional derivatives, gradients, the second partials test, and Lagrange multipliers to approximate and solve optimization problems.
3. Students will be able to demonstrate techniques of multiple integration and compute iterated integrals over rectangular regions, non-rectangular regions, and in other coordinate systems. They will be able to apply multiple integrals in problem situations involving area, volume, surface area, center of mass, moments of inertia, etc.
4. Students will be able to compute line integrals and surface integrals by applying The Fundamental Theorem for line integrals, Green’s theorem, Stoke’s Theorem and the Divergence Theorem. Applying these integrals to solve applications such as mass and work problems is also expected.
Calculus 3 Learning
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/calculus-3-learning.html
