**Course** Description: | Calculus of functions of two and three variables: Parametric
curves, derivatives, gradient, Lagrange multipliers. Multiple
integration, area, volume, polar, cylindrical, and spherical
coordinates. Line integrals and Green's Theorem. Introduction to
surface integrals and Stokes's and Divergence Theorems. This is
an accelerated version of Calculus III for Science and
Engineering that covers fewer topics and applications. |

**Topical Outline:** | 1. Review of vector algebra and geometry.
2. Parametric curves, velocity, acceleration.
3. Partial differentiation: directional derivatives, gradients,
tangent planes, chain rule, maximum/minimum problems, and
Lagrange multipliers.
4. Multiple integration: double and triple integrals, change of
order of integration, applications to computations of areas,
volumes, and physical applications as time allows. Polar,
cylindrical, and spherical coordinates.
4. Line integrals, work, path-independence, and Green's Theorem.
5. Brief survey of surface integrals and flux, curl, divergence,
Stokes's and Divergence Theorems. |