### General

### Applied Multivariate and Vector Calculus

Topics covered include partial derivatives; grad, div, curl and Laplacian operators; line and surface integrals; theorems of Gauss and Stokes; double and triple integrals in various coordinate systems; extrema and Taylor series for multivariate functions.

##### The course will cover the following topics:

: Three-dimensional coordinate systems; vectors; dot product; cross product; equations of lines and planes; vector functions and space curves; derivatives and integrals of vector functions; arc length and curvature; normal, bi-normal and tangent vectors**Vectors**: Functions of several variables; their limit and continuity; partial derivatives; tangent planes; linear approximations; Taylor Series, chain rule; directional derivative; gradient; critical points, maximums and minimums, second derivative test, extreme value theorem, optimization problems**Differentiation**: Double integrals over rectangular domains; iterated integrals and interchanging order of integration; double integrals over general regions; change of variables; double integrals in polar coordinates; triple integrals in cylindrical and spherical coordinates; Jacobian; applications**Integration****Vector**: Vector elds; conservative vector elds; line integrals, fundamental theorem of line integrals; Green's Theorem; parametric surfaces; surface integrals; curl; divergence; Laplace operator; Gauss' divergence theorem; Stokes' theorem__Calculus__

Coverage during review sessions will not include all the topics mentioned above. Topics selected for each review session will be similar to the coverage for the midterms.

**Final Exam Review Topics**1. Vector Fields, evaluation of line integral,conservative and non-conservative fields

2. Divergence and Curl of a vector field

3. Divergence Theorem, Greenâ€™s Theorem, and Gaussâ€™ Theorem and surface integrals