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:
- Vectors: 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
- Differentiation: 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
- Integration: 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
- Vector Calculus: 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
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, Green’s Theorem, and Gauss’ Theorem and surface integrals