Mathematics

### Material to Review for the Final Exam

9.1 - 9.4. Three-dimensional space, vectors, dot product, projection, cross product, determinant. Test 1 problem 1.

9.5. Planes and lines. Test 1 problems 2, 3.

9.6. Quadric surfaces. Test 1 problem 4.

10.1 - 10.4. Space curves, arc length, velocity and acceleration, unit tangent and normal vectors, curvature. Test 1 problem 5.

11.1. Functions of several variables: domain, graph, level curves, level surfaces. (Omit limits and continuity in 11.2.) Test 2 problem 1.

11.3 - 11.7. Partial derivatives, tangent plane, approximation, chain rule, directional derivative, gradient, max-min problems. Test 2 problems 2, 3, 4, 5.

12.1 - 12.5, 12.7. Double and triple integrals; polar, cylindrical and spherical coordinates; mass; reversing order of integration. (Omit the calculation of Riemann sums in 12.1, and omit moments and center of mass in 12.5.) Test 3 all problems.

13.1 - 13.5. Vector fields, line integrals, mass of a wire, conservative vector fields and potential functions, Green's theorem, curl and divergence. Test 4 problems 1, 2, 3.

10.5, 12.6. Parametric surfaces, tangent plane, surface area. Test 4 problem 4.

13.6 - 13.8. Surface integrals, flux integrals, Stokes' Theorem and Divergence Theorem. Recent homework.