# Math 206 (Multivariable Calculus): old exams

Term Date Instructor Topic(s) Text Sections Solutions
W14 02/07/14 Nelson functions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot products, cross products (H-H) 12.1-12.6, 13.1-13.4 yes
W14 03/14/14 Nelson partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiability, critical points, optimization (H-H) 14.1-14.8, 15.1-15.2 yes
F13 09/27/13 Nelson functions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot products (H-H) 12.1-12.6, 13.1-13.3 yes
F13 11/01/13 Nelson cross products, partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiability (H-H) 13.4, 14.1-14.8 yes
F13 12/13/13 Nelson Final: all from 09/27 and 11/01 exams plus critical points, optimization, Lagrange multipliers, double integrals, iterated integrals, parameterized curves, motion, vector fields, line integrals (H-H) 12.1-12.6, 13.1-13.4, 14.1-14.8, 15.1-15.3, 16.1-16.2, 17.1-17.3, 18.1-18.2 yes
W13 02/01/13 Weiss vectors, lines, planes, surfaces, parametrizations, dot and cross products, limits, level curves, differentiation (Barr) 1.1-1.3, 1.5-1.9, 3.1-3.2, 3.4-3.5 yes
F12 10/05/12 Weiss vectors, lines, planes, surfaces, parametrizations, coordinate systems, dot and cross products, limits, level curves, differentiation (Barr) 1.1-1.9, 3.1-3.2, 3.4-3.6 yes
F12 11/09/12 Weiss directional derivatives, div, grad, curl, local extrema, optimization (Barr) 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4-4.5 yes
F12 12/11/12 Weiss Final: all from 10/05 and 11/09 exams plus paths, arclength, line integrals, double integrals, triple integrals, surface area, surface integrals, change of variables, fundamental theorem for path integrals, Green’s Theorem, Stokes’s Theorem (Barr) 1.1-1.9, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4-4.5, 5.1-5.8, 6.1-6.2, 6.4 yes
W12 02/10/12 Nelson functions of two variables, quadric surfaces, vectors, dot product, projections, cross product, lines, planes, vector-valued functions (Barr) 1.1-1.3, 1.5-1.9 yes
W12 03/14/12 Nelson graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivative (Barr) 1.10, 3.1-3.2, 3.4-3.6, 4.1 yes
W12 04/13/12 Nelson Final: all from 02/10 and 03/14 exams plus local extrema, paths, arclength, line integrals, double integrals, fundamental theorem for path integrals, Green’s Theorem (Barr) 1.1-1.3, 1.5-1.10, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4, 5.1-5.3, 6.1-6.2 yes
F11 10/07/11 Nelson functions of two variables, quadric surfaces, vectors, dot product, projections, cross product, lines, planes, vector-valued functions, derivatives and motion (Barr) 1.1-1.3, 1.5-1.10 yes
F11 11/11/11 Nelson graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivative, divergence, curl (Barr) 3.1, 3.2, 3.4-3.6, 4.1-4.2 yes
F11 12/13/11 Nelson Final: all from 10/07 and 11/11 exams plus local extrema, paths, arclength, line integrals, double integrals, fundamental theorem for path integrals, Green’s Theorem (Barr) 1.1-1.3, 1.5-1.10, 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4, 5.1-5.3, 6.1-6.2 yes
W11 02/11/11 Ross (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity; level sets, limits, partial derivatives (Barr) 1.1-1.3, 1.5-1.10, 3.1, 3.2, 3.4 yes
W11 03/18/11 Ross (Exam 2) partial derivatives, chain rule, gradient, directional derivative, Taylor polynomials, use of Maple to find and evaluate partial derivatives in assembly of Taylor polynomials through degree three, local max, min, and saddle points, second derivative test (Barr) 3.6, 4.1, 4.3-4.4 yes
F10 10/08/10 Ross (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity (Barr) 1.1-1.10 yes
F10 11/12/10 Ross (Exam 2) level sets, limits, partial derivatives, Jacobian, total derivative, chain rule, gradient, directional derivative, divergence, curl, Taylor polynomials, local extrema (Barr) 3.1, 3.2, 3.4-3.6, 4.1-4.4 yes
F10 12/16/10 Ross (Final Exam) all from 10/08 and 11/12 exams plus paths, arclength, line integrals, double integrals, surface integrals, fundamental theorem for path integrals, Green’s Theorem, Divergence theorem, Stokes’s Theorem (Barr) 1.1-1.10, 3.1, 3.2, 3.4-3.6, 4.1-4.4, 5.1-5.3, 5.5, 5.6,
6.1-6.4
yes
W10 02/05/10 Haines vectors, lines, planes, surfaces, calculus of vector-valued functions,
dot and cross products, open and closed sets, linear transformations,
quadratic forms, limits, continuity, partial derivatives
(Barr) 1.1-1.10, 2.1-2.5, 3.1-3.4 no
W10 03/12/10 Haines derivatives, chain rule, gradient, divergence, curl, Taylor’s theorem,
local extrema, paths, arclength, line integrals, double integrals, triple
integrals
(Barr) 3.5-3.6, 4.1-4.4, 5.1-5.4 no
W10 04/15/10 Haines Final: all from 02/05 and 03/12 exams plus surface area, surface integrals,
path integrals, change of variables, Green’s Theorem, Divergence Theorem,
Stokes’s Theorem
(Barr) 1.1-1.10, 2.1-2.5, 3.1-3.6, 4.1-4.4, 5.1-5.8, 6.1-6.4 no
F09 10/09/09 Salerno vectors, lines, planes, surfaces, calculus of vector-valued functions,
dot and cross products, open and closed sets, linear transformations,