![]() ![]() MULTIVARIABLE CALCULUS PLUSLocal extrema, paths, arclength, line integrals, double integrals, tripleįinal: all from 02/05 and 03/12 exams plus surface area, surface integrals, Quadratic forms, limits, continuity, partial derivativesĭerivatives, chain rule, gradient, divergence, curl, Taylor’s theorem, Vectors, lines, planes, surfaces, calculus of vector-valued functions,ĭot and cross products, open and closed sets, linear transformations, (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 (Exam 2) level sets, limits, partial derivatives, Jacobian, total derivative, chain rule, gradient, directional derivative, divergence, curl, Taylor polynomials, local extrema (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity (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 (Exam 1) geometry of R^n, quadric surfaces, dot & cross products and applications, planes, lines, path parametrization and velocity level sets, limits, partial derivatives ![]() ![]() Graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivative, divergence, curlįinal: 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 Graphs, level sets, vector fields, limits, continuity, partial derivatives, total derivative, chain rule, gradient, directional derivativeįinal: 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) 3.1-3.2, 3.4-3.6, 4.1-4.2, 4.4-4.5įinal: 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 Vectors, lines, planes, surfaces, parametrizations, coordinate systems, dot and cross products, limits, level curves, differentiationĭirectional derivatives, div, grad, curl, local extrema, optimization Vectors, lines, planes, surfaces, parametrizations, dot and cross products, limits, level curves, differentiation Partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiability, critical points, optimizationįunctions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot productsĬross products, partial derivatives, local linearity, gradients, directional derivatives, chain rule, second-order partial derivatives, differentiabilityįinal: 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 Functions of two and three variables, graphs, surfaces, contour diagrams, limits, continuity, vectors, dot products, cross products ![]()
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