![]() ![]() ![]() (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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