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...Cedar crest college calculus iv lecture notes author e mail address james hammer jmhammer cedarcrest edu july preface this is meant as a teaching aid it can be freely distributed and edited in any way for copy of the lt x document please email these are adapted from stewart s early transcendentals eighth edition ii contents vectors geometry space operations points equations cylinders quadric surfaces vector functions curves derivatives integrals arc length curvature normal bi motion velocity acceleration partial several variables domain range graphs level limits continuity first order higher tangent planes linear approximation chain rule implicit dierentiation directional gradient maximum minimum values local extrema iii absolute lagrange multipliers multiple double over rectangle volumes iterated general regions type change polar coordinates crash course with triple cylindrical spherical fields line plane fundamental theorem green curl divergence forms parametric their areas surface r...