American Institute of Mathematics, 2018. — 308 p. — ISBN 1724366858.Active Calculus Multivariable is different from most existing texts in at least the following ways: The style of the text requires students to be active learners; there are very few worked examples in the text, with there instead being 3 or 4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus ideas. Each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class. There are several WeBWorK exercises in each section along with additional challenging exercises. Contents Multivariable and Vector Functions Functions of Several Variables and Three Dimensional Space Vectors The Dot Product The Cross Product Lines and Planes in Space Vector-Valued Functions Derivatives and Integrals of Vector-Valued Functions Arc Length and Curvature Derivatives of Multivariable Functions LimitsFirst-Order Partial Derivatives Second-Order Partial Derivatives Linearization: Tangent Planes and Differentials The Chain Rule Directional Derivatives and the Gradient Optimization Constrained Optimization: Lagrange Multipliers Multiple Integrals Double Riemann Sums and Double Integrals over Rectangles Iterated Integrals Double Integrals over General Regions Applications of Double Integrals Double Integrals in Polar Coordinates Surfaces Defined Parametrically and Surface Area Triple Integrals Triple Integrals in Cylindrical and Spherical Coordinates Change of Variables
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