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Schlicker S., Austin D., Boelkins M. Active Calculus Multivariable

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Schlicker S., Austin D., Boelkins M. Active Calculus Multivariable
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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