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Read more about Active Calculus Multivariable

Active Calculus Multivariable

(1 review)

Steve Schlicker, Grand Valley State University

David Austin, Grand Valley State University

Matthew Boelkins, Grand Valley State University

Copyright Year: 2017

Last Update: 2018

ISBN 13: 9781548655525

Publisher: Grand Valley State University

Language: English

Formats Available

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Reviewed by James Collins, Assistant Professor, University of Mary Washington on 4/9/19

This book covers most areas of multivariate calculus. However, certain areas, such as Divergence Theorem, and Fundamental Theorem of Line Integrals is not included in the book. I am told it will be added in later additions though. read more

Table of Contents

Preface9 Multivariable and Vector Functions

  • 9.1 Functions of Several Variables and Three Dimensional Space
  • 9.2 Vectors
  • 9.3 The Dot Product
  • 9.4 The Cross Product
  • 9.5 Lines and Planes in Space
  • 9.6 Vector-Valued Functions
  • 9.7 Derivatives and Integrals of Vector-Valued Functions9.8 Arc Length and Curvature

10 Derivatives of Multivariable Functions

  • 10.1 Limits
  • 10.2 First-Order Partial Derivatives
  • 10.3 Second-Order Partial Derivatives
  • 10.4 Linearization: Tangent Planes and Differentials
  • 10.5 The Chain Rule
  • 10.6 Directional Derivatives and the Gradient
  • 10.7 Optimization
  • 10.8 Constrained Optimization:Lagrange Multipliers

11 Multiple Integrals

  • 11.1 Double Riemann Sums and Double Integrals over Rectangles
  • 11.2 Iterated Integrals
  • 11.3 Double Integrals over General Regions
  • 11.4 Applications of Double Integrals
  • 11.5 Double Integrals in Polar Coordinates
  • 11.6 Surfaces Defined Parametrically and Surface Area
  • 11.7 Triple Integrals
  • 11.8 Triple Integrals in Cylindrical and Spherical Coordinates
  • 11.9 Change of Variables

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About the Book

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; 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; the exercises are few in number and challenging in nature.

About the Contributors


Steve Schlicker is a mathematics professor at Grand Valley State University in Allendale, MI. 

David Austin is a mathematics professor at Grand Valley State University in Allendale, MI. 

Matthew Boelkins is a mathematics professor at Grand Valley State University in Allendale, MI. 

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