Active Calculus Multivariable

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Steve Schlicker, Grand Valley State University
David Austin, Grand Valley State University
Matthew Boelkins, Grand Valley State University

Pub Date: 2017

ISBN 13: 978-1-5486555-2-5

Publisher: Grand Valley State University

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Table of Contents

9 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 

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.