# Active Calculus Multivariable

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

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

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

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.

I found this book very accurate with few errors

I don't imagine this book will need updating anytime soon, as Calculus will not be changing. Any updates will simply be to improve the activities, not the material itself.

The book is very clear and easy to understand. The author specifically avoids any confusing mathematical notation in an attempt to make the material accessible.

The book is very consistent.

This book does an incredibly good job of subdividing the various sections into subsections. The author of the book has his students read certain sections before class, as do I. It is very easy to tell students to read through this section of the book. Each subsection within a section is usually around a page.

I particularly like how one section flows into the next, telling one coherent story.

The online version of this text was very helpful to demonstrate visual elements of the material to the class. With multivariate in particular, the visual elements are complex and hard to draw for those of us with little drawing skill. It was helpful to have various graphs online to demonstrate ideas to the students.

I found no grammatical errors in my using of the book.

The author uses both male and female pronouns where applicable, though pronouns in general are not used often.

I have used this book for Multivariate Calculus and enjoyed it very much. It is important to stick to doing the activities and having students do the preview activities before class. Some students have trouble using this book as a standalone book, as it is very different from what they are used to. It may be helpful to pair it with a more traditional free textbook, such as APEX.

## Table of Contents

Preface

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

## Ancillary Material

## 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

### Authors

**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.