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Active Calculus 2.0

(9 reviews)

Matt Boelkins, Grand Valley State University

David Austin, Grand Valley State University

Steve Schlicker, Grand Valley State University

Pub Date: 2017

ISBN 13: 9781974206841

Publisher: Grand Valley State University

Language: English

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Reviewed by John Carter, Associate Professor, Metropolitan State University of Denver on 7/24/19

The text covers all of the core ideas one would expect in a standard 2 semester calculus course. The authors clearly prioritized readability over exhaustiveness, and may be seen as skipping/missing material depending on your priorities. For... read more


Reviewed by Steve Leonhardi, Professor of Mathematics and Statistics, Winona State University on 8/2/18

Reviewer’s note: Please read my “Other Comments” in section #11 first, where I’ve written most of my review, and then return here to read my condensed, individual section comments. Comprehensiveness: The text covers most areas and ideas that I... read more


Reviewed by Brian Katz, Associate Professor, Augustana College (IL) on 6/19/18

This text contains all of the core ideas that I would include in Calculus I & II. It is not trying to be a comprehensive tome, which is for the best, especially because it allows for a text that is readable for learners of Calculus, which is... read more


Reviewed by Cesar Martínez-Garza, Associate Professor, The Pennsylvania State University - Berks College on 2/1/18

This textbook is intended for a two semester Single Variable Calculus sequence. I was mostly pleased with the textbook, although it lacks sections on the Mean value Theorem and parametrization/polar coordinates. However, the book is presented in... read more


Reviewed by Erika Rappold, Instructor, Virginia Tech on 2/1/18

The text was fairly comprehensive. The first portion of the book, which is dedicated to differential calculus, was very thorough. However, the sections on integral calculus was lacking in some of the integration techniques and methods commonly... read more


Reviewed by Bethany Downs, Mathematics Instructor, Portland Community College on 6/20/17

The book covers all major topics of differential and integral calculus. However, the emphasis is on "big-picture" understanding of the topics and has relatively few (in comparison to other texts) formally stated theorems and even fewer proofs. ... read more


Reviewed by Carrie Kyser, Master Instructor, Clackamas Community College on 1/7/16

This book is thorough and up-to-date in all areas of a single-variable differential and integral calculus course. I have been using it in my courses for over a year now, and I haven't found it to be lacking any topic, theorem, or technique. It... read more


Reviewed by M. Paul Latiolais, Professor, Portland State University on 1/7/16

PLEASE BEGIN BY READING THE "OTHER COMMENTS" SECTION AT THE BOTTOM FIRST. It seems to cover all of what we need for the first two quarters of calculus except surface integrals, which we could add or move to the third term. read more


Reviewed by Milos Savic, Assistant Professor, University of Oklahoma on 1/12/15

I thought that the book was thorough in the subjects that were listed, including limits, derivatives, integrals, differential equations, and sequences and series. I would have liked a few chapters on multi-variable calculus, but that wish should... read more


Table of Contents

  • 1 Understanding the Derivative
  • 2 Computing Derivatives
  • 3 Using Derivatives
  • 4 The Definite Integral
  • 5 Finding Antiderivatives and Evaluating Integrals
  • 6 Using Definite Integrals
  • 7 Differential Equations
  • 8 Sequences and Series

About the Book

Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 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; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.

About the Contributors


Matt Boelkins, Professor, Department of Mathematics, Grand Valley State University. PhD in College Teaching of Mathematics, Syracuse University. 

David Austin, Professor, Department of Mathematics, Grand Valley State University.

Steve Schlicker, Professor, Department of Mathematics, Grand Valley State University. PhD, Northwestern University, specializing in Algebraic K-Theory and the Cohomology of Groups.