Active Calculus

Matt Boelkins (Lead author and editor)

Digital versions HTML and PDF
Latex source Yes, by request
XML source Yes, at GitHub
Exercises Yes, but see explanation below
Solutions Yes, available to faculty upon request to the author
License Creative Commons-Attribution-Share Alike
  • Two semester course in single variable calculus
  • Third semester multivariable calculus also available from
  • Paperback version for less than $21
  • Activity-based approach
  • Eight chapters, 683 pages
  • Activity workbook, ~200 pages each (one for ch 1-4, one for ch 5-8)
  • Approximately four challenging exercises in each section along with more routine WeBWorK exercises
  • Online homework (WeBWorK compatible, use as is or customize) mapped to textbook available on Edfinity for $14 to $29/student/term.
  • For more information and to download PDF or to access HTML

Rather than detailed explanations and worked out examples, this book uses activities intended to be completed by the students in order to develop the standard concepts and computational techniques of calculus. The student activities offer structure so that instructors can interactively engage students during class; it’s also possible to assign select activities as homework. In addition to a modest number of more routine anonymous WeBWorK exercises in each section, the text includes 3-4 challenging problems per section. Instructors wanting a more extensive collection of exercises will need to supply their own or use an online homework system such as WeBWork. Active Calculus makes it possible to teach an inquiry-oriented or active learning course without severely restricting the material considered. The book has been publicly available since 2012 and has been used throughout that time at Grand Valley State (the authors’ institution) and for several years at numerous other colleges and universities.

From the preface:

Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore. Following key activities or examples, the presentation normally includes some overall perspective and a brief synopsis of general trends or properties, followed by formal statements of rules or theorems. While we often offer a plausibility argument for such results, rarely do we include formal proofs.


  1. Understanding the Derivative
  2. Computing the 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