Matt Boelkins (Lead author and editor)

Digital versions PDF
Latex source Yes, by request
Exercises Yes, but see explanation below
Solutions No
Creative Commons Attribution-
NonCommercial-Share Alike
  • Two semester course in single variable calculus
  • Third semester multivariable calculus in beta release
  • Paperback version by Orthogonal Publishing for less than $20
  • Activity-based approach
  • Eight chapters, 523 pages
  • Activity workbook, 215 pages
  • Approximately four challenging exercises in each section
  • For more information and to download

Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in order to present the standard concepts and computational techniques of calculus. The student activities provide most of the material to be assigned as homework, but since the book does not contain the usual routine exercises, instructors wanting such exercises will need to supply their own or use a homework system such as WebWork. With this approach Active Calculus makes it possible to teach an inquiry based learning course without severely restricting the material covered. Although this book is new, it has been class tested by the author and his colleagues both at their university and elsewhere.

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