Active Calculus

Preface Instructors! Read this!

This book is different. Before you read further, first read “Students! Read this!”.

Chapters 1-4 are designed to correspond to what is often called differential calculus. Chapters 5-8 correspond roughly to what is often called integral calculus, including chapters on differential equations and infinite series.

Among the three formats (HTML, PDF, print), the HTML is optimal for display in class if you have a suitable projector. The HTML is also best for navigation, as links to internal and external references are much more obvious. We recommend saving a downloaded version of the PDF format as a backup in the event you don't have internet access. It's a good idea for each student to have a printed version of the Activities Workbook, which is available on Amazon (Chapters 1-4²⁰, Chapters 5-8²¹) or as a PDF document by direct request to the author (boelkinm at gvsu dot edu); many instructors use the PDF to have coursepacks printed for students to purchase from their local bookstore.

The text is written so that, on average, one section corresponds to two hours of class meeting time. A typical instructional sequence when starting a new section might look like the following:

• Students complete a Preview Activity in advance of class. Class begins with a short debrief among peers followed by all class discussion. (5-10 minutes)

• Brief lecture and discussion to build on the preview activity and set the stage for the next activity. (5-10 minutes)


• Students engage with peers to work on and discuss the first activity in the section. (15-20 minutes)


• Brief discussion and possibly lecture to reach closure on the preceding activity, followed by transition to new ideas. (Varies, but 5-15 minutes)

• Possibly begin next activity.

The next hour of class would be similar, but without the Preview Activity to complete prior to class: the principal focus of class will be completing 2 activities. Then rinse and repeat.

We recommend that instructors use appropriate incentives to encourage students to complete Preview Activities prior to class. Having these be part of completion-based assignments that count 5% of the semester grade usually results in the vast majority of students completing the vast majority of the previews. If you'd like to see a sample syllabus for how to organize a course and weight various assignments, you can request one via email to the author.

Note that the WeBWorK exercises in the HTML version are anonymous and there's not a way to track students' engagement with them. These are intended to be formative for students and provide them with immediate feedback without penalty. If your institution is a WeBWorK user, we have existing sets of .def files that correspond to the sections in the text; these are available upon request to the author.

In the back matter of the text, you'll find answers to the Activities and to non-WeBWorK Exercises C. Instructors interested in solutions to these should contact the author directly.

You and your students can find additional resources in the GVSU Math 201 YouTube Channel²² and GVSU Math 202 YouTube Channel²³ where there are short video tutorials for every section of the text. Math 201 (GVSU's Calculus I) corresponds to Chapters 1-4 and Math 202 (GVSU's Calculus II) to Chapters 5-8.

The PreTeXt source code for the text can be found on GitHub²⁴. If you find errors in the text or have other suggestions, you can file an issue on GitHub, use the Feedback link²⁵ in the HTML version (found at the bottom left in the main menu), or email the author directly. To engage with instructors who use the text, we maintain both an email list and the Open Calculus blog²⁶; you can request that your address be added to the email list by contacting the author. Finally, if you're interested in a video presentation on using the text, you can see this online video presentation²⁷ to the MIT Electronic Seminar on Mathematics Education²⁸; at about the 17-minute mark, the portion begins where we demonstrate features of and how to use the text.

Thank you for considering Active Calculus as a resource to help your students develop deep understanding of the subject. I wish you the very best in your work and hope to hear from you.