Preface Instructors! Read this!
This is the Second Edition of Active Calculus. Some of what follows regarding how to use this text mentions differences between the first and second editions. You can see a detailed summary of the biggest changes at https://activecalculus.org/acs1e-vs-acs2e/. The first edition remains available at https://activecalculus.org/single1e/.
This book is different. Before you read further, first read “Students! Read this!” More information for instructors can also be found at the home page for the text, at activecalculus.org generally, and especially on the instructors page.
Chapters 1-4 are designed to correspond to what is often called first semester differential calculus. Chapters 5-8 correspond roughly to what is often called second semester integral calculus, including chapters on differential equations and Taylor 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 is ideal (even essential) for each student to have a printed version of the Activities Workbook; free PDFs can be found at the home page for the second edition (scroll down in the left panel and look for links to “download PDF 1-4” and “download PDF 5-8”); many instructors use the PDF to have coursepacks printed for students to purchase from their local bookstore. Print versions of the workbook for this second edition of the text will be available for purchase beginning in January 2026.
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:
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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)
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Brief all-class discussion to build on the preview activity and set the stage for the next activity. (5-10 minutes)
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Students engage with peers to work on and discuss the first activity in the section. (15-20 minutes)
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Brief all-class discussion and possibly lecture to reach closure on the preceding activity, followed by transition to new ideas. (Varies, but 5-15 minutes)
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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 the other 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 has a WeBWorK server, 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. 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 Channel and GVSU Math 202 YouTube Channel 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 of the first edition; for this second edition, some of the video numbering in Chapter 3 won’t match exactly, and there are not yet videos for Chapter 8 of the second edition.
The PreTeXt source code for the text can be found on GitHub. If you find errors in the text or have other suggestions, you can file an issue on GitHub or email the author directly. To engage with instructors who use the text, we maintain a Google group and a blog; you can request to join the Google group via the link at the instructors page.
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.
