Over the past year, we have been busy working on what we plan to release as the 2nd edition of Active Calculus – Multivariable (ACM) in time for Fall 2026 classes. This post provides an update on our progress and plans, plus an invitation to interested instructors to pilot the updated text starting this fall.
To summarize this post: The new 2nd edition of ACM has been substantially reorganized, includes some new content, has integrated SageMath graphics throughout, and will only be available in electronic HTML form for the 2025–26 academic year for anyone interested in teaching from the 2nd edition in a pilot setting. The first edition will remain fully available for the foreseeable future. Read on for more detail.
History and 2nd Edition Overview
The 1st edition of ACM consists of chapters 9–11, written by Steve Schlicker, and chapter 12 on vector calculus, which we wrote. Steve’s chapters were originally written in LaTeX and designed for print/PDF output. PreTeXt enabled the HTML version that most now use, but these chapters have not had a graphics update to enable interactive 3D graphics from SageMath, which we used extensively in chapter 12.
Since Steve is now retired, we have taken over responsibility for the entirety of ACM. As we considered refreshing the graphics and other feedback from instructors, we decided that a 2nd edition that makes more significant revisions was an appropriate approach. The 1st edition will remain available on activecalculus.org, so instructors who do not wish to switch to the 2nd edition will not need to do so. (You will need to update links to point to the 1st edition after the 2nd edition is released, however.) Our focus from this point forward is on the 2nd edition, so typos reported in 1st edition text will only be fixed if that text also appears in the 2nd edition. However, we are happy to accept pull requests on GitHub if folks want to send them to fix typos in the 1st edition.
We have posted a separate page detailing how the 2nd edition will differ from the 1st edition. The 2nd edition of ACM has evolved because in reality, “multivariable calculus” can mean one of three different courses: one that follows chapters 9–11 of the 1st edition and omits vector calculus entirely; one that introduces students to line integrals, the Fundamental Theorem of Calculus for Line Integrals, and Green’s Theorem; and one that proceeds through all of that material plus Stokes’s Theorem and Gauss’s Divergence Theorem. As such, the extent to which certain topics in the new chapters 9–12 are necessary varies depending on the course’s final destination.
New for the 2nd edition of ACM will be an annotated instructor’s version, which is currently available in preview form. This version will not contain any answers or solutions that are not in the student-facing version. However, the start of most sections will contain notes for instructors about where a section’s content is used later on and how to move through a section more quickly, if needed. Occasionally, a note will appear in the margin of the instructor’s version that either expands on the notes at the beginning of the section or lets instructors know that there’s information in those notes relevant to that part of the text. We are still organizing this material, but the new Section 9.7 shows the structure.
Timeline for 2nd Edition
Instructors who are curious about the 2nd edition can see a preview. Throughout July 2025 and the first half of August 2025, further edits will be made to the flow of the writing and formatting of the contents, but the table of contents and structure of discussion and activities will not see significant changes before the Fall 2025 semester starts.
Throughout the 2025–26 academic year, updates will continue to be made to the version of the 2nd edition posted at this location as typos are caught and corrected. Any significant changes will be announced on our Google Group. Instructors interested in teaching from the 2nd edition or participating in a group that reads and gives feedback on it during this academic year should join the Google Group and see the pinned post for instructions on how to contact Nick.
During the 2025–26 academic year, we will not have a PDF version of the 2nd edition available. What solutions have been written can be provided to instructors as a PDF, just as we have done with the 1st edition. However, some solutions still need to be written as the semester goes along. (This would be a great way to give back to our open-source community if you’re interested! Join the ACM Google Group to keep up-to-date on progress and to discuss how to contribute.) An activities workbook will also not be available for Fall 2025. However, PreTeXt support for worksheets that can be printed from the browser has made significant progress, and we intend to have this available for the 2nd edition as a fill-in measure. (Look for further guidance on how to use this feature in August, once we enable it on the preview version of the 2nd edition of ACM. This feature is also coming to the 2nd edition of Active Single, which Matt posted about recently.) For Fall 2026 classes, we do intend to have a PDF/print version available as well as a PDF solutions manual for instructors and a PDF/print activities workbook.
You will likely notice that the 2nd edition needs additional exercises. Our first priority is to solidify and polish the narrative and activities for the changes in the 2nd edition before doing any additional work on exercises. Many sections already have WeBWorK and pencil and paper exercises. For sections with minimal exercises, we recommend the many publicly-available open resources to select computational and conceptual exercises that fit your needs for the time being. In particular, we recommend exercises from APEX Calculus or WeBWorK’s Open Problem Library in addition to problems from other well-known textbooks. Because the depth of coverage differs across the many different versions of multivariable calculus courses, you may also consider using activities not covered in class as excellent conceptual homework problems.
We are excited to share the finalization of the 2nd edition of ACM with the community over the coming year!
Nick Long and Mitch Keller
