Active Calculus – Multivariable

In case you hadn’t heard already, Steve Schlicker is retiring soon (Congrats!) and we have taken over managing and editing Active Calculus – Multivariable (ACM). A few years ago, we started writing material for a chapter on vector calculus topics which many of you have tried and tested. We have incorporated a lot of the feedback and made significant revisions to the materials on vector calculus which will now be included as Chapter 12 of ACM. While the previous versions of this material were rough in spots and sometimes were not parsed into pieces that were right for in class activities, our new presentation has been simplified and activities are more consistent in length and effort levels. Chapter 12 also includes the frequent use of Sage interactive elements when displaying graphics of math elements in 3D. In the summer 2023 edits, we have added WeBWorK and pencil and paper exercises to each of the twelve sections in Chapter 12.

The motivation and presentation of topics in Chapter 12 has been approached from the perspective of trying to measure a particular quantity, like the amount of vector field that flows through a surface or work done by a vector field while moving along a path. Many of these are rooted in physical measurements but the descriptions do not assume any physics background. Since vector calculus is a set of topics that has quite a variety coverage levels at institutions, we tried to make it possible to do surface level coverage or deeper discovery-based activities. In order to aid faculty in planning how they will use Chapter 12, we also have given a flow chart of dependencies for the twelve sections in vector calculus. We selected notations for vector calculus that emphasize the nature of what we are measuring and make notes or comments about other notations that students will see in other sources. For instance, line integrals of vector fields use the notation \(\int_C\vec{F}\cdot d\vec{r}\) to emphasize that we are looking at the accumulation (integral) of the dot product of our vector field with displacement.

ACM (as well as ACS) is now available on Runestone as well. As Matt included in his update post, you should check out all of the amazing features that come with hosting materials on Runestone. (ACM’s Preview Activities are not yet implemented using WeBWorK, but the WeBWorK exercises at the ends of sections can be assigned in Runestone.)

Over the next couple of years, Mitch and I will be working on edits to other parts of ACM including creating a solutions manual and updating other elements across ACM for consistency and easy of use (for students and faculty). Please join us in the ACM users Google Group to make any suggestions for corrections or improvements, as well as get updates on other elements of our work.


Mitch Keller and Nick Long

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