Active Calculus - Multivariable

I want to first thank my family, Jane, Nixon, and Vivian, for their support of me during this and my too many other projects. I am also immensely thankful of my coauthor Mitch and our excellent workflow and cooperation which has served as a model for many others. I want to acknowledge my other colleagues, especially Jane Long, Jeremy Becnel, and Jacob Turner, who have encouraged me through this project and helped refine my crazy ideas. The Second Edition of ACM is much better because the authoring tools of PreTeXt have really delivered in helping authors write excellent materials without having to build everything themselves. In particular, I would like to thank Rob Beezer for his leadership of PreTeXt and Oscar Levin for the excellent work he has done on PreTeXt and the pretext-tools extension. Finally, I would like to thank SFA for giving me Faculty Development Leave to work on ACM half-time for the 24-25 academic year.

Few journeys are straightforward, and my path to the release of the 2nd edition of Active Calculus - Multivariable has been particularly winding. (Perhaps appropriate for a text that features representing curves with vector-valued functions!) I started drafting the first sections of what is now Chapter 13 while a faculty member at Washington & Lee University because I needed to teach some vector calculus in multivariable calculus. I met Matt Boelkins at a Project NExT reception at the Joint Mathematics Meetings, and he encouraged me to apply to the American Institute of Mathematics workshop on open-source textbooks to work on Applied Combinatorics. Next came an invitation to work on finishing my work on vector calculus to supplement Steve Schlicker’s work on the 1st edition. Tom Judson mentioned that he had this colleague Nick Long who was doing some interesting things with virtual reality for multivariable calculus and might make a good collaborator. That connection led us to releasing the vector calculus chapter in stages through a wonderfully productive collaboration. As Steve entered retirement and decided that further work on ACM was not high on his priority list, I was happy to have the opportunity to continue working with Nick on this 2nd edition, which has turned into a much larger revision than we originally imagined. I am thankful for how each of those folks helped move my role in this project forward, and especially to Nick for being a pleasure to work with.

I join Nick’s heartfelt thanks to the PreTeXt community for providing the tools to make this text possible. Rob Beezer’s foundational and ongoing work makes me wonder how little sleep a human needs to survive. Oscar Levin’s enthusiasm for expanding features and providing tools that make it feasible for a wide range of authors to write in PreTeXt has been instrumental particularly in making collaborative efforts such as ACM possible. Although the preview version of the 2nd edition of ACM benefits only slightly from David Austin’s PreFigure (static) graphics library, I am excited about how we will be able to bring a greater degree of consistency and polish to our static graphics before releasing the 2nd edition in final form. I am also incredibly grateful to David Austin and Kathy Yoshiwara for regular meetings as an OER author group. Their generosity in reading (and sometimes re-reading) sections of ACM as we worked through them has made me a better writer and editor, and this book has improved considerably because of their feedback.

This text is an extension of the single variable Active Calculus by Matt Boelkins. The initial drafts of this multivariable edition were written by Steve Schlicker; editing and revisions were made by David Austin and Matt Boelkins. David Austin is responsible for the beautiful full-color graphics in Chapters 9 through 11. Many people at GVSU have shared their ideas and resources, which undoubtedly had a significant influence on the product. We thank them for all of their support. Most importantly, we would like to thank the students who have used this text and offered helpful advice and suggestions.

In advance, we also thank our colleagues throughout the mathematical community who have or will read, edit, and use this book, and hence contribute to its improvement through ongoing discussion. The following people have used early drafts of this text and have generously offered suggestions that have improved the text.

Early HTML versions of this text were made possible only because of the amazing work of Rob Beezer and his development of PreTeXt. Dr. Schlicker’s ability to take advantage of Rob’s work is largely due to the support of the American Institute of Mathematics, which funded him for a weeklong workshop in Mathbook XML in San Jose, CA, in April 2016. David Farmer also deserves credit for the original conversion of the text from LaTeX to PreTeXt. The PreTeXt community continues to provide enormous support and capabilities to all of the authors as we continually strive to provide an excellent text while updating the utility of this resource.

We are interested in your suggestions for improvments to this text, including any errors or inconsistencies you may find. Please join the Active Calculus - Multivariable Google Group to see updates and provide feedback to the authors.

David Austin, Matt Boelkins, Steven Schlicker, Mitch Keller, Nick Long -2023.