Active Prelude to Calculus

This book is different. Think of it as a workbook, rather than worked-book.

Research shows people learn better when they interactively engage and struggle with ideas themselves, rather than passively watch others. Instead of reading worked examples or watching an instructor complete examples, Active Prelude engages students with Activities that prompt them to grapple with concepts and develop deep understanding. Students should spend time in class working with peers on Activities and getting feedback from them and their instructor. Each section begins with a short introduction and a Preview Activity; students should read the short introduction and complete the Preview Activity prior to class (and instructors should require this).

Students should read the Students! Read this! section; instructors should likewise read that section, as well as the Instructors! Read this!, both of which are in the preface.

Every student should acquire a copy of the Student Activities Workbook, which is available in low-cost print from Amazon or as a free PDF from the links below on the left. Many instructors also have their university bookstore print a coursepack from the PDF. Students should complete all of the activities in the relevant sections of the text and use the workbook to keep a careful record of their work.

There’s a related online resource that users absolutely shouldn’t miss: the MTH 124 playlist on the GVSU Math YouTube page. The 123 screencasts for MTH 124 correspond to chapters 1-5 and are listed in order by section number.

Instructors should visit the Instructors page to learn more about available supporting materials and to join the Google Group for Instructors.

Active Prelude to Calculus is designed as a college-level preparatory text for students who aspire to take calculus and who either need to take a course to ready them for calculus or want to do some additional self-study, especially students who will go on to study from Active Calculus Single Variable. The text is centered around about 120 activities designed for student engagement with core ideas. The HTML version of the text includes about 150 anonymous, interactive exercises; static versions of those problems are included in PDF and print.

Many of the core topics of the course are likely familiar to students who have completed high school. At the same time, we take a perspective that emphasizes each topic’s importance in calculus. The text requires students to engage actively with the material, to view topics from multiple perspectives, and to develop deep conceptual understanding of ideas. In Active Prelude, one of our top goals is to keep the focus narrow by centering the content on ideas most relevant for calculus. See more about the motivating forces behind the text in the Our Goals section of the text’s preface.