Preface Instructors: Read this!
This text contains most of the content you would expect from a typical first semester calculus course, though may be lighter in some areas (for example, there are no sections for implicit differentiation or related rates). It also contains content that you would not expect from a typical first semester calculus course. Chapter 1 contains pre-calculus content as well as an introduction to discrete-time dynamical systems, and chapter 3 contains some applications of derivatives in analyzing discrete-time dynamical systems. We approach Chapter 4 from the perspective of analyzing continuous-time dynamical systems (differential equations), and cover most of the standard first semester concepts in integration while doing so.
Among the two formats (HTML, PDF), 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, and Desmos interactives can be used directly from the HTML version. We recommend saving a downloaded version of the PDF format as a backup in the event you don’t have internet access. A PDF of just the Activities or a PDF of just the exercises can be made available by direct request of the author (jeffrey dot shriner at colostate dot edu).
The text is written so that each section corresponds to one to two hours of class meeting time. A typical instructional sequence when starting a new section might look like the following:
- Students complete a Warm-Up in advance of class. Class begins with a short debrief among peers followed by all class discussion. (5-10 minutes)
- Brief lecture and discussion to build on the Warm-Up and set the stage for the next activity. (5-10 minutes)
- Students engage with peers to work on and discuss the first activity in the section. (10-15 minutes)
- Brief discussion and possibly lecture to reach closure on the preceding activity, followed by transition to new ideas. (Varies, but 5-15 minutes)
- Possibly repeat with the next activity, and summarize section at the very end.
If the section was not completed, the next hour of class would be similar, but without the Warm-Up at the beginning of class.
There is a suite of Desmos activities 6 that can be used (or copied and modified) to accompany the text. They were created to be used for a final hands-on experience of important topics during a full class period after the relevant content has already been covered in class.
The Exercises in the text are meant to be conceptual problems for students to engage with in writing and orally. We recommend also using an online homework system (such as WeBWorK) to provide students more procedural practice in which they can receive immediate feedback.