Preface Students: Read this!
This book is different.
The text is available in HTML and PDF, both of which are free. If you are going to use the book electronically, the best mode is the HTML version. The HTML version looks great in any browser, including on a smartphone, and the links are much easier to navigate in HTML than in PDF. It also gives you access to the interactive elements of the text. Some particular direct suggestions about using the HTML follow among the next few paragraphs. It is also wise to download and save the PDF, since you can use the PDF offline, while the HTML version requires an internet connection.
This book is intended to be read sequentially and engaged with, much more than to be used as a lookup reference. For example, each section begins with a short introduction and a Warm-Up; you should read the short introduction and complete the Warm-Up prior to class, even if your instructor does not require you to do so. Most Warm-Up activities can be completed in 10-20 minutes and are intended to be accessible based on the understanding you have from preceding sections. There are not answers provided to Warm-Up activities, as these are designed simply to get you thinking about ideas that will be helpful in work on upcoming new material. There is great benefit in thinking about these questions before class, even if you are unsure about the correctness of your answers.
As you use the book, think of it as a workbook, not a worked-book. There is a great deal of scholarship that shows people learn better when they actively engage and struggle with ideas themselves, rather than passively watch others. Thus, instead of reading worked examples or watching an instructor complete examples, you will engage with Activities that prompt you to grapple with concepts and develop deep understanding. You should expect to spend time in class working with peers on Activities and getting feedback from them and from your instructor. Your goal should be to do all of the activities in the relevant sections of the text and keep a careful record of your work. Answers to the activities are not provided in the text, though you can get answers by asking questions in class or outside of class (such as in office hours).
Each section concludes with a Summary, which re-visits the Motivating Questions from the beginning of the section. After you have read the section and worked the Activities, you should attempt to answer these questions in your own words first. You can then expand answers to check your understanding. This is a good place to find a short list of key ideas that are most essential to take from the section.
At the end of each section, you’ll find written Exercises. These are designed to encourage you to connect ideas, investigate new situations, and write about your understanding. You are encouraged to work these exercises with others, focusing on your process rather than a final answer. Answers to selected exercises are provided in Appendix A. Worked solutions are not provided, so you are encouraged to discuss your thought process and reasoning for exercises with others, even if your final answer matches what is listed in the back. Your process and reasoning are the most important things for deepening your understanding and ensuring you can use important concepts on your own in the future, so use the answers as a guide, but not a replacement for engaging in the exercises with others.
The best way to be successful in mathematics generally and calculus specifically is to strive to make sense of the main ideas. We make sense of ideas by asking questions, interacting with others, attempting to solve problems, making mistakes, revising attempts, and writing and speaking about our understanding. This text has been designed to help you make sense of calculus in the context of the life sciences. We wish you the best as you undertake the large and challenging task of doing so!