Active Calculus 2.0
This textbook is intended for a two semester Single Variable Calculus sequence. I was mostly pleased with the textbook, although it lacks sections on the Mean value Theorem and parametrization/polar coordinates. However, the book is presented in both online and pdf formats. The online version is somewhat interactive, so one simply has to click on the appropriate section and the web browser is directed to the respective section of the text. On the other hand, the book includes a section on the Qualitative Behavior of Solutions of Differential Equations, as well as a section on Euler's Method.
Overall, the book could be used for a standard 2-semester Calculus sequence, however, the instructor will have to introduce additional material and proofs.
The concepts are presented clearly and accurately. I did not find any errors on concepts, notation, or grammar.
As a Calculus textbook, this book will remain relevant for generations to come. It mostly follows in the typical layout of a traditional Calculus textbook. It's online format, though, has opened interesting venues since the book contains links to Java applets using GeoGebra in the author's website. This ability makes it outperform paper or PDF texts. Additionally, the book can be downloaded and customized (if the instructor is experienced in web publishing).
The material is presented clearly. Each sections begins with "Motivating Questions" as a means to introduce the material. In general, I found this text to be less "wordy" than a traditional Calculus textbook. However, I found the lack of proofs to be a considerable weakness in the presentation. Calculus without proofs transforms from an exercise in logic to a belief system.
The structure throughout the textbook is very consistent. All sections are organized in the same format and the notation is very clear and consistent. The exercises are appropriate, although the problems at the end of the text are few.
The essential ideas of Calculus cannot be segmented, and this book succeeds in presenting the material very cohesively. However, the material is grouped in a traditional format, so the sections in any one chapter are relevant to each other.
Every section in the book has the same structure and organization. The sections begin with a "Motivating Question" followed by conceptual explanations. In may of sections there are "Preview Activities" and WeBWorK exercises at the end of the section. Each section is properly referenced to relevant chapters, sections, and graphs throughout the text, so a simple click on a link will open a window with the information pertinent to the material being presented. I found this to be very valuable.
The interface works well and the full online version is available on github. The only problem I found was my computer not being able to open an Java Applet in the author's website in one instance. On a different day, I was able to open the same applet without a problem.
I did not find a single grammatical error. While I may have missed a run-on sentence, nothing distracted my attention to recognize as an obvious grammatical flaw.
Calculus has been relevant for 400 years and will continue to be relevant for generations to come. No issues here.
I liked the presentation in general. This book has a lot of potential. Using WeBWork exercises is great because the students can practice concepts on their own textbook with immediate feedback. As mentioned earlier, lack of mathematical proofs is a serious omission for a well-rounded Calculus textbook, which this one can be. The hyper links and applets make this book an interactive tool that can be continuously improved to become a fully interactive Calculus website.