If you will pardon the pun, differentiating between calculus books is often a matter of picking rather fine nits of difference. That is not the case here; this book has some significant differences from the others.
On the positive side, there is no initial recapitulation of the topics of precalculus, which is something that I have long considered to be a waste of trees and ink. If you are going to use a book to learn calculus, start the process on page one. There is also only a trivial mention of the use of calculators and computers. I firmly believe that incorporating the use of symbolic computation software into calculus courses is a divergence with questionable gain.
The main negative criticism is that the title is accurate in that this is a book almost totally devoted to differential calculus. Integration is introduced only at the end and largely to illustrate the concept of the antiderivative and to reinforce the applications of the derivative. A second and companion book covering integral calculus has also been published so this is not a major criticism. However, having to purchase two books to cover the main areas of calculus is something that many will dislike.
In the area of the “viewed positively by some and negatively by others” is the practice of moving the technical details of the concepts to internal appendices that appear right after the chapters. This will allow the details to be skipped if desired but others would prefer to see them incorporated into the explanations of what is actually being done. Exercises are given at the end of the sections with answers to the odd-numbered ones included in an appendix at the end of the book.
The book also comes in a PDF form with embedded links to online instructional videos of an instructor describing the concepts with chalk and an old-fashioned chalkboard. The videos are not professionally made; they are basically what an instructor would do in writing and talking. Some editing could have been done; for there are segments where all that is happening is that the instructor is erasing the board. The “patience for seven seconds” rule of online action will be sorely and repeatedly tested. This patience will also be tested while the videos are downloaded; I had to wait several minutes for the videos to completely download so that they could play. My examination was done using an academic internet connection so this would be what most students students would experience. The videos cover main concepts as well as key examples to further illustrate the concepts.
If your interest is solely in teaching or learning differential calculus, then this book has many solid points and would meet your needs. However, I personally cannot see where the market is for this restricted presentation of calculus, most people would need to purchase the second book as well.
Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.