When reviewing a general calculus text, the main question the reviewer needs to answer is “how is this book different from the existing mainstream choices?” The answer, in this case, is that the book is more ambitious and moves at a faster pace than most competing textbooks. It also makes a few unusual choices in the order in which the topics are covered.
Derivatives of functions are discussed very early, two or three weeks into the semester. This is before limits or continuity are covered. Even differential equations are (briefly) treated before continuity. Integration is started at the end of the first semester, and the Fundamental Theorem of Calculus and integration by substitution are squeezed in there.
The second volume contains all that you would see in Calculus II if taught from competing textbooks, plus deep incursions to Calculus III territory, such as early parts of multivariate calculus, polar coordinates, and vector-valued functions.
There are a bit fewer exercises than in other textbooks, (about 40 per section), but they still seem to be sufficient. As usual, the odd-numbered ones come with their numerical answers included.
So the book may be a good choice for you think that your students need a faster-than-usual pace, or if your students take only two semesters of calculus, but still need to know about multivariate functions. The book is by Freeman Custom Publishing, meaning that it is printed on demand.
Miklós Bóna is Professor of Mathematics at the University of Florida.