APEX Calculus
The text covers all necessary topics for Calculus I and II. However, no justification or proof for the derivatives of the natural exponential and natural logarithmic functions are provided. They are simply stated among the basic rules for differentiation without development. Most topics in Multivariable Calculus are included, with the exception of vector fields. No review of Precalculus topics is included, nor is any historical development of calculus. Conversational discussions of theorems are used in place of formal proofs in many cases throughout the entire text. An index is included, and the search function is accurate.
If the text is to be used for Calculus I and II only, I would rate its overall comprehensiveness at 4-5, based on the comments above. For Multivariable Calculus, I would rate it at 3.
For the most part, the accuracy of the mathematical content is excellent. In a careful reading of the Calculus I material, a few typographical errors and one mathematical error (which might also have been typographical) were found. Since there is no discussion of people in the text, it contains no content that I would construe as biased.
There is no topic in the text which would make the material outdated, though a lack of interactive apps, web links, and computer-generated graphics may make it appear less stimulating than the modern for-profit, online textbook. Updates may be made difficult by the choice of numbering definitions, theorems and key ideas from 1 to n throughout the text, rather than by chapter and number (e.g. Thm. 2.5).
The text is extremely readable for the first-time calculus student. My notes repeatedly include the words "clear", "understandable", and "straightforward". The explanations of the concepts of the limit, the derivative, differentials, integration, sequences, and series are conversational, accurate, and lucid. Applications are well-explained, though in some cases (e.g. the disk and washer methods of determining volumes) more and better graphs and pictures would be appreciated.
Notation and terminology are consistent.
For the most part, chapter sections are divided as expected for a calculus text. Section 6.1 is remarkably long, including not only integration by substitution, but trigonometric integrals as well. Institutions that include only basic u-substitutions in Calculus I and trigonometric integrals in Calculus II will need to divide this section. As noted earlier, the text is quite readable, and the division of chapters into sections, and further into segments of concept development, and examples are appropriate.
The organization of the text is logical and consistent, and its flow is smooth. As previously noted, theorems are not generally justified with formal proofs but with conversational discussions. Topics are ordered appropriately, except, in my opinion, for the presentation of the derivatives of exponential and logarithmic functions without background development.
Navigating by use of the table of contents, bookmarks, or by page number is error-free. Highlighting and "sticky notes" are available. An index is included, but the search tool is quick and easy to use. Graphs are clear. No other pictures or images are included, and no internet links are included (which could become outdated). If students/instructors choose to print a hard copy of the text, there is blank space at the bottom of each page for hand-written notes.
The only grammatical errors found (notably, all in section 2.1) were likely typographical. Sentence structure, choice of words, and punctuation were all very good.
This item is not very applicable to the text, as no mention of culture or ethnicity is made. A check of several examples and application problems that refer to people appear to refer to women as often as they refer to men.
Problem sets are included at the end of each section, and answers to selected problems (most of the odd problems) are found at the end of the text. However, the sets of problems are generally more limited that what is found in a traditional textbook, and answers are sometimes spare. (For example, proofs are "left to the reader".) No review sections or problem sets are included at the end of chapters.