Homework Helpers: Calculus

I took calculus over 40 years ago and have found this book great for regaining an understanding of the subject. The book is very good because it is clearly written and interesting. Just one gripe. Although mathematics is an exact science, the author implies that one can numerically prove a limit, in the case where both the numerator and denominator approach 0 (Lesson 5.1). Fortunately, I was patient ; because about 130 pages later, she covers L'Hospital's Rule (Lesson 12-2). She should have mentioned that the numerical solution was a stopgap and that she would cover the exact solution in Lesson 12-2.

This is an excellent review aid or supplement, although the title "Homework Helper" is a misnomer. The book concentrates on important "need to know" concepts, while generally skipping the "nice to know" ones. As expected in a book this small, both breadth and depth of coverage are limited. This is a strength and a weakness. The smaller size means the book keeps its focus on key concepts, i.e., the foundations of introductory calculus. It also means the book is easier to hold and use than typically much more massive introductory calculus texts and, of course, it means the book can be completed in a much shorter time. However, it also means calculus coverage is significantly limited. Thus, while this is a nice text to help establish a solid calculus foundation, it would be significantly less value as a "homework helper". If extended homework help is needed, more comprehensive problem-solving supplements, particularly those containing a greater variety of problems and solutions, would be required. Over a quarter of the book is devoted to an introductory precalculus review, which includes linear, quadratic, exponential, logarithmic, and trigonometric functions, and the difference quotient. Even though the book presents introductory material in preparation for calculus, readers will need some prior experience with algebra, as terms and symbols are occasionally introduced without prior explanation, e.g., the symbol for union in lesson 1-2. Following the precalculus introduction, the book moves on to limits, continuity, and differential and integral calculus. Of the material devoted to differentiation and integration, about 80% covers differential calculus. The material is presented along with examples that include all key solution steps. Readers may want to try solving the in-text examples before seeing the author's solutions. This is probably a good idea both to insure the concepts just presented were understood, but also in view of the relatively limited sets of additional practice problems. Each chapter is divided into "bite-sized" sections of just a few pages each with, typically, two to five practice problems per section. While this may seem a relatively small number of problems per section, the problems are generally well-chosen to reinforce the main concepts and the sections themselves are small. Appropriately, solutions to all practice problems are provided. The author's writing style is "user-friendly" and the material is presented in a well-organized fashion that reduces those "what did she just say" moments, making this a calculus book that is enjoyable and easy to read. The book provides a relatively quick introduction to basic precalculus and calculus terms and concepts. It is particularly well-suited to serve as a "no fluff" review of the basics for those with previous calculus experience, even if in the somewhat distance past. It covers introductory calculus, primarily differential calculus, in adequate detail so that readers, sho

Originally, I rated this item as 4 stars, but as I've actually used it for my class, I now rate this item as 5 stars. This is a great book for learning calculus. It's very good about explaining concepts in much better detail than my text book, or my professor. I especially found the sections on limits and continuity helpful. I highly recommend this book for anyone learning or reviewing calculus.