11 of 11 people found the following review helpful:
4.0 out of 5 stars
Excellent review aid for those with prior calculus experience, but with deficiencies that limit its value for newcomers., December 8, 2008
This review is from: Homework Helpers: Calculus (Homework Helpers) (Paperback)
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, should be able to begin a course requiring a calculus foundation. Although later augmentation with additional calculus topics will be required, depending on the course. Unlike some calculus books, the concentration here is on basic concepts, rather than on rigorous mathematics and proofs.
There are some deficiencies which diminish the value of this text as a supplement for newcomers to calculus.
The minor deficiencies occur in the depth and breadth of coverage, and in layout and design, An annotated bibliography, providing references where more detailed coverage of additional calculus topics might be found, would have been quite helpful. Here, the author provides neither the list of references she used in preparing this book, nor "pointers" to supporting and augmenting references. Neither beginning chapter objectives nor closing chapter summaries are provided, both would have been appreciated. The spacing between lines in a paragraph is frequently not maintained, particularly if a line contains certain mathematical constructs. This can occasionally be distracting.
The major defects occur in the technical editing, which was not as carefully done as might be hoped. These defects are shown as early as the first Chapter. For example, on page 18 the four quadrants of the Cartesian coordinate system are presented. These are inexplicably numbered in clockwise order, rather than counterclockwise order as appropriate. One of the answers in Lesson 1-3 is given as 2sqrt(6-1) + 1 while the correct answer is 2sqrt(6-x) + 1. As solutions are fully worked out, most errors in the problem solutions sets are obvious. However within text errors such as that on page 77 where the range of the arctangent function is given as [-pi/2,pi/2] when it should be (-pi/2,pi/2), i.e., endpoints excluded, or the quadrants error mention above, will not be obvious to first timers. For those refreshing their prior knowledge, these errors will, hopefully, be easily identified. However, for new learners who may not easily catch these mistakes and need reassurance that they understand the material, these errors may prove disconcerting.
Without the more than expected number of errors, this book would easily rate five stars. Even recognizing the errors, this is an excellent book for self-study for those with prior, or ongoing in-class, calculus experience. The author has the unique ability to clearly, concisely, and interestingly explain the core of the subject. For readers with prior calculus experience, most errors will be easy to catch, and even help to establish they are understanding the materials. For these readers this book can be easily completed in two weeks or less. For those using this in conjunction with an on-going class, obviously, more time will be required.
The move from calculus basics to application problems, particularly in the sciences, is substantial. Thus, while this book provides a strong foundation to build upon, exposure to further calculus topics and additional calculus problem-solving experience will be required to feel comfortable applying calculus to a broader range of subjects.
In conclusion, this is a book that can be highly recommend for self-study, for the quality and style of its writing, excellent core coverage, and its relatively low cost. The "bite-sized" sections make it particularly easy to stop at almost any point, without feeling you are pausing in the middle of the discussion of a new concept. However, the larger than expected number of errors would suggest its greatest value will be to those needing to refresh prior calculus experience or students currently enrolled in a calculus course, and not for those new to calculus and studying on their own.
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