Most helpful critical review
12 of 18 people found the following review helpful
Very substandard text, although the idea is good
on April 20, 1999
I've actually used this as a textbook for a class taught by one of the book's writers, and although the instructor himself is brilliant--one of the best teachers I've ever had--the text is absolutely horrendous. The professors who put the text together are opposed to the idea that a book should be based entirely on formulas. Furthermore, they detest the fact that most books give a few example problems in the text upon which EVERY PROBLEM that a student encounters in the excercises will be based. Thus, the teachers decided to write a book wherein hardly any procedural (as opposed to conceptual) examples are given, and which is composed mostly of text. In this way, the teachers hoped to create a MENTAL CONCEPT of the mathematical ideas that are presented. As an added bonus to this tactic, the book is able to introduce a variety of subjects that are normally addressed in a traditional calculus course, since the text focuses primarily on concept rather than implementation. I wholeheartedly agree with the intentions of this book; the execution of these intentions, however, is tremendously disappointing.
In trying to create a mental concept of the mathematics WITHOUT basing that concept on formulas that a student can blindly apply, the writers have intentionally neglected to give the formulas for many important calculus operations. They describe the CONCEPTS behind the equations and the operations only, hoping that the students will be able to figure out what the formulas are themselves; only at later points in the text do they give the actual formulas (sometimes the way they present the formulas are so confusing that you'd wish they hadn't given them; a supreme example of this is their discussion of the formula for integration by parts). Paradoxically, therefore, by trying to form a concept of calculus that does not rely on formulas, the writers have neglected to COMPLETE the concept that they attempt to present, for without discussion of the formulas, the concepts are incomplete, in my opinion.
While I do not necessarily disagree with the idea of having the students figure out the formulas for themselves (after all, it makes them think very seriously about the subject matter) the student is simply not given enough information in the book to be able to do so. Half of the students dropped the class I'm taking now, and of those I talked to, most dropped the class because they were not able to solve the problems with the information they were given in the text (of course, they perceived their incapability as arising from their own failures, which is probably not the case).
Moreover, while I also support the idea of having a book that does not rely on examples as the primary teaching tool, the fact that procedural examples are almost completely omitted is detrimental to the book's efficacy. Examples are helpful in that they show the student how to think mathematically in order to solve certain problems. Thus, without examples, the student often does not know how to approach a problem encountered in the excercises, making it very difficult to tackle them.
Finally, the problems themselves: the amazing majority of the problems have more than one step; there will be a 1.a, 1.b, 1.c, etc. However, each of these sub-problems will consist of at least four computational steps of considerable complexity, so the problems are INCREDIBLY complex, long and tedious (at least I, and the other people I work with, think so). These multi-stepped problems are also very difficult because they require the student to incorporate methods that were not adequately explained, so it takes even longer to solve them. Then, as if this weren't enough, the problems are VERY poorly worded. It is very difficult to figure out what the problem is asking the student to do; sometimes my professor, who had a hand in writing the book, will not know what a problem is asking for (hopefully he did not write the ones he does not himself understand). All in all, therefore, the problems are also seriously defective.
Were these professors to seriously revise this book, it is likely that it could become one of the best textbooks on calculus available. In its present form, though--despite the fact that the intentions of the book are good--the book is completely inadequate for its task.