Customer Reviews

Calculus, 8th Edition

5 star:		(9)
4 star:		(8)
3 star:		(9)
2 star:		(3)
1 star:		(3)

 

 

When I was 15, this was the book that I taught myself Calculus from. Now that I'm a professor, this is the book that I use to teach Calculus. In this review I will give the pros and cons of using this book from both a student's and teacher's perspective.

A Student's Perspective

When learning Calculus, I read every page of this book and did every problem. Students will complain that examples and discussion in each chapter seem inadequate to do all of the problems at the end of the section. I feel that this is part of the design of this book. The problems are intended to be instructional. Indeed this book has a corresponding student solutions manual that helps students to check their work and see if they are "getting it". The problems in the book range from extremely elementary up to moderately challenging. If, instead of instructional problems, this book had given enough examples and text to explain all of the ideas, it would have to be over 2000 pages long. Students should think of the problems in each section as being part of the instruction instead of problems to test previously acquired skills.

When teaching myself from this book, I was able to do all but a few of the problems. Granted I had to spend a considerable amount of time struggling with some of them, but for a talented and dedicated student, every problem in the book is accessible and most are extremely instructive. I should also mention that the book is very well written. Having never actually read a math text book from cover to cover back then, I didn't have too much problem tackling this one. It's very rare that a math text be thorough, informative, and easy to read. This one manages to be all three.

The main drawback of the book is that the students solutions manual is absolutely essential and will be an additional cost. Even if money is tight, as it often is for students, make certain that you buy this manual.


A Teacher's Perspective

As I said above, the problems in this book are intended to be instructional. For this reason it is imperative that a teacher not just lecture from the text and examples, but dig into the problems and carefully choose the most instructive ones for in-class presentations or homework assignments. If you only lecture from the text and examples, you'll only be teaching your class a small fraction of what this book has to offer. If you use this for a course, do as many examples as you have time for. I dedicate one lecture per week to doing nothing but working problems. It might be best to work though the even numbered problems for your class, as the odd numbered ones all appear in the student solutions manual.

The layout of the book is a little bit flawed. This book is aimed at three semester Calculus sequences in state universities and liberal arts colleges. It is not a meant to challenge exceptionally bright students. For this reason parts of chapter 2 seem inappropriate- specifically the sections on the rigorous definition of limits and continuity. If you're teaching a calculus course to non-math majors at modest universities, why would you force students to wade through the muck of mathematical proofs of continuity and existence of limits? In my experience the students absolutely hate this part of the course and gain nothing from it. If you have a few bright kids in your class, you can work with them on an independent study of the more theoretical areas such as this. Also, there are few chapters in the book that are out of place. For example, the chapter on integrating to find the volumes and surface areas of solids of revolution comes way too early while the chapters on transcendental functions, inverse functions, and L'Hopital's Rule come way to late.

Overall the presentation of new ideas is very good in this book, with one notable exception. The book introduces the natural logarithm (ln x) through it's definition in terms of the antiderivative of 1/x. From there it uses the inverse function theorem to derive the exponential function and it's properties. I, and my students, find it more natural to define the Euler number, e, in terms of continuously compounded interest, and then derive the natural logarithm and its properties from the exponential function. It's a matter of taste, but the later approach seemed more lucid to my students. You may want to supplement your lectures in this way.

One of my favorite features of this book is that not only does it cover all the material from a traditional three semester Calculus sequence, but it also has chapters on analytical and numerical solutions to ordinary differential equations as well as an appendix containing more theoretical material for brighter students. If you find yourself teaching an unusually talented bunch of kids, the appendix on mathematical induction as well as the aforementioned sections on ODEs and proofs of continuity and existence of limits can make great supplements to challenge those eager to dive into mathematics.

It's hard to believe that this puzzling, error-filled book is in its 7th edition.

I've been using the book for two semesters in a distance learning program. In this setting, where the reader needs to learn from the book rather than from an instructor, the book is inadequate. It's single strength - brevity - doesn't make up for its weaknesses: mystifying explanations, worked examples that omit important steps, and errors. Many times, this book made me laugh out loud when, after literally hours of effort, I finally understood what the authors were trying to communicate. There is no way I could have completed my classes had I not had Swokowski to refer to.

Beyond these weaknesses, the book is loaded with throw-away Horatio Algerisms ("Skill at this, like most worthwhile activities, depends on practice.") and hokey humor ("We have no desire to let this text suffer from the standard ailment of older texts, called `revisionitis.'") These give the book a dated, musty feel: it's as if you are looking back at how calculus used to be taught 40 years ago.

Finally, six weeks into the first semester, the binding failed, converting the book into an expensive, 900-page, loose-leaf folder. Overall, not a book I enjoyed spending time with.

The professor from the University of Wisconsin makes good points. We have long since adopted this textbook at the University of North Carolina, where I have taught from this text for about 5 years. This text appeals to the professional mathematician in an almost irresistible way as it elucidates clearly those aspects of basic calculus which appeal to US as mathematicians---namely, there is a fairly rigorous discussion of Riemann integration, there is dogged attention to historical factoids, and so forth---aspects lacking from other texts. However, my students are universally non-plussed. Every semester, my evaluations are CHOCK full of students who specific comment that they didn't like their text and were actually using a different text that they checked out of the library. That, unfortunately, is the proof in the pudding. My students dislike the text, universally. In the book's favor however, as mentioned by the professor from Wisconsin, the topic order is very logical, the book is as small as it can be, it does its best to take some advantage of calculator technology, and treats most topics rigorously. I am sure however that the advantages of this book are largely lost on the students. I myself would advocate for a different text, if it were up to me. I have seen no reason to justify this fairly expensive book in lieu of one of the somewhat cheaper standard texts.

There are two types of electronic suppliments that come with this book. One is MyMathLab and the other is MathXL. The geniuses at Pearson decided to make them completely incompatible. So, if you get one code, it won't work with the other system.

Geniuses.

The ISBN for MathXL is: 0-13-142924-8
The ISBN for MyMathLab is: 0-13-230811-8

This is a good book for calculus. I usually go to class and do not undestand the professor because he speaks a different language then come home and figure it out from the book. The solutions manual is a must have for this course unless you have an excellent teacher or tudor. I find it helpful to check my problems half-way through completing them to make sure I am on the right track. And when I do not understand the text book instructions, the solutions manual usually puts me on track.

Ok, let me start by stating that because this is "the shortest mainstream calculus" text out there, it does _not_ mean this has less value. It would _seem_ to be so, but this is the exception to the rule where shorter texts means dumber texts.
Explaining mathematics is a bit of an art: you have to choose in what sequence things are to be layed out to the reader, so this means you have to choose how you will relate the explanations to one another. The Purcell I read (the 1st edition - it was my dad's) is quite masterfull at that. Often, when my college standard text got the explanations too verbose and confused, I looked for my Purcell copy and there it was, crystal clear: short, mathematically rigorous, to the point.
(I don't give 5s to any but very exceptional books)

I am in something of a unique position to critique this book. You see, I have, due to the fact that I attended different schools and therefore had different teachers for Calculus I, II, and III, been forced to buy three different ... calculus textbooks.

I feel that this book in many ways is the best. Keep in mind, however, that this isn't saying much. For the most part, calculus (and math in general) textbooks are somewhat difficult to learn from. This stems from the fact that we students like to see lots of worked out example in order to "get" it (buy Schaum's outline or REA's Problem Solver for lots of worked examples). In many cases, a calculus book like this will give you, perhaps, one example for a given procedure and leave it to you to deduce the rest.

Still, I like the fact that this book contains the material for Calc. I, II, and III. If nothing else, it saves us some money.

One final comment: as another reviewer on amazon has already noted, the binding on this book is quite poor. I have seen many other students in my class with books in which the pages have started falling out. Perhaps Prentice Hall should provide us with a better binding for a hundred bucks.

I was looking at calculus books for my mathematics department at the University of Wisconsin, and was delighted to find this book. It's concise without being overwhelming, accurate without being too wordy, and the topics are arranged in the order in which they should be taught. I will definitely recommend this book to my department for adoption!

To provide a bit more detail: First of all, at 800 pages, this book is one of the "leanest" on the market; the authors have clearly made an effort to stick with the essentials. Still, the instructor can choose to skip some of the harder topics or proofs; the book can be used with technology; etc. Most importantly, the authors don't "lie" to the reader: When some proof is too hard for this book, they will give you some intuition and then send you to a more advanced book to see the "real" proof. Finally, the book is written very carefully, no tricky details are glossed over or swept under the rug.

Overall, this is a great book! Try it!

This is probably a good reference for advanced math students, teachers, mathematicians, etc. For newcomers to calculus, it's just hard to understand. As an adult learner who has learned math from books and is no stranger to self-directed studies, this book's math-speak explanations and "abracadabra" examples had all the calc newbies in my Calc I class bamboozled. Even my instructor had difficulty explaining the difference between her methods and the book's. Upon consulting other texts, the same concepts were easily revealed. The student solutions manual is, at times, as obscure as the text, sometimes leaving out significant steps. Some problems are explicated with different notation. In my humble opinion, Sylvanus Thompson's *Calculus Made Easy* and the HarperCollins' *Introduction to Calculus* and other "easy calc" books are better for introducing basic concepts to the calculus newbie.

Unless you are a math major and delight in a book that challenges you to create proofs of formulas that it has not yet even introduced, do your best to use some other text. This book does a fine job of teaching the material that it presents in its concise and clear chapters. Then come the problem sets, where you are confronted with material that in some cases is presented in subsequent portions of the book (ha ha), and in some cases is not presented at all. Another annoying feature of the problem sets is that the odd problems, for which answers are provided, are often more straightforward, whereas the even problems are harder and require more elaborate calculations. The book could do a better job of matching odd and even problems by type and "degree of difficulty".

I would say for extremely gifted math students who plan to become math majors, mastering calculus using this book may be akin to climbing high mountain peaks without oxygen, but for the rest of us, it is merely a hard slog. The redeeming feature is that this book may better prepare you for other courses in which the profs show "no mercy" and take the sink or swim approach. Just don't expect to be coddled if you use this book.