Customer Reviews

Calculus

5 star:		(17)
4 star:		(7)
3 star:		(9)
2 star:		(10)
1 star:		(13)

 

 

I took calculus over 20 years ago using a book by Howard Anton. Wanting to brush up on my skills, I recently took a Calc II and Calc III course for review. The book I used this time around was Stewart's "Calculus", 5th edition. I thought it would be a breeze, but trust me, after 20 years, it wasn't. Thinking there might be a more helpful calculus book out there I decided to see what else might be available. In my search I came across several other excellent calculus books, but after all was said and done, I have to say that the Stewart textbook is really one of the best.

One of the of the calculus books that almost always received a lot of praise was "Calculus With Analytic Geometry", by Ron Larson. In fact it received such high praises, I found a good deal on a used copy of the seventh edition and bought it to supplement the Stewart text. And I have to admit, I found the layout in the Larson text to be much better than the Stewart text. With Stewart, I was constantly having to highlight things and draw in boxes or add notes to show where examples ended and text began, or what an example was supposed to be teaching, or what specific step in an example was key. In the Larson text, all of this is nicely laid out. Each example is labeled to indicate what it is about, and colored text, annotations, arrows, etc. are used to clearly show where the important points are. When it came to explanations though, I did not find the Larson text to give any better explanations than the Stewart text. In fact, I often felt the Stewart text provided slightly better explanations. I would read the Stewart text and then read the Larson text and think, "Gee, I'm glad Stewart pointed this or that out". Overall though, the differences were minor. In fact, sometimes it seemed that the text was almost identical, and it was only after careful reading that the differences could be noted.

In at least one case, Larson presents material I haven't seen anywhere else that really simplifies some integrals, and that is the tablature method, which is just a short hand way of doing multiple integration by parts, but it can really save you a lot of time.

As a main text for a multi-semester course in calculus, either the Stewart or the Larson text would be excellent. I found the Stewart text to be less inviting and slightly more difficult to read, but generally, (with a few exceptions), a little more thorough overall.

Another excellent book to supplement any calculus text is "The Calculus Tutoring Book" by Carol and Robert Ash. This book covers most of the material covered in a standard text like Stewart's or Larson's, but in a much friendlier style. It strips away a lot of the formalism found in a standard text so that what you are left with is a practical guide to doing calculus problems. It is not packaged with a bunch of computer generated graphs and figures. Instead everything is hand sketched. At first this may seem like a drawback, but once you get used to it, you realize how much you can do with your own pencil and paper. In my opinion, this is one of the best supplemental calculus texts you can buy. It would even serve as an excellent review book in its own right.

One other calculus text that I came across and really liked was "Calculus: An Intuitive and Physical Approach" by Morris Kline. It does not follow along quite as nicely with a standard calculus sequence and so isn't quite as easy to use as a supplement, but when I did use this book, I found the explanations to be very clear and useful.

So there it is. Stewart's Calculus, 5th edition, is an excellent text even though it is a little difficult to read sometimes. Larson's "Calculus With Analytic Geometry", seventh edition, runs a very close second, with some advantages not found in the Stewart text. Since both of these are very formal calculus texts though, "The Calculus Tutoring Book" by Carol and Robert Ash is an excellent supplemental book to consider as it offers a friendlier, more practical perspective. And if you still haven't had enough, "Calculus: An Intuitive and Physical Approach" by Morris Kline is well written and provides additional insight and perspective.

As a footnote, though I imagine the review about the cover of Stewart's text was meant to be tongue in cheek, I personally like the cover and find that it works well on several levels. Although the f-hole of a violin and the integration symbol of calculus have nothing to do with each other, it is a nice visual image, and if one thinks of the violin as an instrument used in performing some of the greatest works in the world of music, calculus may be thought of as an instrument used in performing some of the greatest calculations in the world of math. Finally, the image was mathematically generated, so all in all, I don't think it's a bad choice for the cover of this text.

There is a reason why the reviews of Stewart's Calculus textbook vary so widely. It's because Stewart is challenging. Some instructors favor Stewart because they are steeped enough in the Math to appreciate Stewart's applications and explanations of Calculus's uses in so many fields of study. But students who struggle with Math may have a difficult time with Stewart's rigor, and his algebraic/conceptual jumps. Let's review some specific qualities of this book:

o Text: The text is pretty clearly written, with no errors I know of, but makes some conceptual leaps periodically.

o Layout: The layout is excellent. It makes great use of consistent color coding and typographical conventions to identify classes of concepts. (I.e., It's always easy to spot and distinguish Examples, Proofs, Rules, and New Sections.)

However, there are some algebraic manipulations that are sometimes combined into one line that should probably be expanded out and explained better. Even though students are expected to understand the algebra at this point, it's often crucial to explain _why_ certain algebraic manipulations are being done. Usually there is a certain form of an expression or equation that is useful or desirable for a specific reason. Such reasons need to be explicated side-by-side with the steps to reach the desired form, instead of just skipping to the desired form (as sometimes is done).

o Terminology: In some places Stewart talks about "constants" when what he really means are "scalars." There is a distinction between these two concepts that is important in other fields of math that could be confused. He also uses different letters to identify "any real number" or "a particular real number" than is standard in many other texts. This also could lead to confusion.

o Graphics: The integration (pun intended :) of graphs and diagrams to supplement functions, step-by-step processes, and proof descriptions in this text is frequent, helpful, and very well done.

o Exercises: The exercises for each section start off easy and in close step with the concepts and example problems that have been demonstrated in the preceding section. However, Stewart's problems ramp up in difficulty quickly. Exercises in the the middle or near the end of a set often have no direct prototypes in the preceding text for students to lean on. Some instructors might consider this an asset, but when assigned carelessly can be a frustration to students. One improvement from Fourth Edition to Fifth Edition was the "red flagging" of many exercises of especial difficulty.

o Proofs: Simple theorems and rules are proved in the text as they are introduced. More complicated proofs are provided in appendices in the back. The text is pretty thorough about proofs.

o Worst section: I think the hardest section for students to understand (and unfortunately one of the most important in Calculus) is the section titled "The Precise Definition of a Limit". Stewart has a habit in this section, when manipulating an absolute value of epsilon expression, to abbreviate it all on one line without explaining _why_ he is performing the operations that he is. He should expand these out to multiple algrebraic lines, possibly with some text explaining that he is trying to get the epsilon expression to match the delta expression. It is impossible to be too verbose, explicit, and careful with this section. And certainly more of each of these could be used in Stewart's rendition.

Other reviewers mentioned the sections on the Chain Rule, Integration by Substitution, and Integration by Parts -- all of which could be improved. Substitution and Parts could be improved by drawing the little grids of what u and du represent (that many instructors write underneath these kind of exercises before substituting).

To summarize, if you're good at math this is probably a good text for you. If you (or your students) have weaknesses, stick with something simpler -- Larson's Calculus text is excellent and good to compare against this one.

The background behind this math book is interesting. Widely used at many American colleges, this book has to provide fundamental building blocks for people going on in mathematics, engineering, computer science, and many related disciplines. Does it succeed?

Yes, but with limitations (coming from a math major anyway). This book is a fairly rigorous treatment of calculus, but not from a theoretical standpoint. Stewart is ok at explaining things, but some sections on proofs he is horrendous at explaining the concept (see "the precise definition of a limit," among others). On the mechanics of problems, though, he is very good at forcing the reader to learn by repitition, as he includes a high number of problems. Unfortunately he does not include nearly enough examples, and later on this is a TERRIBLE problem in his multivariable calculus text (as I am experiencing right now).

Stewart does a good job with about 75 or 80% of the text.
rather weak points:
section 2.4 (the precise definition of a limit)
chapter 6 (applications of integration)
9.3-9.5 (further apps of integration)
10.5 and 10.7 (diff eq-logistic equation, predator-prey systems(wtf?))

Actually it's not all that bad at all. Stewart does an excellent job with the rest of the material, and his inclusion of abbreviated proofs is a welcome thing. This book serves as an introduction for many people to mathematical rigor, so Stewart is smart not to scare people away with long, elegant proofs and such. An abbreviated proof is better than no proof at all, and if you have a good enough professor or you are taking an Honors calc course, you might be treated to the full proofs.

A lack of analytic geometry is a big issue as our high schools choose to ignore this subject, and Chapter 11 adresses this fairly competently (although this is treated better in his third-semester book). One chapter of material is not enough for this great subject, but we can't really blame Stewart for that. It's the High School's fault, not his, for failing to prepare us.

This was a pretty good book. Although as I view Apostol's book as much more thorough and rigorous, this book serves well as a satisfactory introduction for people who don't need as much rigor. All in all, a slightly above average book, that many people will use.

note- chapter 10 (diff eq) and chapter 18 from multivariable (second order diff eq) were particularly well-written (besides the parts of ch10 I mentioned). It would be interesting to see what Stewart could come up with with a diff eq book.

Note- This review refers to the single variable fifth edition of the text.

Like many reviewers here, I purchased James Stewart's Calculus: Single Variable Early Transcendentals for two semesters of junior calculus. The book is hefty and expensive, close to $150, yet I when I finished junior calculus, I felt distinctly ripped off. I was further surprised to learn that this particular textbook was one of the most widely used in colleges throughout North America. How could a thoroughly inferior textbook become so popular? I asked myself.

The problem, as I see it, is that James Stewart attempted two different approaches for this text, and failed miserably at both. On one hand, he presents the material in a mathematically rigorous fashion. On the other, he tries to present it in an intuitive way, so that students getting their first taste of calculus can better understand the material. Essentially, Stewart tries to satisfy both the professor and the student, but ends up pleasing neither. Mathematical proofs, for examples, are presented in ultra-condensed form, and are unlikely to please anyone looking for mathematical rigor.

More worrisome, however, is the poor mathematical exposition for the unfortunate student. Most maddeningly in his examples, Stewart has a habit of omitting several key steps of algebraic manipulation, leaving the student to throw up their arms at how Stewart arrived at the answer. As many college freshmen will have little to no experience with calculus, I feel it is critical that the author show exactly how a particular problem is to be solved, with no steps omitted. Ironically for a calculus textbook, the section on the Fundamental Theorem of Calculus is one of the most shoddily presented in the whole book, giving little explanation as to how and why the concepts of integration and differentiation are related. To make matters worse, the tone of book itself is consistently dry, lifeless, and slightly condescending with the constant use of "we" and "let's" throughout. In short, Stewart does not seem to write with a student struggling through freshmen calculus in mind, which is bad news for the student indeed.

Another irritating habit of Stewart's is presenting example problems that are much simpler than those found at the end of each section (or worse, on a student's examination), yet even then, Stewart cannot provide a decent explanation of how to arrive at the solution. The actual problems themselves ramp up in difficulty very quickly, and the accompanying solution manual ineffective at conveying the means to arrive at the solution. Woe betide the student whose professor decides to pull problems from this textbook for use on examinations!

As if that were not bad enough, the organization of the book is also suspect. There are many sections detailing "real world" applications of math to the physical and life sciences, most of which are thoroughly unncessary, and detract from the theory that a math text should focus on. Chapters are scattered about with irregularity, and are at worse unnecessary entirely. The section of differential equations, for example, should have been left for a senior class where they could be studied in the proper detail. Combined with the overuse of pictures and diagrams (many of which have no relevance to the topic), the end result is a book that is bloated and needlessly expensive.

Although I wouldn't recommend anyone purchase this text, students will likely not have any choice in the matter. Should you end up stuck with this text, I suggest reading others for better explanations, such as Schaum's outline of calculus. By itself, I do not recommend this book to anyone wishing to learn calculus.

The usefulness of this book varies depending on the purpose for which the reader bought it. If you are a scientist or engineer who is primarily interested in applications and computations, then this book would be an excellent choice- Stewart puts heavy emphasis on the mechanics of calculus (which also makes this book a good choice for the standard AP Calc courses.)

However, if you wish to truly understand calculus and the theory behind it, then I would advise buying Spivak's "Calculus" instead. In particular, future math majors should avoid Stewart (and any similar calc books) at all costs. Stewart is a terrible book for students wishing to study upper division math since there is very little theory, and the theory that is present is poorly explained. In contrast to Stewart, Spivak is completely proof-oriented; the problem sets (which are about 30 in number per chapter) force the students to develop a deep understanding of the principles of calculus. This understanding leads to the student's ability to solve computational problems quite effectively, but with the added advantage of allowing the student to see *why* a certain method works, and what a certian formula really means. Most importantly, Spivak teaches the student to be intuitive and creative while at the same time being mathematically rigorous. In short, Spiavk will teach you to think like a mathematician, while Stewart will teach you to think like a scientist or engineer.

This book was used at my undergraduate and graduate institutions; I am currently forced to teach out of it. I don't understand why it's considered such a great book. I have seen many students confused by it, and I find it mediocre as a reference text.

This book attempts to combine theory with applications from the start, and the result is confusion. A few early sections are too computational. The use of decimals and persistent presentation of applications keeps students separated from the theory, and keeps them hung up on the setup of problems before they fully understand the mathematics. But the applications are shallow and won't greatly help students who will later encounter the material in physics, engineering, or business.

It is my belief that calculus should be presented in a simple and pure way so that students can master the fundamentals, and then (simple) applications be presented later. Instead, this book introduces fairly complex and "ugly" applications right from the start.

The wording of homework questions is frequently confusing and detracts from students' ability to focus on the actual material. This book (like many intro calc books) is also lacking in mathematical rigor and has confusing presentations of some of the critical theoretical foundations of calculus (such as the definition of the limit) and insufficient explanations of why certain theorems hold, what they mean, and how to use them. The net effect is that students using this book often fail to master the fundamentals of the subject, and find calculus overwhelming and confusing.

The book's covering of advanced topics is better than the earlier chapters, but there are far better calculus books out there, and I would not under any circumstances recommend this one.

this is actually a review for the separate volumes of single variable and multivariable, which i believe are combined as one in this edition.

i learned calc from the single variable vol. in highschool, and then a few years later when i decided to study math in college, went back to it to brush up on the basics of solving problems (which was much needed after years of studying literature). the text is basically laid out by introducing a few examples and then stating a theorem, or vice versa, and then presenting many problems which more or less increase in difficulty, although many of the problems are all at the same level, so that i dont think one really gets to test the level of their understanding (nor really develop a deeper understanding). but if you just need to know how to solve problems, and are not interested in pure math (i.e. for most other scientific disciplines), then this book is probably perfect for you. however, if you start to study more advanced mathematics, you will quickly realize that this book is really a very crude introduction. there are few proofs, and many of the proofs supplied use quite a bit of hand waving--and as an introductory text, there is little or no discussion of writing proofs, nor anything on logic, axioms, set theory, the real numbers, etc. this is a problem because every so often an exercise comes up where you are asked to prove something, and from this text alone one would most likely be unable to do so. for a really thorough and rigorous introductory development of the calculus, check out spivak. that book blew my socks off.

now, for the multivariable stuff, we used this in a two term sequence at my university. one thing i found very impressive were the illustrations/graphics, which very often provided helpful visualizations--but at times i felt that the development of certain ideas was overly emphasized with illustrations, so that the purely theoretical understanding suffered. all in all i found it a decent introduction to vector calculus, but i would have really liked to see a lot more on greens and stokes theorems etc since these are not only so important but so incredibly fascinating--but again there would have had to have been a much more rigorous construction of the theory and probably introductions to topology etc that would really be beyond the scope of this book. ive used bressoud's second year calc, edwards advanced calc, hubbard vector calc, and davis/snider intro to vector analysis as supplements/extensions of this text. i cant say that i recommend any of them above this text, as i think they are a bit beyond it--but they can all work together to really develop a good basic understanding of vector calc.

The author of the book obviously has a great degree of mastery of calculus and the systematic structure of the book is well arranged and everything is thoroughly defined in mathematical terms. That's about the only thing positive however I can say about this book. I don't care how well Stewart knows Calculus and how well he shows it off, that does not equal students comprehending this subject. The biggest drawback of this book is that the author makes frequent conceptual leaps and constantly skips steps in problem solving which often make it extremely hard to figure out how the author arrived at a particular conclusion or solution. Not only that, the book is stuffed with unnecessary filler in order to increase it's size and hence make more money of it. Application to economics and natural sciences, linear approximation, graphing calculator section and etc. are of course interesting, but they are absolutely non essential to the 1st two semesters of Calculus. There is quite a bit of material to master in the subject as it is and an average class absolutely has no time to go in anything but the essential material. I'd say half of the book can be thrown away. The extra stuff might be helpful as reference but unnecessary for an average Calc class. Morever, what angered me was the clear marketing scheme for the book: this new fith addition is virtually the same as half thinner 4th addition, and features lots of non essential material...obviously to make more money without actually writing another book...by canceling the print of 4th edition and making colleges and highschool buy the new, more expensive, more useless 5th edition. This book can be very frustrating for students when the try to master calculus and will give you lots of hedache before you actually throughly understand something and without the guidance of a good professor the 5th addition is not the most helpful material. This book might stimulate your intellect if you are a math whiz, but for most, average joe people just trying to master calculus this book will cause much unpleasantness.

I've used 2 different books for my calculus curriculum, and this is as good as any other text, if not better. The layout makes sense. Stewart starts off easy with good motivation and examples. He then develops the theory of calculus step by step. His exercises, which emphasize computatin rather than proof, range from trivial to rather difficult (the hardest usually lie in the "Problems Plus" section). The notation used in the book is consise, and especially so in the multivariable sections.

While this book is very good in most respects, there are a few points I'd like to complain about... First off, the price. $150+ is ridiculus! Sure, if you're going into some hard science that requires 3 calc courses, you'll have that broken up over 3 semesters, so it's not so bad. But those needing only 1 or 2 courses are kinda getting shafted. Second, those persuing a math degree will find themselves at a disadvantage when they get into their advanced calculus (or other abstract math courses, for the matter) since most elementary calc books don't emphasize proof writing much at all. It would be nice to see a little more theory as well.

I have used two calculus books in my lifetime so far. This one was the second and I just ended up confused. I recomend you find some other textbook. The pictures are nice, but I don't think that the book is well written and easy to follow.