Rating: 
Summary: Not for the faint of heart!
Review: I have heard talk that this is the best calculus text out there. If so, mathematics professors really need to get their publishing act together. This may be a tour-de-force of math knowledge, in which author James Stewart expounds just how much of an expert he is on the subject, but it is NOT a good book to LEARN from. I took calculus about a year ago and used this text to refresh my knowledge for an upcoming class. It took me multiple passes through the Chain Rule section (actually, quite easy stuff!) to jog my memory. The way Stewart explains things makes a prerequisite in astrophysics required for learning from the book. I will grant that it's colorful and well illustrated, which is the reason for the second star, but that probably only serves to double the price of the textbook. You'll probably have to get the solutions guide to learn from this at all- and boy do they make a killing off you in the process! There is a lot of non-essential extra information that really should be in different sections, but is instead the first thing you'll read about a fundamental concept. I was particularly irked by how Stewart demonstrates how different differential notation can be used to show formulae. This is ridiculous. He should stick with one all the way through, and put the rest in footnotes. If you instructor uses this text, you had better hope he's better at explaining things, or you'll be up the creek.
Rating: 
Summary: The best there is - and I'm familiar with the others
Review: I was one of the pre-publication reviewers for the second edition of this book. I have not been shy about telling a publisher that their book stinks if that's my opinion. But the Stewart book was then, and remains now, IMHO, the best introductory calculus text available. Please note that the majority of negative reviews came from people who have seen exactly one calculus book, and they clearly don't like calculus! But I have taught from three of the most popular books, and I've read most of the others. There may be other books which take a radically entertaining, non-traditional, and more superficial approach to the subject, and those books may meet with approval from people who really don't want to learn calculus. But of those (many) books which cover the traditional topics in an introductory calculus course, no other author has written a text as learnable as Stewart's. On every topic, Stewart is clearly conscious of the fact that his reader doesn't already know the subject, and he has given some thought to exactly what has to be explained in order for the student to learn successfully. Remember, most textbooks are not written for students: they are written for the professors who are going to choose the books. Professors are not generally impressed with a book which spends a half page clearly describing the meaning of a theorem which can be written with a one-line equation. But students will appreciate the effort Stewart has exerted to help them learn. Stewart does not sugar-coat or resort to gimmicks or superficiality in order to make the material learnable. All the material is there, it's just presented with an awareness that the reader is trying to learn calculus for the first time. If you are taking a calculus course with any other book, try to get a cheap used copy of the Stewart to use as a supplement. It will help!
Rating: 
Summary: Why Such Varied Reviews?
Review: 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.
Rating:
Summary: excellent!
Review: This is the best calculus textbook i've ever read.It helps me to
gain many useful concepts by text and plot.
This book is wrote in a logical way.
By reading the book,I like calculs more.
Spending time reading this book will save your time understanding what is calculus.
Anyway, if you are now confused about which calculs book should be put on your bookshelf,Stewart's calculs is the only choice.
Rating: 
Summary: A very good (but not excellent) calculus book
Review: I have seen exactly three calculus textbooks in my lifetime -- one, when I was teaching myself calculus in high school, two, when I was in Cal I, and three, while I've been in Cal II. I will preface my upcoming comments with the disclaimer that I do consider myself a little bit of a math-head and like most math classes I've taken in the past, even the ones with the teachers/professors who stink. Now that I've said that, I have to say that this calculus textbook is by far the best one I've seen, and really work in helping out the student with their calculus. Unless one is a complete idiot or is not really applying themselves in the subject, one can go rather far with this textbook. It is very organized in its presentation of the methodology and examples, its problem sets are thorough and really work to get the student involved in actually learning how to do things such as derivatives and integrals, and its wide span of what it covers in the subject is impressive, starting from the beginner's level and going up to the advanced level. I was even able to teach myself how to do double and triple integration with the help of this textbook, during a period when I found myself tiring of doing trigonometric substitution. Now, the one thing I found lacking from this book that would've made this book a true wonder was a review section so that one could go over concepts previously taught (and eventually forgotten) in trigonometry, college-level algebra, and geometry. I feel that had these concepts been included in a review section either in the beginning of the text as Chapter One (which the Cal I professor could skip if they so choose) or in the appendix as Appendix A (or B or C, etc.) I feel that had such a review section been included, especially for people such as myself who haven't taken the aforementioned subjects in years, I would truly love this book. Otherwise, I like it and would still recommend it.
Rating:
Summary: Negatives outweigh possitives
Review: Negatives: Let's face it, the book is dry. It breaks down concepts into steps and recalls the number of the particular step, rather than the concept of the step (hope I didn't confuse anybody). Expanded explanations of algebraic manipulation/tricks would have been helpful. Because of the previous statement, I have gone through the whole book and still sometimes wonder how he got from point A to point B. Positives: Forces ones mind to expand beyond the terrible habit of memorization (in most chapters). If one knows all the algebra that the book composes of, then that one is an algebraic god (not kidding). Don't excpect to get much out of this book without alot of time.
Rating: 
Summary: Save your money
Review: This Books is the same as the 4th, this is bull droppings! Change the title some what and charge an arm and a leg!
Rating:
Summary: Too much padding, not enough emphasis on mathematical ideas
Review: Maybe not the worst book out there, but close to it. Fails miserably as a mathematics text. The sheer amount of superflous material in this book is amazing. Chapter 1 should be cut out completely(students should be more than familiar with this material before entering a calc course), and the sections on tangents and velocities, rates of change in the natural and social sciences, related rates, linear approximations and differentials, graphing with calulus and calculators, optimization problems, applications to business and economics, newton's method, anti-derivatives, work, integration using computer algebra systems, applications to physics and engineering, applications to economics and biology, all of chapter 10, motion in space: velocity and acceleration, and chapter 18 should be cut out. Differential equations are mostly better left for differential equations courses where they can be delt with in proper depth. The sections on Newton's method and linear approximations are better left in a numerical analysis course (or perhaps computer science course). All that other stuff (the so-called "applied math") does more harm than good. Most applications in the text are entirely trivial and some topics are covered in a depth that is misleading (the section on work, for example, entirely omits the role of vectors). Cut out the above material (about 300 pages or so) and you have an entirely passable text, but as it stands Stewart's text is a perfect example of the prevailing sentiment that it's more important to teach students the "exciting" applications of maths while omitting the necessary rigorous treatment of mathematical ideas.
Rating:
Summary: Very good, but not for beginners.
Review: This book gives clear and detailed explanations of concepts and ideas involved. Many theorems are proved and challenging problems appear at the ends of section exercises. I studied multivariable calculus in part from Langs book, but Steward probably gives greater insight. However, I use it to review Calculus concepts and methods while taking Advanced Calculus. For someone completely new to the subject, a simpler introductory text might be of help.
Rating:
Summary: Simply Trash
Review: I do not understand the popularity of this book. It is difficult to follow and the exercises serve to trip you up rather than illustrate the techniques. If you have a weak lecturer, then this book is completely useless.
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