mathematics

James Stewart's book is one of the several standard textbooks in single and multivariable calculus circulating in the marketplace. If you wish to learn the calculus rigourously, then this is the book to work through. However, it is not for the faint-hearted so far as mathematics is concerned; it is very dense and rigorous in many areas, filled with abstract definitions based on set theory (something nonmathematicians no doubt will have a hard time with). It also has many difficult and seemingly unsolvable problems, especially with the tedious integration drills with trig functions; once you understand you can easily find most of these exotic integrals using CAS or tables, you wonder what all the effort was for. The multivariable calculus and differential equations sections are thorough, and Stewart's treatment of vectors and vector calculus is surprisingly fresh and clear of jargon.

On the positive side, the book is filled with many fascinating problems and projects related to the 'real' world, ranging from psychology to physics and astronomy. Interesting computational projects include proving Kepler's laws from Newton's gravity, the flight of a baseball, the calculus of rainbows, how to split a pizza the most effecient way, designing a dumpster with the most area and so on. Anyone with a heart for applied mathematics will not be dissapointed, nor those who demand rigor, given each theorem is carefully defined, and many rigorously proved.

In summary, it is a standard, solid textbook that will provide a solid foundation for further studies in maths and the sciences. Its main drawback is its difficulty and rather formidable complexity and rigor (I would recommend starting calculus using an easier, more intuitive text like Kline or the Schaum's outlines series on calculus) which make it slow and heavy going for the nonmathematician. It is also not the best place to quickly learn the 'basics' of calculus for say, physics or engineering; for that I'd recommend 'Mathematical Techniques, 2nd Ed' by Jordan and Smith.

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!

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.