Customer Reviews

Calculus: Early Transcendentals (Stewart's Calculus Series)

5 star:		(20)
4 star:		(19)
3 star:		(3)
2 star:		(5)
1 star:		(5)

 

 

I am a college Calculus instructor, and I find this book terrible for many reasons. For students looking for a solid but much more inviting introduction to Calculus, I highly recommend Larson's book over Stewart's.

Here is a point-by-point breakdown of the faults I find in Stewart's text:

Clarity of Explanation and Content Level

Stewart's explanations are often verbose, unclear, and written at a
level too high for the average Calculus student. Several of my students
have told me reading the book only confused them and did not
clarify the concepts. An introductory text should offer simpler, clearer, and more concise explanations more appropriate to the typical Calculus student.

Presentation

In this day and age, students expect visually engaging presentations that will hold their attention. Stewart's presentations are drab and uninteresting. His book is everywhere packed with dense plain text and
formulas, giving the impression that Calculus is hard, dull, and very
complex, further intimidating students who are already scared of the
subject. Students are much more likely to carefully read a text that is
visually appealing and makes Calculus seem interesting and less
intimidating. This will also help reduce their anxiety over what many
already consider a very difficult course.


Readability

Another important aspect of presentation is layout and readability. Here
Stewart's text is again dismal: His pages are overstuffed with text and
graphics throughout the book, making it difficult to reference a
theorem, particular type of example, etc. It is hard to see where one
example or proof ends and another begins. The average student is not
going to read the entire contents of a section in full detail, but will
rather reference the topics s/he is having trouble with, in order to get
the details on a theorem or to find an example problem to help with a
homework exercise. This is very difficult to do in Stewart's text due to
the crowded and confusing layout.

Homework Exercises

Stewart's text is again particularly poor in terms of his homework sets in that he tends to offer a few low-level problems and then suddenly jump into extraordinarily difficult problems with no warning or transition. Stewart also tends to couch exceedingly difficult problems between a series of relatively straightforward ones, again without warning, which is very frustrating for students who find themselves struggling over what they think is an easy problem.

All in all, I strongly advise against this text, and would urge other Calculus instructors and mathematics departments to choose another Calculus book for their classes.

I used this textbook in a Calculus 3 course, so my primary experience is with chapters 12-16, but I did find myself referencing chapters 3, 4, 7, and 10 extensively to refresh my memory (and to learn some things I hadn't learned in high school BC Calculus).

The exposition is, for lack of a better word, "meh". It relies mostly on giving a few definitions, working through a few simple examples, then throwing hordes of problems at the reader. Now, this is perfectly fine for a lower division mathematics textbook -- such a process builds mathematical maturity (at least for me it did), but I would've liked the text, if anything, to rely *less* on showing by example and more on providing mathematical motivation for the given topics (the "big picture" of what we're trying to do, so to speak, rather than a few examples of technical details). The text's quality in this regard also has a fairly steep downward slope as the book progresses -- the text was readable and informative for, perhaps, the first 11 chapters, but from chapters 12-16 it's just really hard to learn from it on your own (and believe me, when you miss class, you have to do that).

Now, to the good part of the book (and the reason why the book gets a good 4 star rating rather than a 2 star one): problems! This book is filled to the brim with tons of exercises that range from routine to fairly difficult (and a special "problems plus" section, outside of the main exercise sets, that range from difficult to nightmarishly difficult). DO YOUR HOMEWORK! Seriously, if you are taking a course with this book, then you owe it to yourself to do the problems that are assigned at the *very least*. They are, for the most part, interesting and will help you build your mathematical ability and, more importantly, understand the material. Do extra problems, think about them, understand what you're doing instead of simply looking for the right thing to plug into. Believe me, it's worth it.

So the final verdict? The text isn't very well written and the examples are pretty poorly chosen (this especially applies to the last 1/3 of the book), but the problem sets are wonderful.

--Ashraf Eassa

I took the first level of Calculus during my freshman year of college, when this book was used as a required text. It was often confusing in it's working of examples and often skipped steps, as it assumed that the student would understand why. I can see how this would be O.K. for those mathematically inclined, but for me, however, it ended up being a nightmare and I constantly had to get help from the tutoring center in understanding the material. I ended up getting a C in the course at the end of the semester. When it came time to take the second level of Calculus, the textbook was changed to Rogawski's Early Transcendentals. Rogawski was a lot easier to understand, examples were worked in great detail, the text was clear and to the point, and it even provided hints. I ended the class with an A. In addition, this book is quite hefty, making it a chore to drag to school every day. If you are looking for a book that will help you understand the already difficult subject matter better, look elsewhere, preferably to Rogawski.

This book is written for those intending to move onwards in math, rather than those who are learning calculus for practical purposes. In general, the book is not user-friendly and at times throws in "points of interest" about math and calculus that are not labeled well, and can thus confuse/ distract the reader. The book does not contextualize what it attempts to teach and as a result, forces the reader to skim a chapter to understand the general thrust and conclusion, before attempting a detailed reading. I do not know of better calculus books, but for one inclined to search, this is not the one at which to stop.

In this review, I am using as a reference the edition from 2008 of James Stewart's Single Variable Calculus, Early Transcendentals, 6E, Volume I: Chapters 1-6. My review focuses on Chapter 2: Limits and Derivatives. This review has turned out to also be a review in contrast, of the edition from 2001 of Thomas' Calculus, Early Transcendentals, 10th edition. A recent edition of that book is Thomas' Calculus Early Transcendentals (12th Edition). The rating given is for Stewart's book. I would rate this 10th edition of Thomas' book at 5 stars.

Stewart's Calculus textbook is widely used across the United States to introduce students to higher mathematics. Its impact is far-reaching. It has the power to influence a student's self-confidence, and implicitly thereby, to encourage or discourage further studies in mathematics. A textbook is the map to the territory of the subject. If the map cannot be understood and followed, the subject cannot be learned. Because college mathematics departments are locked into a learning sequence that insists upon calculus before abstract algebra, even though this algebra doesn't rely upon the concepts of calculus, books like Stewart's Calculus have the power to support, hinder, or even stop, a student's progress in college level mathematics.

The fundamental mathematical concepts of calculus are: Limit, Continuity, Derivative, and Integral. The first three are introduced in chapter two, the last in chapter five, of Stewarts Calculus, 6th edition. How well does he do?

Not very well. Stewart seems to have no idea what needs to be said and what can be left for some other time. His book is cluttered and bloated with unnecessary "help" that can only get in the way and obscure the core purpose of learning. It's impossible to critique this book with adequate supporting detail in a relatively short review. In general: He seems to have no intuitive sense of how to present ideas clearly.

When introducing the concepts of Limit, Continuity, and Derivative, he loses the point of what he is supposed to be teaching and gets caught up almost immediately in giving unnecessarily complex examples rather than covering the topics efficiently and with clarity, then moving on. When he introduces the formal epsilon-delta definition of limit, he botches the opportunity to make it clear and helpful. He should have either not bothered or done a better job.

Here's an example of how Stewart doesn't think through what he's trying to teach. On page 119 he's just introduced the definition of a function continuous at a point. He's going to define discontinuous at a point, and this is what he writes [I'll use angled brackets to indicate italic, and asterisks for bold]:

"If <f> is defined near <a> (in other words, <f> is defined on an open interval containing <a>, except perhaps at <a>), we say that <f> is *discontinuous at a* (or <f> has a *discontinuity* at <a>) if <f> is not continuous at <a>."

Ignoring the stylistic and cognitive clutter of the parenthetical insertions, this definition, abstractly, is of the logical form {if p then (if q then r)}, where r denotes the clause where the terminology *discontinuous at a* is introduced; but notice that isn't how he structures it. Stewart says, in effect, "if p, then r if q" which is, of course, logically equivalent, so he's not technically wrong, but stylistically he fails to communicate well. The sentence reads as you go along as if it's going to tell you that if <f> is defined near <a> that it is *discontinuous at a* -- and it is only after you reach the end of the sentence you see what is actually being said. This stylistic infelicity (to speak kindly of it) most likely arose from blindly following the convention of defining mathematical terms in the form: We call such and such an object an O if [condition C]. But in this instance it could lead to reader confusion and frustration.

Here's how the same idea is introduced in the 10th edition (2001) of Thomas' Calculus, page 125:

"If a function <f> is not continuous at a point <c>, we say that <f> is *discontinuous* at <c> and <c> is a *point of discontinuity* of <f>. Note that <c> need not be in the domain of <f>."

Which is clearer? Going further in comparing these two books on the topic of continuity, Thomas' Calculus first defines *continuity at a point* (both at an interior point and at a left or right endpoint), then after introducing discontinuity as quoted above, the next paragraph gives the additional terminology of *right-continuous* and *left-continous*, and after explaining how this additional terminology is used in relation to continuity at end points, we are told that: "A function is continuous at an interior point <c> of its domain if and only if it is both right-continuous and left-continuous at <c> (Figure 1.46)." The figure is well designed and helpful.

This is followed by two very short examples, and then they mention the three conditions of the Continuity Test. There is another example and then they show a collection of six graphs that represent types of discontinuity and they quickly mention terminology such as *jump continuity*, *infinite discontinuity*, and *oscillating discontinuity*. They are building up to where they can mention algebraic combinations of continuous functions on the next page and after that the composition of continuous functions, and following that, the Intermediate Value Theorem. So they introduce more terminology and tell us on page 127:

"A function is *continuous on an interval* if and only if it is continuous at every point of an interval. A *continuous function* is one that is continuous at every point of its domain. A continuous function need not be continuous on every interval. For example, y=1/x is not continuous on [-1,1] (Figure 1.51)."

This is all presented in a style that is very efficient and clean. The authors are aware of where they are headed and don't go off the path or linger along the way. Stewart, on the other hand, is a tourist. He finds everything of equal interest and seems to have no purpose but to linger and wander about. He actually touches on a few topics in this section that Thomas' book avoids, but he does it at the expense of clarity. He presents the continuity test immediately after defining how a function is continuous at a point, but then he doesn't reach the definition of a function continuous from the right or left (which Thomas' book gave at the same time as defining continuity at a point) until after he's given a page worth of examples and talked about discontinuities.

To define *continuous on an interval* Stewart writes, on page 121:

"A function <f> is *continuous on an interval* if it is continuous at every number in the interval. (If <f> is defined only on one side of an endpoint of the interval, we understand <continuous> at the endpoint to mean <continuous from the right> or <continuous from the left>."

Notice that *continuous function* is not mentioned in this definition. In fact, he never formally defines it. It almost shows up implicitly in a theorem statement about rational functions on page 122: "Any rational function is continuous wherever it is defined; that is, it is continuous on its domain." He starts to use the term explicitly, without giving its meaning, within the proof of the related theorem that any polynomial function is continuous everywhere, i.e. on the Real numbers. The sentence in the proof is: "This equation is precisely the statement that the function f(x)=x^m is a continuous function." (x^m signifies x with exponent m.) If you look up "continuity of a function" in the index, you're referred to page 119, which defines continuity at a number.

Now, let's compare how the two books state the Intermediate Value Theorem.

Here's Stewart:

"Suppose that <f> is continuous on the closed interval [a,b] and let N be any number between f(a) and f(b), where f(a) is not equal to f(b). Then there exists a number <c> in (a,b) such that f(c)=N." He uses the inequality sign in the text.

Here's Thomas' Calculus:

"A function y=f(x) that is continuous on a closed interval [a,b] takes on every value between f(a) and f(b). In other words, if k is any value between f(a) and f(b), then k=f(c) for some c in [a,b]." They use y[subscript 0] where I wrote k.

Thomas' book includes a graph within the highlighted box giving the theorem and labels the theorem: The Intermediate Value Theorem for Continuous Functions. Stewart gives the necessary specification of continuity within the statement but not in the name of the theorem. Afterwards he gives two graphs. Both books refer soon after stating the theorem (Stewart takes longer) to the necessity of continuity as a condition of the theorem's truth. Stewart says: "It is important that the function <f> in Theorem 10 be continuous. The Intermediate Value Theorem is not true in general for discontinuous functions (see Exercise 44)." In Thomas' book we read: "The continuity of <f> on the interval is essential to Theorem 10. If <f> is discontinuous at even a point of the interval, the theorem's conclusion may fail, as it does for the function graphed in Figure 1.55." Which of these appears more helpful?

At this point, Stewart moves backward in relation to Thomas' Calculus and discusses limits at infinity and horizontal asymptotes (in Thomas' book these are discussed before continuity). Stewart then proceeds to tangents, velocities, and rates of change. Both books are heading towards a definition of the derivative, and the tangent is an important stop along the way. What's interesting, though, is how this is achieved in the two books.

Stewart, suddenly in a hurry, tosses the reader into the deeper end without preparation:

"If a curve C has equation y=f(x) and we want to find the tangent line to C at the point P(a, f(a)), then we consider a nearby point Q(x, f(x)), where x is not equal to a, and compute the slope of the secant line PQ: m[subscript PQ]= f(x)-f(a) / x-a . Then we let Q approach a number m. If m[subscript PQ] approaches a number m, then we define <tangent t> to be the line through P with slope m. (This amounts to saying that the tangent line is the limiting position of the secant line PQ as Q approaches P. See Figure 1.)"

Not stopping to catch his breath, he then gives the definition of the *tangent line* using the limit as x approaches a for the quotient given above. In an example, he introduces the alternative form using f(a+h)-f(a) / h with the limit as h approaches zero. This quotient is then used in his discussion of velocity, then also in the definition of the *derivative of a function at a number a*, where he introduces the notation f'(a). He then backtracks and rewrites this limit f'(a) using the quotient form of f(x)-f(a) / x-a with the limit as x approaches a, after which he remarks that: "The tangent line to y=f(x) at (a,f(a)) is the line through (a, f(a)) whose slope is equal to f'(a), the derivative of f at a." Notice that this is the derivative at a point, not the general derivative of the function.

He then switches to rates of change and the *increment* of x, using the [delta]x notation. Of course, the [delta]x / [delta]y quotient notation is only temporary and is soon altered to dy/dx once the general derivative of a function is introduced in the final section of the chapter. By the end of the chapter he has gone back to the f(a+h)-f(a) / h quotient form, swapped out the constant a for the variable x and used the new form to define the *derivative of f*, after which he defines *differentiable at a* and *differentiable on an open interval*, and also introduces higher derivatives, and proves the theorem that: "If f is differentiable at a, then f is continuous at a."

Chapter 3, which I won't discuss (nor any further chapters) concerns differentiation rules. Chapter 4 is on applications of differentiation. The last two chapters of this particular volume are on integration. Integration techniques are not covered. I am referring to the edition from 2008 of James Stewart's Single Variable Calculus, Early Transcendentals, 6E, Volume I: Chapters 1-6.

Thomas' Calculus, 10th edition, ends the chapter on limits and continuity with a discussion on tangent lines. They are not hasty but they don't dawdle either. They discuss the concept of tangent lines, as usual, with clarity, and then when they introduce the formal definition of *slope* and *tangent line*, unlike Stewart, they immediately use the quotient form f(t+h)-f(t) / h and take the limit as h approaches zero, provided the limit exists. (They use x[subscript 0] where I wrote t. Likewise in what follows.) They give some examples, then remark that the quotient used above is called the *difference quotient of f at t with increment h*, and that if it has a limit as h approaches zero, that the limit is called the *derivative of f at t*. They don't bother to write f'(t), which, to my mind, is good sense, because the differentiability of a function is not yet generally defined, at least explicitly, so f'(x) is meaningless, and therefore, f'(t) would, at this point, be an anomalous use of function notation. The notation f'(x) is properly introduced along with the definition of *derivative* of a function, at the beginning of their next chapter.

This particular edition of Thomas' Calculus discusses limits and continuity in their chapter 1, derivatives in chapter 2, and applications of differentiation in 3. As in Stewart, the integral and applications of integration follow in two more chapters.

Students have no choice which textbook their professor assigns. If you're stuck with Stewart and having troubles, take a look at Thomas' Calculus. It may help.

As a "returning" student (after many years) preparing to audit a Calc II course this fall, I've checked out a LOT of calculus texts--on Amazon, libraries, used bookstores, etc. A dozen of such texts, easily. I'm no mathematician by any stretch (an undergrad degree in computer science), but I'm not exactly a stranger to the material and actually completed Calc I and II successfully. During the Nixon Administration, I think. Still interested in math though, and incredibly, I now qualify for a (cough) senior discount on the tuition rates. All right--my first tip to ANYONE taking a calculus course (and as a former teacher myself) is to not rely ENTIRELY on the class "required" text. Or the teacher, for that matter. For something like calculus, it almost DEMANDS that you have some "backup" from DAY ONE. Maybe one or two books, if it's tough stuff, and you need two or three different explanations or "covers" of the same material. Finding the right book (in case the "required" one is real stinker or you've got a less-than-your-dream-teacher--it's always possible) can be a little work, but can be rewarding, too--including saving you a lot of money or bad grades because you didn't learn the material or could have got more bang-per-buck textbook-wise. The Stewart book (and others like it) come in at ten pounds and close to two hundred bucks sometimes. They're typically used for at least two (and possibly three) semesters. There's enough of "the undergrad calculus canon" here for three semesters, easy, and I wouldn't be surprised if there are a whole PASSEL of campuses using this book. I believe there are even "special editions" of Stewart customized for specific colleges and universities, and Thomson is definitely a heavy-hitter in the college-textbook publishing game. I've even TAUGHT from some of their high-quality texts. This Stewart text is the one the class I'M taking will require. It's NOT THAT DIFFERENT from many others, though, and material-wise, it seems to adequately cover the obligatory "stuff," including chapters on partial derivatives and second-order differential equations. The exact same material (down to chapter and section headings, in many cases) can be found in other texts. For a REQUIRED SUPPLEMENTAL book though, for undergrad calculus, I can't recommend highly enough Adrian Banner's book "The Calculus Lifesaver." I think it's under twenty bucks, paperbound, and it's HANDS DOWN the best "supplemental" text I've found. I can't really comment in any comparitive way on this (Calculus "Early Transcendentals") text. I've seen preferences for the Larson book which (surprise) covers pretty much exactly the same topics, and gets just as many NEGATIVE reviews(!). And it's over $150, also. This book seems OK, but guess what? If you can find the plain "Calculus" one (same author, same title, and the identical cover), just lacking the words "Early Transcendentals" in smaller letters beneath "Calculus" they seem to differ by exactly ONE CHAPTER. That chapter is IN the "Calculus" edition (6th ed., 2008, ISBN13 ending with: 1160-6), but DROPPED from the "Calculus, Early Transcendentals" edition (6th ed., 2008, ISBN13 ending with: 11668). Incredibly, though this Amazon ("Early Transcendentals") edition is priced at about $185, new, hardcover, I found a used copy of the "Calculus" text for WAAAAYYYYY less. Like ten bucks. Hardcover, barely used. The extra chapter is on "Inverse functions, exponential, logarithmic, and inverse trig functions", and after that chapter, the two books are identical, except the chapter numbers differ by one. Go figure. Another thing: I found the textbook for the same course I took years ago (Calculus with Analytical Geometry, by Thomas, 1974, I think), and I'll bet I could have got through this course with it, nearly 40 years later. Bottom line: If you just need this book for a class requirement, are cringing at the price tag (it'll be over $200 at your college bookstore, for sure) or are only taking maybe just one calculus course, shop around a little--there will be plenty of used copies around, and a slightly-different (or slightly older, like the 5th, copyright 2003) edition might be just as good. If you're just interested in the material or are an autodidact, there's plenty of as-good-or-better stuff available out there, a lot less dearly, and a lot of it is free as PDF downloads.

The obvious: this book is long, bulky and expensive. However, there is the option of buying it used, and if you don't intend to do all three courses of calculus (or you spend a lot of time carrying your books around), it may make sense to buy the book in parts -- it's also sold in Calc 1/Calc 2/Multivariable sections.

As for the content, the text is nothing spectacular: while Stewart manages to nail some things, presenting them clearly and succinctly, there are also many long useless passages. My advice: don't try to read the book, just study his examples, which are often (but not always) quite good, and hope your teacher does a better job explaining the concepts that missed out on a good explanation here.

For good examples, good problems, good page layout and a favorable comparison to other mainstream university-level calculus texts, I rate it a 4/5.

Many reviewers have commented that the book is "horrible at teaching calculus", "horrible for first-time students", "leaves steps out of proofs", etc. I have not found any of these criticisms to be true.

The layout of the text is extremely neat and well-organized. You can read pages at a time and not feel bored. In fact, Stewart's ability to explain a concept without drawing it out overly long is a godsend. That being said, if you have big gaps in your knowledge of precalculus or trigonometry, you will not be babied in this book. He has diagnostic tests at the beginning though so that you can assess if you're ready to take on the material - if you do know the required material, the diagnostic tests are actually pretty fun.

This book is definitely complete - it has sections on everything you'll need for your Calc I, Calc II and Calc III courses, including a little section on curvature.

The problems are great - in each section, there are an abundance of problems which are similar enough to give you a good handle on the topic, especially if you're someone who needs to practice a concept a lot before getting it, but which are different enough to prepare you for most anything that will come your way, as long as you take the time to do enough of them.

It's hard to say this without seeming mean, but I think a lot of the reviewers imagine that there is some magic book out there which makes calculus easy. You can buy a book like "Calculus for Dummies" or "Calculus Made Easy" or another book like that, which will get you the formulas you need without much explanation, or water down the proofs so that they're more comprehensible, but the truth is that calculus will never be easy. Math at the calculus level and above takes real contemplation sometimes. To really get something out of any good book on calculus, you will have to sit there thinking, staring at the wall sometimes. And that's okay! The list of great mathematicians who didn't spend lots and lots of time on learning the subject is very few, probably even zero.

So to conclude, if you are trying to skate through a calculus class by reading as little as possible, then don't buy this book. But if you are looking for a book which explains things neatly and clearly and will give you a great foundation for more advanced calculus and analysis courses, this is your book.

(Oh, and yes this book is overpriced and Stewart has the money to buy a house that costs $24 million, but you shouldn't blame him. It's publishers that want to put out so many editions and god knows that the entire college textbook market is way overpriced.)

Explanations, problems, and content are superb. I used this textbook for Calculus I, II, and III. It was the first textbook I ever kept in college. If you're a Math, Physics, Chemistry, Computer Science, or Engineering major you'll have to take calculus and this book is a great learning tool.

I used this book for Calc 2 & 3 when I was a freshman undergrad at U of I. I don't think that this book was the most helpful option back then because it proves a lot that doesn't need to be understood at that level, and it neglects some of the very basic, broad overviews that Thomas & Finney provide.

However, I am currently looking through both Stewart and Thomas & Finney because I've needed to brush up on several concepts for a mathematical model that I'm building of evolution. I find that now Stewart's proofs are more helpful for following the intuitive leaps that higher-level authors use, whereas Thomas & Finney doesn't quite say enough. For passing math tests in undergrad calc, T & F is probably the better book, and perhaps as a reference for people doing purely applied math. Stewart's book has underrated explanatory power for people looking to interpret mathematical arguments. Unfortunately, I can't comment on how it compares to other texts besides T & F, and there are doubtless better books out there for that job. Still, this book isn't as bad as its rap, even if its best use is unclear.