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Calculus: Early Transcendentals, Hybrid Edition (with Enhanced WebAssign with eBook Printed Access Card for Multi Term Math and Science) Paperback – Jan 19 2011

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Product Details

  • Paperback: 1056 pages
  • Publisher: Brooks Cole; 7 edition (Jan. 19 2011)
  • Language: English
  • ISBN-10: 1111426686
  • ISBN-13: 978-1111426682
  • Product Dimensions: 25.1 x 21.3 x 3.6 cm
  • Shipping Weight: 1.8 Kg
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: #54,408 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description


Diagnostic Tests. A Preview of Calculus. 1. FUNCTIONS AND MODELS. Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Review. 2. LIMITS AND DERIVATIVES. The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. The Precise Definition of a Limit. Continuity. Limits at Infinity; Horizontal Asymptotes. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. 3. DIFFERENTIATION RULES. Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Derivatives of Logarithmic Functions. Rates of Change in the Natural and Social Sciences. Exponential Growth and Decay. Related Rates. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Hyperbolic Functions. Review. 4. APPLICATIONS OF DIFFERENTIATION. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. The Mean Value Theorem. How Derivatives Affect the Shape of a Graph. Indeterminate Forms and L'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Newton's Metho. Antiderivatives. Review. 5. INTEGRALS. Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Net Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. 6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Applied Project: Where to Sit at the Movies. Review. 7. TECHNIQUES OF INTEGRATION. Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. 8. FURTHER APPLICATIONS OF INTEGRATION. Arc Length. Discovery Project: Arc Length Contest. Area of a Surface of Revolution. Discovery Project: Rotating on a Slant. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Probability. Review. 9. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Models for Population Growth. Applied Project: Calculus and Baseball. Linear Equations. Predator-Prey Systems. Review. 10. PARAMETRIC EQUATIONS AND POLAR COORDINATES. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Calculus with Parametric Curves. Laboratory Project: Bezier Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Review. 11. INFINITE SEQUENCES AND SERIES. Sequences. Laboratory Project: Logistic Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. 12. VECTORS AND THE GEOMETRY OF SPACE. Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Quadric Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. 13. VECTOR FUNCTIONS. Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler's Laws. Review. 14. PARTIAL DERIVATIVES. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Differentials. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. 15. MULTIPLE INTEGRALS. Double Integrals over Rectangles. Iterated Integrals. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical and Spherical Coordinates. Applied Project: Roller Derby. Discovery Project: The Intersection of Three Cylinders. Change of Variables in Multiple Integrals. Review. 16. VECTOR CALCULUS. Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. 17. SECOND-ORDER DIFFERENTIAL EQUATIONS. Second-Order Linear Equations. Nonhomogeneous Linear Equations. Applications of Second-Order Differential Equations. Series Solutions. Review. APPENDIXES. A Numbers, Inequalities, and Absolute Values. B Coordinate Geometry and Lines. C Graphs of Second-Degree Equations. D Trigonometry. E Sigma Notation. F Proofs of Theorems. G The Logarithm Defined as an Integral. H Complex Numbers. I Answers to Odd-Numbered Exercises.

About the Author

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

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By Stacey Noddin on June 24 2015
Format: Hardcover Verified Purchase
Very happy with the book. It was excellent for my daughters course.
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144 of 153 people found the following review helpful
Excellent but Dense: A comparative Review Jan. 24 2006
By R. Markham - Published on
Format: Hardcover
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.
128 of 137 people found the following review helpful
Why Such Varied Reviews? Feb. 26 2004
By A Customer - Published on
Format: Hardcover
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.
112 of 131 people found the following review helpful
Horrible for the first-time Calculus student April 17 2008
By Scott - Published on
Format: Hardcover
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.


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.


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.
20 of 21 people found the following review helpful
If I could rate it 3.5 stars, I would Oct. 12 2005
By Greg Schreiter - Published on
Format: Hardcover
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.
24 of 26 people found the following review helpful
crap exposition, great problems Dec 20 2009
By A. Eassa - Published on
Format: Hardcover Verified Purchase
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