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Jan. 19 2011 1111426686 978-1111426682 7

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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

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 is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is 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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Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com: 3.7 out of 5 stars  307 reviews
85 of 100 people found the following review helpful
1.0 out of 5 stars Horrible for the first-time Calculus student April 17 2008
By Scott - Published on Amazon.com
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.
24 of 26 people found the following review helpful
4.0 out of 5 stars crap exposition, great problems Dec 20 2009
By Ashraf Eassa - Published on Amazon.com
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
25 of 28 people found the following review helpful
By Let's Compare Options Preptorial - Published on Amazon.com
Format:Hardcover|Verified Purchase
This is one of the best calculus textbooks ever written, with the most intuitive examples and illustration of any text out there. It is #2 in all the courses we survey, and in the top 3 of Library purchases for books with 1,200 pages or more. That said:

1. Make SURE you get the 7th edition, it is heavily revised.

2. Many of the reviews trash talking this book (it IS a five star text!) are due to purchasers not knowing what "hybrid" means. THE PAPERBACK VERSION OF THIS BOOK IS DIFFERENT! A "hybrid" is a class that combines online with brick and mortar class attendance, and some publishers are now creating "hybrid" texts with some material integrated with the online LMS (learning management system of the school or teacher) and the text. NEVER BUY a HYBRID TEXT if you are not taking a class!

3. Some folks saw the price of this book, then bought the "paperback" at far less, from a third party on Amazon. THIS IS A BIG MISTAKE! If you get a hybrid book, and the third party is honest and says you don't get access codes, you'll be missing half the book in this case! Worse, if the book says "hybrid" you MUST get a second access code from the teacher who is giving the class-- DO NOT BUY a hybrid for self study!!

Sadly, the circus around this text is limiting the great value of the HARD COVER, COMPLETE text for self study. It is one of the best there is in gentle examples of derivative applications, even in multivariate and ODE forms. It's target is those who didn't do particularly well in HS calc, or never had any including limits, or are rusty, so please evaluate it on its own merits, not the mistaken hybrid reviews.

BTW Amazon is NOT ripping anyone off with this-- you just need to understand that hybrid MEANS incomplete! In many cases you can save money with a used paperback, but NOT HERE!!

Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
17 of 18 people found the following review helpful
3.0 out of 5 stars Meh... Dec 20 2007
By Me - Published on Amazon.com
I taught Multivariable Calculus using this book as a TA. You will learn multivariable calculus, it's just as good as any other calculus text but with two major problems!

1) It does Taylor no justice! The multivariable version of the Taylor Approximation is absent. The author mentions linearizing a given function [of two variables] and thats it! C'mon! This is such an important aspect of math, physics, engineering, etc... why drop it?

2) The chapter on Gauss' Theorem, Stokes Theorem (Green's as well), and the Fundamental Theorem of Calculus is poor, it provides little by way of intuitively understanding these integral theorems. As an added bonus (sarcasm), students, I find, have a harder time geometrically and physically understanding what the Curl and Divergence of vector fields represent! This is most unfortunate, especially for future physicists and engineers!

There are books out there that would complement Stewart on this: "Div, Grad, Curl, And All That" by Schey is one of them; the book written by Marsden and Tromba is also a good place to go for both the integral theorems and the Taylor Polynomial.

Other than this unfortunate turn of events, Stewart IS a good book. I do recommend Thomas' Calculus instead - the problem with that (as well as with Stewart) is that the price is so high. Get an older edition, you won't be missing much, you'll only gain insight and an appreciation for calculus as an undergrad.
42 of 50 people found the following review helpful
1.0 out of 5 stars not a correct book Aug. 31 2011
By gnoik - Published on Amazon.com
Format:Paperback|Verified Purchase
It is showed by the website that just the cover is different between the hardcover and papaerwork , but the substance in the book is also different with the hardcover one. There is no exercises in this book and I cannot use it for my class. Someone has told me this book is made for a unique school to use. and the code in the book is useless. I cannot enter in the website without a class key.

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