Single Variable Calculus: Early Transcendentals / Edition 6

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Overview

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

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Editorial Reviews

Booknews
In the new edition of this introductory text, Stewart (McMaster U.) presents all topics geometrically, numerically, algebraically, and verbally, for better conceptual understanding by students. Topics include functions and models; derivatives; differential equations; and infinite sequences and series. Annotation c. by Book News, Inc., Portland, Or.
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Product Details

  • ISBN-13: 9780495011699
  • Publisher: Cengage Learning
  • Publication date: 1/25/2007
  • Series: Available 2010 Titles Enhanced Web Assign Series
  • Edition description: 6TH
  • Edition number: 6
  • Pages: 912
  • Sales rank: 302,418
  • Product dimensions: 8.81 (w) x 10.30 (h) x 1.35 (d)

Meet 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 Brooks/Cole, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.
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Table of Contents

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. Principles of Problem Solving. 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. Problems Plus. 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. Problems Plus. 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 LHospitals Rule. Writing Project: The Origins of LHospitals Rule. Summary of Curve Sketching. Graphing with Calculus and Calculators. Optimization Problems. Applied Project: The Shape of a Can. Applications to Business and Economics. Newtons Method. Antiderivatives. Review. Problems Plus. 5. Integrals. Areas and Distances. The Definite Integral. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Indefinite Integrals and the Total Change Theorem. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Review. Problems Plus. 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. Problems Plus. 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. Problems Plus. 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. Applications to Economics and Biology. Probability. Review. Problems Plus. 9. Differential Equations. Modeling with Differential Equations. Direction Fields and Eulers Method. Separable Equations. Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay. Applied Project: Calculus and Baseball. The Logistic Equation. Linear Equations. Predator-Prey Systems. Review. Problems Plus. 10. Parametric Equations and Polar Coordinates. Curves Defined by Parametric Equations. Laboratory Project: Families of Hypocycloids. Tangents and Areas. Laboratory Project: Bezier Curves. Arc Length and Surface Area. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections. Conic Sections in Polar Coordinates. Applied Project: Transfer Orbits. Review. Problems Plus. 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. Representation of Functions as Power Series. Taylor and Maclaurin Series The Binomial Series. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Problems Plus. 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.

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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted April 4, 2008

    Not a great text for understanding the basic concepts...

    My instructor uses this textbook, so I had to read it. I wasn't new to calculus when I started reading this Text, but it really confused me out of my wits. No ways anyone can understand the basic concepts of calculus using this book. It is terrible. I'm so much used to self-teaching, so this book really frustrated me. It states that something is done in a certain way, but does not explain why it is put in that manner. The questions at the end of each section are hard to solve, because there aren't any examples in the section to support the questions. It makes calculus appear awfully absurd and baseless.

    2 out of 3 people found this review helpful.

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  • Anonymous

    Posted October 30, 2007

    Definitely not for beginners! Absolutely not for self-teaching!

    This book may be good for people that already studied calculus and need to retake a course, but as a learning source (especially for a beginner) it's terrible. Every section has its textual reading to explain the concepts and formulas to be covered in that section, but the sample problems and their solutions make no sense because they are just solved for you. The author doesn't do a thorough job of explaining why that X goes there or why this Y gets multiplied by D over X as H approaches zero! The solutions are just worked out and you have to look at some cryptic mess of formulas and variables and try to see what was done for each step of the solution because it's not explained in plain English. And if that wasn't bad enough, the actual assignment exercises at the end of each section can't be easily 'paired' up to the sample solutions from the textual reading so you have to put more work into trying to solve those. Just so frustrating. This was a required text book for college and I can honestly say I've never spent so much time trying to understand the concepts and examples presented in a math book and felt so discouraged because after four chapters I have nothing to show for it. Calculus is still a mystery to me.

    2 out of 3 people found this review helpful.

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  • Anonymous

    Posted November 13, 2007

    A reviewer

    Calculus is not a subject learned by reading. You must do the problems and dedicate the time. This text provides straight forward examples and approaches (at least as straight forward as is humanly possible) for learning calculus. However, to succeed you must do the problems at the end of each chapter. Consider buying the solution manual for odd problems. Also, search the internet for solutions to the problems. Many sites available.., e.g., cramster.com. In the end, your knowledge will be determined by the time you put in doing the problems.

    1 out of 3 people found this review helpful.

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