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Single Variable Calculus: Concepts and Contexts / Edition 5

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Overview

James Stewart's well-received SINGLE VARIABLE CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept.
In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.
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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: 9780534496777
  • Publisher: Cengage Learning
  • Publication date: 6/28/2004
  • Edition description: Older Edition
  • Edition number: 5
  • Pages: 632
  • Product dimensions: 8.62 (w) x 10.00 (h) x 0.97 (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

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. Problems Plus. 6. APPLICATIONS OF INTEGRATION. Areas between Curves. Volume. Volumes by Cylindrical Shells. Work. Average Value of a Function. Review. Problems Plus. 7. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS. Inverse Functions, Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*, See the Preface. Exponential Functions and Their Derivatives. Logarithmic Functions. Derivatives of Logarithmic Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Inverse Trigonometric Functions, Applied Project: Where to Sit at the Movie. Hyperbolic Functions. Indeterminate Forms and L'Hospital's Rule, Writing Project: The Origins of L'Hospital's Rule. Review. Problems Plus. 8. 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. 9. 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. 10. DIFFERENTIAL EQUATIONS. Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations, Applied Project: How Fast Does a Tank Drain?, 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. 11. 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. Problems Plus. 12. 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. Laboratory Project: An Ellusive Limit. 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. Answers To Odd-Numbered Exercises. Index.

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