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More About This Textbook
Overview
Success in your calculus course starts here! James Stewart's CALCULUS texts are worldwide bestsellers for a reason: they are clear, accurate, and filled with relevant, realworld 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 builtin learning aids will help you build your mathematical confidence and achieve your goals in the course!
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.Product Details
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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 bestselling 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.
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. PredatorPrey 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 SecondDegree Equations. D: Trigonometry. E: Sigma Notation. F: Proofs of Theorems. G: The Logarithm Defined as an Integral. H: Complex Numbers. I: Answers to OddNumbered Exercises.