ISBN-10:
1429204184
ISBN-13:
2901429204186
Pub. Date:
02/28/2007
Publisher:
Freeman, W. H. & Company
Single Variable Calculus: Early Transcendentals / Edition 1

Single Variable Calculus: Early Transcendentals / Edition 1

by Jon Rogawski
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  • Product Details

    ISBN-13: 2901429204186
    Publisher: Freeman, W. H. & Company
    Publication date: 02/28/2007
    Edition description: Older Edition
    Pages: 800
    Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

    About the Author

    About Jon Rogawski
    Jon Rogawski received his undergraduate degree (and simultaneously a master's degree in mathematics) at Yale, and a Ph.D. in mathematics from Princeton University, where he studied under Robert Langlands. Prior to joining the Department of Mathematics at UCLA, where he is currently Full Professor, he held teaching positions at Yale and the University of Chicago, and research positions at the Institute for Advanced Study and University of Bonn.

    Jon's areas of interest are number theory, automorphic forms, and harmonic analysis on semisimple groups. He has published numerous research articles in leading mathematical journals, including a research monograph entitled "Automorphic Representations of Unitary Groups in Three Variables" (Princeton University Press). He is the recipient of a Sloan Fellowship and an editor of The Pacific Journal of Mathematics.

    Jon and his wife Julie, a physician in family practice, have four children. They run a busy household and, whenever possible, enjoy family vacations in the mountains of California. Jon is a passionate classical music lover and plays the violin and classical guitar.

    Table of Contents

    Chapter 1 PRECALCULUS REVIEW
    1.1 Real Numbers, Functions, Equations, and Graphs
    1.2 Linear and Quadratic Functions
    1.3 The Basic Classes of Functions
    1.4 Trigonometric Functions
    1.5 Inverse Functions
    1.6 Exponential and Logarithmic Functions
    1.7 Technology: Calculators and Computers

    Chapter 2 LIMITS
    2.1 Limits, Rates of Change, and Tangent Lines
    2.2 Limits: A Numerical and Graphical Approach
    2.3 Basic Limit Laws
    2.4 Limits and Continuity
    2.5 Evaluating Limits Algebraically
    2.6 Trigonometric Limits
    2.7 Intermediate Value Theorem
    2.8 The Formal Definition of a Limit

    Chapter 3 DIFFERENTIATION
    3.1 Definition of the Derivative
    3.2 The Derivative as a Function
    3.3 Product and Quotient Rules
    3.4 Rates of Change
    3.5 Higher Derivatives
    3.6 Derivatives of Trigonometric Functions
    3.7 The Chain Rule
    3.8 Implicit Differentiation
    3.9 Derivatives of Inverse Functions
    3.10 Derivatives of Logarithmic Functions
    3.11 Related Rates

    Chapter 4 APPLICATIONS OF THE DERIVATIVE
    4.1 Linear Approximation and Applications
    4.2 Extreme Values
    4.3 The Mean Value Theorem and Monotonicity
    4.4 The Shape of a Graph
    4.5 Graph Sketching and Asymptotes
    4.6 Applied Optimization
    4.7 L'Hoˆpital's Rule
    4.8 Newton's Method
    4.9 Antiderivatives

    Chapter 5 THE INTEGRAL
    5.1 Approximating and Computing Area
    5.2 The Definite Integral
    5.3 The Fundamental Theorem of Calculus, Part I
    5.4 The Fundamental Theorem of Calculus, Part II
    5.5 Net or Total Change as the Integral of a Rate
    5.6 Substitution Method
    5.7 Integrals of Exponential and Logarithmic Functions
    5.8 Exponential Growth and Decay

    Chapter 6 APPLICATIONS OF THE INTEGRAL
    6.1 Area Between Two Curves
    6.2 Setting Up Integrals: Volumes, Density, Average Value
    6.3 Volumes of Revolution
    6.4 The Method of Cylindrical Shells
    6.5 Work and Energy

    Chapter 7 TECHNIQUES OF INTEGRATION
    7.1 Numerical Integration
    7.2 Integration by Parts
    7.3 Trigonometric Integrals
    7.4 Trigonometric Substitution
    7.5 Integrals of Hyperbolic and Inverse Hyperbolic
    Functions
    7.6 The Method of Partial Fractions
    7.7 Improper Integrals

    Chapter 8 FURTHER APPLICATIONSOF THE INTEGRAL AND TAYLOR POLYNOMIALS
    8.1 Arc Length and Surface Area
    8.2 Fluid Pressure and Force
    8.3 Center of Mass
    8.4 Taylor Polynomials

    Chapter 9 INTRODUCTION TO DIFFERENTIAL EQUATIONS
    9.1 Separable Equations
    9.2 Models Involving y'= k(y-b)
    9.3 Graphical and Numerical Methods
    9.4 The Logistic Equation
    9.5 First-order Linear Equations

    Chapter 10 INFINITE SERIES
    10.1 Sequences
    10.2 Summing an Infinite Series
    10.3 Convergence of Series with Positive Terms
    10.4 Absolute and Conditional Convergence
    10.5 The Ratio and Root Tests
    10.6 Power Series
    10.7 Taylor Series

    Chapter 11 PARAMETRIC EQUATIONS, mPOLAR COORDINATES, AND CONIC SECTIONS
    11.1 Parametric Equations
    11.2 Arc Length and Speed
    11.3 Polar Coordinates
    11.4 Area and Arc Length in Polar Coordinates
    11.5 Conic Sections

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