Calculus

by Rogawski, Jon

• ISBN13: 9781429210669
• ISBN10: 1429210664
• Format: Hardcover
• Copyright: 2007-06-22
• Publisher: W. H. Freeman

Summary

This new text presents calculus with solid mathematical precision but with an everyday sensibility that puts the main concepts in clear terms. It is rigorous without being inaccessible and clear without being too informalit has the perfect balance for instructors and their students.

Author Biography

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, and Graphs
    1.2 Linear and Quadratic Functions
    1.3 The Basic Classes of Functions
    1.4 Trigonometric Functions
    1.5 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 Trigonometric Functions
    3.7 The Chain Rule
    3.8 Implicit Differentiation
    3.9 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 Newton's Method
    4.8 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
    
  Chapter 6 APPLICATIONS OF THE INTEGRAL
    6.1 Area Between Two Curves
    6.2 Setting Up Integrals: Volume, Density, Average Value
    6.3 Volumes of Revolution
    6.4 The Method of Cylindrical Shells
    6.5 Work and Energy
    
  Chapter 7 EXPONENTIAL FUNCTIONS
    7.1 Derivative of f(x)=b^x and the Number e
    7.2 Inverse Functions
    7.3 Logarithms and their Derivatives
    7.4 Exponential Growth and Decay
    7.5 Compound Interest and Present Value
    7.6 Models Involving y'= k(y-b)
    7.7 L'Hoˆpital's Rule
    7.8 Inverse Trigonometric Functions
    7.9 Hyperbolic Functions
    
  Chapter 8 TECHNIQUES OF INTEGRATION
    8.1 Numerical Integration
    8.2 Integration by Parts
    8.3 Trigonometric Integrals
    8.4 Trigonometric Substitution
    8.5 The Method of Partial Fractions
    8.6 Improper Integrals
    
  Chapter 9 FURTHER APPLICATIONS OF THE INTEGRAGAL TAYLOR POLYNOMIALS
    9.1 Arc Length and Surface Area
    9.2 Fluid Pressure and Force
    9.3 Center of Mass
    9.4 Taylor Polynomials
    
  Chapter 10 INTRODUCTION TO DIFFERENTIAL EQUATIONS
    10.1 Solving Differential Equations
    10.2 Graphical and Numerical Methods
    10.3 The Logistic Equation
    10.4 First-Order Linear Equations
    
  Chapter 11 INFINITE SERIES
    11.1 Sequences
    11.2 Summing an Infinite Series
    11.3 Convergence of Series with Positive Terms
    11.4 Absolute and Conditional Convergence
    11.5 The Ratio and Root Tests
    11.6 Power Series
    11.7 Taylor Series
    
  Chapter 12 PARAMETRIC EQUATIONS, POLAR COORDINATES, AND CONIC SECTIONS
    12.1 Parametric Equations
    12.2 Arc Length and Speed
    12.3 Polar Coordinates
    12.4 Area and Arc Length in Polar Coordinates
    12.5 Conic Sections
    
  Chapter 13 VECTOR GEOMETRY
    13.1 Vectors in the Plane
    13.2 Vectors in Three Dimensions
    13.3 Dot Product and the Angle Between Two Vectors
    13.4 The Cross Product
    13.5 Planes in Three-Space
    13.6 Survey of Quadric Surfaces
    13.7 Cylindrical and Spherical Coordinates
    
  Chapter 14 CALCULUS OF VECTOR-VALUED FUNCTIONS
    14.1 Vector-Valued Functions
    14.2 Calculus of Vector-Valued Functions
    14.3 Arc Length and Speed
    14.4 Curvature
    14.5 Motion in Three-Space
    14.6 Planetary Motion According to Kepler and Newton
    
  Chapter 15 DIFFERENTIATION IN SEVERAL VARIABLES
    15.1 Functions of Two or More Variables
    15.2 Limits and Continuity in Several Variables
    15.3 Partial Derivatives
    15.4 Differentiability, Linear Approximation,and Tangent Planes
    15.5 The Gradient and Directional Derivatives
    15.6 The Chain Rule
    15.7 Optimization in Several Variables
    15.8 Lagrange Multipliers: Optimizing with a Constraint
    
  Chapter 16 MULTIPLE INTEGRATION
    16.1 Integration in Several Variables
    16.2 Double Integrals over More General Regions
    16.3 Triple Integrals
    16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
    16.5 Change of Variables
    
  Chapter 17 LINE AND SURFACE INTEGRALS
    17.1 Vector Fields
    17.2 Line Integrals
    17.3 Conservative Vector Fields
    17.4 Parametrized Surfaces and Surface Integrals
    17.5 Surface Integrals of Vector Fields
    
  Chapter 18 FUNDAMENTAL THEOREMS OF VECTOR ANALYSIS
    18.1 Green's Theorem
    18.2 Stokes' Theorem
    18.3 Divergence Theorem
    
  APPENDICES
    A. The Language of Mathematics
    B. Properties of Real Numbers C. Mathematical Induction
    and the BinomialTheorem D. Additional Proofs of Theorems
    
  ANSWERS TO ODD-NUMBERED EXERCISES