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 chapter one FUNCTIONS
  1.1　Functions
  1.2　Arithmetic Operations on and Composition of Functions
  1.3　Families of Functions
  1.4　Inverse Functions; Inverse Trigonometric Functions
  1.5　Exponential and Logarithmic Functions
  1.6　Parametric Equations
 chapter two LIMITS AND CONTINUITY
  2.1　Limits(An Intuitive Approach)
  2.2　Computing Limits
  2.3　Limits at Infinity; End Behavior of a Function
  2.4　Limits (Discussed More Rigorously)
  2.5　Continuity
  2.6　Continuity of Trigonometric and Inverse Functions
 chapter three THE DERIVATIVE
  3.1　Tangent Lines, Velocity, and General Rates of Change
  3.2　The Derivative Function
  3.3　Techniques of Differentiation
  3.4　The Product and Quotient Rules
  3.5　Derivatives of Trigonometric Functions
  3.6　The Chain Rule
  3.7　Related Rates
  3.8　Local Linear Approximation; Differentials
 chapter four DERIVATIVES OF LOGARITHMIC, EXPONENTIAL, AND INVERSE TRIGONOMETRIC FUNCTIONS
  4.1　Implicit Differentiation
  4.2　Derivatives of Logarithmic Functions
  4.3　Derivatives of Exponential and Inverse Trigonometric Functions
  4.4　L’H pital’s Rule; Indeterminate Forms
 chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS
  5.1　Analysis of Functions I: Increase, Decrease, and Concavity
  5.2　Analysis of Functions II: Relative Extrema
  5.3　More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology
  5.4　Absolute Maxima and Minima
  5.5　Applied Maximum and Minimum Problems
  5.6　Rolle’s Theorem; Mean-Value Theorem
 chapter six INTEGRATION
  6.1　An Overview of the Area Problem
  6.2　The Indefinite Integral
  6.3　Integration by Substitution
  6.4　The Definition of Area as a Limit
  6.5　The Definite Integral
  6.6　The Fundamental Theorem of Calculus
  6.7　Evaluating Definite Integrals by Substitution
  6.8　Logarithmic Functions from the Integral Point of View
 chapter seven APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY AND ENGINEERING
  7.1　Area Between Two Curves
  7.2　Volumes by Slicing; Disks and Washers
  7.3　Volumes by Cylindrical Shells
  7.4　Length of a Plane Curve
  7.5　Work
  7.6　Fluid Pressure and Force
 chapter eight PRINCIPLES OF INTEGRAL EVALUATION
  8.1　Integration by Parts
  8.2　Trigonometric Integrals
  8.3　Trigonometric Substitutions
  8.4　Integrating Rational Functions by Partial Fractions
  8.5　Improper Integrals
 chapter nine MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
  9.1　First-Order Differential Equations and Applications
  9.2　Modeling with First-Order Differential Equations
  9.3　Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring
 chapter ten INFINITE SERIES
  10.1　Sequences
  10.2　Monotone Sequences
  10.3　Infinite Series
  10.4　Convergence Tests
  10.5　The Comparison, Ratio, and Root Tests
  10.6　Alternating Series; Conditional Convergence
  10.7　Maclaurin and Taylor Polynomials
  10.8　Maclaurin and Taylor Series; Power Series
  10.9　Convergence of Taylor Series
  10.10　Differentiating and Integrating Power Series
 chapter eleven THREE-DIMENSIONAL SPACE; VECTORS
  11.1　Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
  11.2　Vectors
  11.3　Dot Product; Projections
  11.4　Cross Product
  11.5　Parametric Equations of Lines
  11.6　Planes in 3-Space
  11.7　Quadric Surfaces
  11.8　Cylindrical and Spherical Coordinates
 chapter twelve VECTOR-VALUED FUNCTIONS
  12.1　Introduction to Vector-Valued Functions
  12.2　Calculus of Vector-Valued Functions
 chapter thirteen PARTIAL DERIVATIVES
  13.1　Functions of Two or More Variables
  13.2　Limits and Continuity
  13.3　Partial Derivatives
  13.4　Differentiability, Differentials, and Local Linearity
  13.5　The Chain Rule
  13.6　Directional Derivatives and Gradients
  13.7　Tangent Planes and Normal Vectors
  13.8　Maxima and Minima of Functions of Two Variables
  13.9　Lagrange Multipliers
 chapter fourteen MULTIPLE INTEGRALS
  14.1　Double Integrals
  14.2　Double Integrals over Nonrectangular Regions
  14.3　Double Integrals in Polar Coordinates
  14.4　Parametric Surfaces; Surface Area
  14.5　Triple Integrals
  14.6　Triple Integrals in Cylindrical and Spherical Coordinates
  14.7　Change of Variables in Double Integrals; Jacobians
 chapter fifteen TOPICS IN VECTOR CALCULUS
  15.1　Vector Fields
  15.2　Line Integrals
  15.3　Independence of Path; Conservative Vector Fields
  15.4　Green’s Theorem
  15.5　Surface Integrals
  15.6　Applications of Surface Integrals; Flux
  15.7　The Divergence Theorem
  15.8　Stokes’ Theorem
 appendix
  SELECTED PROOFS
  ANSWERS TO SELECTED EXERCISES
  GLOSSARY