Preface xiv
 To the Student xxvi
 A Preview of Calculus
 1 functions and Models
  1.1 Four Ways to Represent a Function
  1.2 Mathematical Models：A Catalog of Essential Functions
  1.3 New Functions from Old Functions
  1.4 Graphing Calculators and Computers
  1.5 Exponential Functions
  1.6 Inverse Functions and Logarithms Review
 Principles of Problem Solving
 2 Limits and Derivatives
  2.1 The Tangent and Velocity Problems
  2.2 The Limit of a Function
  2.3 Calculating Limits Using the Limit Laws
  2.4 The Precise Definition of a Limit
  2.5 Continuity 124
  2.6 Limits at Infinity；Horizontal Asymptotes tangents，Velocities and Other Rates of Change
  2.8 Derivatives
   Writing Project·Early Methods for Finding Tangents
  2.9 The Derivative as a Function Review
   Problems Plus
 3 Differentiation Rules
  3.1 Derivatives of Polynomials and Exponential Functions
  3.2 The Product and Quotient Rules
  3.3 Rates of Change in the Natural and Social Sciences
  3.4 Derivatives of Trigonometric Functions
  3.5 The Chain Rule
  3.6 Implicit Differentiation
  3.1 Higher Derivatives
   Applied Project·Where Should a Pilot Start Descent?
   Applied Project·Building a Better Roller Coaster
  3.8 Derivatives of Logarithmic Functions
  3.9 Hyperbolic Functions
  3.10 Related Rates
  3.11 Linear Approximations and Differentials
   Laboratory Projcot·Taylor Polynomials
   Review
   Problems Plus
 4 Applications of Differentiation
  4.1 Maximum and Minimum Values
   Applied Project·The Calculus of Rainbows
  4.2 The Mean Value Theorem
  4.3 How Derivatives Affect the Shape of a Graph
  4.4 Indeterminate Forms and L'Hospital's Rule
   Writing Project· The Origins of L'Hospital'e Rule
  4.5 Summary of Curve Sketching
  4.6 Graphing with Calculus and Calculators
  4.7 Optimization Problems
   Applied Project·The Shape of a Can
  4.8 Applications to Business and Economics
  4.9 Newton's Method
  4.10 Antiderivatives
   Review
   Problems Plus
 5 Integrals
  5.1 Areas and Distances
  5.2 The Definite Integral
   Discovery Project·Area Functions
  5.3 The Fundamental Theorem of Calculus
  5.4 Indefinite Integrals and the Net Change Theorem
   Writing Project·Newton, Leibniz, and the Invention of Calculus
  5.5 The Substitution Rule
  5.6 The Logarithm Defined as an Integral
   Review
   Problems Plus
 6 Applications of Integration
  6.1 Areas between Curves
  6.2 Volumes
  6.3 Volumes by Cylindrical Shells
  6.4 Work
  6.5 Average Value of a Function
   Applied Project·Where to Sit at the Movies
   Review
   Probleme Plus
 7 Techniques of Integration
  7.1 Integration by Parts
  7.2 Trigonometric Integrals
  7.3 Trigonometric Substitution
  7.4 Integration of Rational Functions by Partial Fractions
  7.5 Strategy for Integration
  7.6 Integration Using Tables and Computer Algebra Systems
   Discovery Project·Patterns in Integrals
  7.7 Approximate Integration
  7.8 Improper Integrals
   Review
   Problems Plus
 8 Further Applications of Integration
  8.1 Arc Length
   Discovery Project·Arc Length Contest
  8.2 Area of a Surface of Revolution
   Discovery Project·Rotating on a Slant
  8.3 Applications to Physics and Engineering
  8.4 Applications to Economics and Biology
  8.5 Probability
   Review
   Problems Plus
 9 Differential Equations
  9.1 Modeling with Differential Equations
  9.2 Direction Fields and Euler's Method
  9.3 Separable Equations
   Applied Project·How Fast Does a Tank Drain?
   Applied Project·Which Is Faster, Going Up or Coming Down?
  9.4 Exponential Growth and Decay
   Applied Project·Calculus and Baseball
  9.5 The Logistic Equation
  9.6 Linear Equations
  9.7 Predator-Prey Systems
   Review
   Problems Plus
 10 Parametric Equations and Polar Coordinates
  10.1 Curves Defined by Parametric Equations
   Laboratory Project·Running Circles around Circles
  10.2 Calculus with Parametric Curves
   Laboratory Project·B●zier Curves
  10.3 Polar Coordinates
  10.4 Areas and Lengths in Polar Coordinates
  10.5 Conic Sections
  10.6 Conic Sections in Polar Coordinates Review
   Problems Plug
 11 Infinite Sequences and Series
  11.1 Sequences
   Laboratory Project·Logistic Sequences
  11.2 Series
  11.3 The Integral Test and Estimates of Sums
  11.4 The Comparison Tests
  11.5 Alternating Series
  11.6 Absolute Convergence and the Ratio and Root Tests
  11.7 Strategy for Testing Series
  11.8 Power Series
  11.9 Representations of Functions as Power Series
  11.10 Taylor and Maclaurin Series
   Laboratory Project·An Elusive Limit
  11.11 The Binomial Series
   Writing Project·How Newton Discovered the Binomial Series
  11.12 Applications of Taylor Polynomials
   Applied Project·Radiation from the Stars
   Review
   Problemo Plus
 12 Vectors and the Geometry of Space
  12.1 Three-Dimensional Coordinate Systems
  12.2 Vectors
  12.3 The Dot Product
  12.4 The Cross Product
   Discovery Project·The Geometry of a Tetrahedron
  12.5 Equations of Lines and Planes
   Laboratory Project·Putting 3D in Perspective
  12.6 Cylinders and Quadric Surfaces
  12.7 Cylindrical and Spherical Coordinates
   Laboratory Project·Families of Surfaces
   Review
   Problems Plus
 13 Vector Functions
  13.1 Vector Functions and Space Curves
  13.2 Derivatives and Integrals of Vector Functions
  13.3 Arc Length and Curvature
  13.4 Motion in Space：Velocity and Acceleration
   Applied Projact·Kepler's Laws
   Review
   Problems Plus
 14 Partial Derivatives
  14.1 Functions of Several Variables
  14.2 Limits and Continuity
  14.3 Partial Derivatives
  14.4 Tangent Planes and Linear Approximations
  14.5 The Chain Rule
  14.6 Directional Derivatives and the Gradient Vector
  14.7 Maximum and Minimum Values
   Applied Project·Designing a Dumpster
   Discovery Project·Quadratic Approximations and Critical Points
  14.8 Lagrange Multipliers
   Applied Project·Rocket Science
   Applied Project·Hydro-Turbine Optimization
   Review
   Problems Plus
 15 Multiple Integrals
  15.1 Double Integrals over Rectangles
  15.2 Iterated Integrals
  15.3 Double Integrals over General Regions
  15.4 Double Integrals in Polar Coordinates
  15.5 Applications of Double Integrals
  15.6 Surface Area
  15.7 Triple Integrals
   Discovery Project·Volumes of Hyperspheres
  15.8 Triple Integrals in Cylindrical and Spherical Coordinates 1033
   Applied Project·Roller Derby
   Discovery Project·The Intersection of Three Cylinders
  15.9 Change of Variables in Multiple Integrals
   Review
   Problems Plus
 16 Vector Calculus
  16.1 Vector Fields
  16.2 Line Integrals
  16.3 The Fundamental Theorem for Line Integrals
  16.4 Green's Theorem
  16.5 Curl and Divergence
  16.6 Parametric Surfaces and Their Areas
  16.7 Surface Integrals
  16.8 Stokes'Theorem
   Writing Project-Three Men and Two Theorems
  16.9 The Divergence Theorem
  16.10 Summary
   Review
   Problems Plus
 17 Second-Order Differential Equations
  17.1 Second-Order Linear Equations
  17.2 Nonhomogeneous Linear Equations
  17.3 Applications of Second-Order Differential Equations
  17.4 Series Solutions
   Review
  Appendixes A1
  A Numbers, Inequalities, and Absolute Values
  B Coordinate Geometry and Lines
  C Graphs of Second-Degree Equations
  D Trigonometry
  E Sigma Notation
  F Proofs of Theorems
  G Complex Numbers
  H Answers to Odd-Numbered Exercises
  Index A12