Note: Each chapter concludes with Review Exercises and P.S. Problem Solving | |

Preparation for Calculus | |

Graphs and Model | |

Linear Models and Rates of Change | |

Functions and Their Graphs | |

Fitting Models to Data | |

Limits and Their Properties | |

A Preview of Calculus | |

Finding Limits Graphically and Numerically | |

Evaluating Limits Analytically | |

Continuity and One-Sided Limits | |

Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions | |

Differentiation | |

The Derivative and the Tangent Line Problem | |

Basic Differentiation Rules and Rates of Change | |

The Product and Quotient Rules and Higher-Order Derivatives | |

The Chain Rule | |

Implicit Differentiation Section Project: Optical Illusions | |

Related Rates | |

Applications of Differentiation | |

Extrema on an Interval | |

Rolle''s Theorem and the Mean Value Theorem | |

Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |

Concavity and the Second Derivative Test | |

Limits at Infinity | |

A Summary of Curve Sketching | |

Optimization Problems Section Project: Connecticut River | |

Newton''s Method | |

Differentials | |

Integration | |

Antiderivatives and Indefinite Integration | |

Area | |

Reimann Sums and Definite Integrals | |

The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |

Integration by Substitution | |

Numerical Integration | |

Logarithmic, Exponential, and Other Transcendental Functions | |

The Natural Logarithmic Function: Differentiation | |

The Natural Logarithmic Function: Integration | |

Inverse Functions | |

Exponential Functions: Differentiation and Integration | |

Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |

Differential Equations: Growth and Decay | |

Differential Equations: Separation of Variables | |

Inverse Trigonometric Functions: Differentiation | |

Inverse Trigonometric Functions: Integration | |

Hyperbolic Functions Section Project: St. Louis Arch | |

Applications of Integration | |

Area of a Region Between Two Curves | |

Volume: The Disk Method | |

Volume: The Shell Method Section Project: Saturn | |

Arc Length and Surfaces of Revolution | |

Work Section Project: Tidal Energy | |

Moments, Centers of Mass, and Centroids | |

Fluid Pressure and Fluid Force | |

Integration Techniques, L''Hocirc;pital''s Rule, and Improper Integrals | |

Basic Integration Rules | |

Integration by Parts | |

Trigonometric Integrals Section Project: Power Lines | |

Trigonometric Substitution | |

Partial Fractions | |

Integration by Tables and Other Integration Techniques | |

Indeterminant Forms and L''Hocirc;pital''s Rule | |

Improper Integrals | |

Infinite Series | |

Sequences | |

Series and Convergence Section Project: Cantor''s Disappearing Table | |

The Integral Test and p-Series Section Project: The Harmonic Series | |

Comparisons of Series Section Project: Solera Method | |

Alternating Series | |

The Ratio and Root Tests | |

Taylor Polynomials and Approximations | |

Power Series | |

Representation of Functions by Power Series | |

Taylor and Maclaurin Series | |

Conics, Parametric Equations, and Polar Coordinates | |

Conics and Calculus | |

Plane Curves and Parametric Equations Section Project: Cycloids | |

Parametric Equations and Calculus | |

Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |

Area and Arc Length in Polar Coordinates | |

Polar Equations of Conics and Kepler''s Laws | |

Vectors and the Geometry of Space | |

Vectors in the Plane | |

Space Coordinates and Vectors in Space | |

The Dot Product of Two Vectors | |

The Cross Product of Two Vectors in Space | |

Lines and Planes in Space Section Project: Distances in Space | |

Surfaces in Space | |

Cylindrical and Spherical Coordinates | |

Vector-Valued Functions | |

Vector-Valued Functions Section Project: Witch of Agnesi | |

Differentiation and Integration of Vector-Valued Functions | |

Velocity and Acceleration | |

Tangent Vectors and Normal Vectors | |

Arc Length and Curvature | |

Functions of Several Variables | |

Introduction to Functions of Several Variables | |

Limits and Continuity | |

Partial Derivatives Section Project: Moireacute; Fringes | |

Differentials | |

Chain Rules for Functions of Several Variables | |

Directional Derivatives and Gradients | |

Tangent Planes and Normal Lines Section Project: Wildflowers | |

Extrema of Functions of Two Variables | |

Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline | |

Lagrange Multipliers | |

Multiple Integration | |

Iterated Integrals and Area in the Plane | |

Double Integrals and Volume | |

Change of Variables: Polar Coordinates | |

Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail | |

Surface Area Section Project: Capillary Action | |

Triple Integrals and Applications | |

Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres | |

Change of Variables: Jacobians | |

Vector Analysis | |

Vector Fields | |

Line Integrals | |

Conservative Vector Fields and Independence of Path | |

Green''s Theorem Section Project: Hyperbolic and Trigonometric Functions | |

Parametric Surfaces | |

Surface Integrals Section Project: Hyperboloid of One Sheet | |

Divergence Theorem | |

Stoke''s Theorem Section Project: The Planimeter | |

Appendices | |

Additional Topics in Differential Equations | |

Proofs of Selected Theorems | |

Integration Tables | |

Precalculus Review | |

Rotation and the General Second-Degree Equation | |

Complex Numbers | |

Business and Economic Applications | |

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