(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.) | |

Functions | |

Functions and Their Graphs | |

Identifying Functions; Mathematical Models | |

Combining Functions; Shifting and Scaling Graphs | |

Graphing with Calculators and Computers | |

Exponential Functions | |

Inverse Functions and Logarithms | |

Limits and Continuity | |

Rates of Change and Limits | |

Calculating Limits Using the Limit Laws | |

Precise Definition of a Limit | |

One-Sided Limits and Limits at Infinity | |

Infinite Limits and Vertical Asymptotes Continuity | |

Tangents and Derivatives | |

Differentiation | |

The Derivative as a Function | |

Differentiation Rules for Polynomials, Exponentials, Products and Quotients | |

The Derivative as a Rate of Change | |

Derivatives of Trigonometric Functions | |

The Chain Rule and Parametric Equations | |

Implicit Differentiation | |

Derivatives of Inverse Functions and Logarithms | |

Inverse Trigonometric Functions | |

Related Rates | |

Linearization and Differentials | |

Applications of Derivatives | |

Extreme Values of Functions | |

The Mean Value Theorem | |

Monotonic Functions and the First Derivative Test | |

Concavity and Curve Sketching | |

Applied Optimization Problems | |

Indeterminate Forms and L'Hopital's Rule Newton's Method Antiderivatives | |

Integration | |

Estimating with Finite Sums | |

Sigma Notation and Limits of Finite Sums | |

The Definite Integral | |

The Fundamental Theorem of Calculus | |

Indefinite Integrals and the Substitution Rule | |

Substitution and Area Between Curves | |

Applications of Definite Integrals | |

Volumes by Slicing and Rotation About an Axis | |

Volumes by Cylindrical Shells | |

Lengths of Plane Curves | |

Moments and Centers of Mass | |

Areas of Surfaces of Revolution and The Theorems of Pappus Work | |

Fluid Pressures and Forces | |

Integrals and Transcendental Functions | |

The Logarithm Defined as an Integral | |

Exponential Growth and Decay | |

Relative Rates of Growth | |

Hyperbolic Functions | |

Techniques of Integration | |

Basic Integration Formulas | |

Integration by Parts | |

Integration of Rational Functions by Partial Fractions | |

Trigonometric Integrals | |

Trigonometric Substitutions | |

Integral Tables and Computer Algebra Systems | |

Numerical Integration | |

Improper Integrals | |

Further Applications of Integration | |

Slope Fields and Separable Differential Equations | |

First-Order Linear Differential Equations | |

Euler's Method | |

Graphical Solutions of Autonomous Equations | |

Applications of First-Order Differential Equations | |

Conic Sections and Polar Coordinates | |

Conic Sections and Quadratic Equations | |

Classifying Conic Sections by Eccentricity | |

Quadratic Equations and Rotations | |

Conics and Parametric Equations; The Cycloid | |

Polar Coordinates | |

Graphing in Polar Coordinates | |

Area and Lengths in Polar Coordinates | |

Conic Sections in Polar Coordinates | |

Infinite Sequences and Series Sequences | |

Infinite Series | |

The Integral Test | |

Comparison Tests | |

Table of Contents provided by Publisher. All Rights Reserved. |