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

Preliminaries Real Numbers and the Real Line Lines, Circles, and Parabolas | |

Functions and Their Graphs | |

Identifying Functions; Mathematical Models | |

Combining Functions; Shifting and Scaling Graphs | |

Trigonometric Functions | |

Graphing with Calculators and Computers | |

Limits and Derivatives | |

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 | |

The Derivative as a Rate of Change | |

Derivatives of Trigonometric Functions | |

The Chain Rule and Parametric Equations | |

Implicit Differentiation | |

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 | |

WorkFluid Pressures and Forces | |

Transcendental Functions | |

Inverse Functions and their Derivatives | |

Natural Logarithms | |

The Exponential Functionax and loga xExponential Growth and Decay | |

Relative Rates of Growth | |

Inverse Trigonometric Functions | |

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 | |

The Ratio and Root Tests | |

Alternating Series, Absolute and Conditional Convergence | |

Power Series | |

Taylor and Maclaurin Series | |

Convergence of Taylor Series; Error Estimates | |

Applications of Power Series | |

Fourier Series | |

Appendices | |

Mathematical Induction | |

Proofs of Limit Theorems | |

Commonly Occurring Limits | |

Theory of the Real Numbers | |

Complex Numbers | |

The Distributive Law for Vector Cross Products | |

Determinants and Cramer's Rule | |

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