Note: Each chapter includes an Algebra Review, Chapter Summary, Study | |

Strategies, Review Exercises, and Sample Post-Graduation Exam Questions | |

A Precalculus Review | |

The Real Number Line and Order | |

Absolute Value and Distance on the Real Number Line | |

Exponents and Radicals | |

Factoring Polynomials | |

Fractions and Rationalization | |

Functions, Graphs, and Limits | |

The Cartesian Plane and the Distance Formula | |

Graphs of Equations | |

Lines in the Plane and Slope | |

Functions | |

Limits | |

Continuity | |

Differentiation | |

The Derivative and the Slope of a Graph | |

Some Rules for Differentiation | |

Rates of Change: Velocity and Marginals | |

The Product and Quotient Rules | |

The Chain Rule | |

Higher-Order Derivatives | |

Implicit Differentiation | |

Related Rates | |

Applications of the Derivative | |

Increasing and Decreasing Functions | |

Extrema and the First-Derivative Test | |

Concavity and the Second-Derivative Test | |

Optimization Problems | |

Business and Economics Applications | |

Asymptotes | |

Curve Sketching: A Summary | |

Differentials and Marginal Analysis | |

Exponential and Logarithmic Functions | |

Exponential Functions | |

Natural Exponential Functions | |

Derivatives of Exponential Functions | |

Logarithmic Functions | |

Derivatives of Logarithmic Functions | |

Exponential Growth and Decay | |

Integration and Its Applications | |

Antiderivatives and Indefinite Integrals | |

The General Power Rule | |

Exponential and Logarithmic Integrals | |

Area and the Fundamental Theorem of Calculus | |

The Area of a Region Bounded by Two Graphs | |

The Definite Integral as the Limit of a Sum | |

Volumes of Solids of Revolution | |

Techniques of Integration | |

Integration by Substitution | |

Integration by Parts and Present Value | |

Partial Fractions and Logistic Growth | |

Integration Tables and Completing the Square | |

Numerical Integration | |

Improper Integrals | |

Functions of Several Variables | |

The Three-Dimensional Coordinate System | |

Surfaces in Space | |

Functions of Several Variables | |

Partial Derivatives | |

Extrema of Functions of Two Variables | |

Lagrange Multipliers | |

Least Squares Regression Analysis | |

Double Integrals and Area in the Plane | |

Applications of Double Integrals | |

Trigonometric Functions | |

Radian Measure of Angles | |

The Trigonometric Functions | |

Graphs of Trigonometric Functions | |

Derivatives of Trigonometric Functions | |

Integrals of Trigonometric Functions | |

L'Hocirc;pital's Rule | |

Probability and Calculus | |

Discrete Probability | |

Continuous Random Variables | |

Expected Value and Variance | |

Series and Taylor Polynomials | |

Sequences | |

Series and Convergence | |

p-Series and the Ratio Test | |

Power Series and Taylor's Theorem | |

Taylor Polynomials | |

Newton's Method | |

Appendices | |

Alternate Introduction to the Fundamental Theorem of Calculus | |

Formulas | |

Differentiation and Integration Formulas | |

Formulas from Business and Finance | |

Differential Equations | |

Solutions of Differential Equations | |

Separation of Variables | |

First-Order Linear Differential Equations | |

Applications of Differential Equations The following Appendices available at the text-specific website at college.hmco.com: | |

Properties of Measurement | |

Review of Algebra, Geometry, and Trigonometry | |

Units of Measurement | |

Graphing Utility Programs | |

Graphing Utility Programs | |

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