Preliminaries | |

Precalculus Review | |

Precalculus Review II | |

The Cartesian Coordinate System | |

Straight Lines | |

Functions, Limits, and the Derivative | |

Functions and Their Graphs | |

The Algebra of Functions | |

Functions and Mathematical Models | |

Limits | |

One-Sided Limits and Continuity | |

Derivative | |

Differentiation | |

Basic Rules of Differentiation | |

The Product and Quotient Rules | |

The Chain Rule | |

Marginal Functions in Economics | |

Higher-Order Derivatives | |

Implicit Differentiation and Related Rates | |

Differentials | |

Applications of the Derivative | |

Applications of the First Derivative | |

Applications of the Second Derivative | |

Curve Sketching | |

Optimization | |

Optimization II | |

Exponential and Logarithmic Functions | |

Exponential Functions | |

Logarithmic Functions | |

Compound Interest | |

Differentiation of Exponential Functions | |

Differentiation of Logarithmic Functions | |

Exponential Functions as Mathematical Models | |

Integration | |

Antiderivatives and the Rules of Integration | |

Integration by Substitution | |

Area and the Definite Integral | |

The Fundamental Theorem of Calculus | |

Evaluating Definite Integrals | |

Area Between Two Curves | |

Applications of the Definite Integral to Business and Economics | |

Volumes of Solids of Revolution | |

Additional Topics in Integration | |

Integration by Parts | |

Integration Using Tables of Integrals | |

Numerical Integration | |

Improper Integrals | |

Calculus of Several Variables | |

Functions of Several Variables | |

Partial Derivatives | |

Maxima and Minima of Functions of Several Variables | |

The Method of Least Squares | |

Constrained Maxima and Minima and the Method of Lagrange Multipliers | |

Total Differentials | |

Double Integrals | |

Applications of Double Integrals | |

Differential Equations | |

Differential Equations | |

Separation of Variables | |

Applications of Separable Differential Equations | |

Approximate Solutions of Differential Equations | |

Probability and Calculus | |

Probability Distributions of Random Variables | |

Expected Value and Standard Deviation | |

Normal Distributions | |

Taylor Polynomials and Infinite Series | |

Taylor Polynomials | |

Infinite Sequences | |

Infinite Series | |

Series with Positive Terms | |

Power Series and Taylor Series | |

More on Taylor Series | |

The Newton's Method | |

Trigonometric Functions | |

Measurement of Angles | |

The Trigonometric Functions | |

Differentiation of Trigonometric Functions | |

Integration of Trigonometric Functions | |

Inverse Functions | |

Table | |

Answers to Odd-Numbered Exercises | |

Index | |

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