Preface | |

To the Student | |

Diagnostic Tests | |

A Preview of Calculus | |

Functions and Models | |

Four Ways to Represent a Function | |

Mathematical Models: A Catalog of Essential Functions | |

New Functions from Old Functions | |

Graphing Calculators and Computers | |

Exponential Functions | |

Inverse Functions and Logarithms | |

Parametric Curves | |

Laboratory Project: Running Circles around Circles | |

Review | |

Principles of Problem Solving | |

Limits and derivatives | |

The Tangent and Velocity Problems | |

The Limit of a Function | |

Calculating Limits Using the Limit Laws | |

Continuity | |

Limits Involving Infinity | |

Derivatives and Rates of Change | |

Writing Project: Early Methods for Finding Tangents | |

The Derivative as a Function | |

What Does | |

Say about | |

Review | |

Focus on Problem Solving | |

Differentiation Rules | |

Derivatives of Polynomials and Exponential Functions | |

Applied Project: Building a Better Roller Coaster | |

The Product and Quotient Rules | |

Derivatives of Trigonometric Functions | |

The Chain Rule | |

Laboratory Project: BTzier Curves | |

Applied Project: Where Should a Pilot Start Descent? | |

Implicit Differentiation | |

Inverse Trigonometric Functions and their Derivatives | |

Derivatives of Logarithmic Functions | |

Discovery Project: Hyperbolic Functions | |

Rates of Change in the Natural and Social Sciences | |

Linear Approximations and Differentials | |

Laboratory Project: Taylor Polynomials | |

Review | |

Focus on Problem Solving | |

Applications of Differentiation | |

Related Rates | |

Maximum and Minimum Values | |

Applied Project: The Calculus of Rainbows | |

Derivatives and the Shapes of Curves | |

Graphing with Calculus and Calculators | |

Indeterminate Forms and l'Hospital's Rule | |

Writing Project: The Origins of l'Hospital's Rule | |

Optimization Problems | |

Applied Project: The Shape of a Can | |

Newton's Method | |

Antiderivatives | |

Review | |

Focus on Problem Solving | |

Integrals | |

Areas and Distances | |

The Definite Integral | |

Evaluating Definite Integrals | |

Discovery Project: Area Functions | |

The Fundamental Theorem of Calculus | |

Writing Project: Newton, Leibniz, and the Invention of Calculus | |

The Substitution Rule | |

Integration by Parts | |

Additional Techniques of Integration | |

Integration Using Tables and Computer Algebra Systems | |

Discovery Project: Patterns in Integrals | |

Approximate Integration | |

Improper Integrals | |

Review | |

Focus on Problem Solving | |

Applications of Integration | |

More about Areas | |

Volumes | |

Discovery Project: Rotating on a Slant | |

Volumes by Cylindrical Shells | |

Arc Length | |

Discovery Project: Arc Length Contest | |

Average Value of a Function | |

Applied Project: Where To Sit at the Movies | |

Applications to Physics and Engineering | |

Discovery Project: Complementary Coffee Cups | |

Applications to Economics and Biology | |

Probability | |

Review | |

Focus on Problem Solving | |

Differential Equations | |

Modeling with Differential Equations | |

Direction Fields and Euler's Method | |

Separable Equations | |

Applied Project: How Fast Does a Tank Drain | |

Applied Project: Which Is Faster, Going Up or Coming Down | |

Exponential Growth and Decay | |

Applied Project: Calculus and Baseball | |

The Logistic Equation | |

Predator-Prey Systems | |

Review | |

Focus on Problem Solving | |

Infinte Sequences and Series | |

Sequences | |

Laboratory Project: Logistic Sequences | |

Series | |

The Integral and Comparison Tests | |

Estimating Sums | |

Other Convergence Tests | |

Power Series | |

Representations of Functions as Power Series | |

Taylor and Maclaurin Series | |

Laboratory Project: An Elusive Limit | |

Writing Project: How Newton Discovered the Binomial Series | |

Applications of Taylor Polynomials | |

Applied Project: Radiation from the Stars | |

Review | |

Focus on Problem Solving | |

Appendixes | |

Intervals, Inequalities, and Absolute Values | |

Coordinate Geometry | |

Trigonometry | |

Precise Definitions of Limits | |

A Few Proofs | |

Sigma Notation | |

Integration of Rational Functions by Partial Fractions | |

Polar Coordinates | |

Complex Numbers | |

Answers to Odd-Numbered Exercises | |

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