## Calculus: The Language of ChangeCalculus: The Language of Change is an innovative new introductory text that blends traditional and reform approaches, and focuses on understanding calculus as its own language. With accessible writing and presentation, the text allows students to gradually understand the language - first by reviewing vocabulary, and then by quickly moving to present calculus conceptually, computationally, and theoretically. Within this framework, derivatives and integrals are developed side by side, coverage of theory is offered at various levels, and computing devices are incorporated generically. A full range of student and instructor resources make Calculus: The Language of Change an outstanding course package. |

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### Contents

Introducing the Pictures | 14 |

Approximating Derivatives | 64 |

Algebraic Methods | 124 |

The Basic Theory | 230 |

ChapferG Modeling Tools | 286 |

Aspects of Integration | 396 |

Polynomial Approximations | 506 |

Chapters Infinite Series | 572 |

Complex Calculus | 752 |

The Deeper Theory | 814 |

### Common terms and phrases

algebra answers to problems antiderivative APPENDIX calculus Chain Rule Challenging Problems Chapter Compare your answer complex numbers compute constant contours converges absolutely cos(x curve defined Definition difference quotient differential equation distance equal equilibrium point Euler's method EXAMPLE Find EXERCISES Extreme Value Theorem formula geometric given in problem graph height Here's HINTS increasing infinite infinity initial value problem inverse limit look lower sum Maclaurin polynomial Maclaurin series mathematics Mean Value Theorem meters miles negative Note partial sums picture plane population positive number Problem du jour proof Proposition prove quadratic radius radius of convergence rate of change real number rectangle relative maximum Section 7.4 sequence series converges Simpson's Rule sin(jc sin(x slope ſº Solution solve Suppose surface tangent Taylor polynomial Taylor series Taylor's Theorem tion upper sum Value Theorem variable velocity zero