## Introduction to Calculus and Analysis Volume II/2: Chapters 5 - 8From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991 |

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### Contents

Integral to Repeated Single | 543 |

Theorem Stokess Theorem | 551 |

GENERAL THEORY | 624 |

ous dependence on the parameter | 625 |

Stokess Theorem | 642 |

Integrals over Simple Surfaces | 651 |

Variables 11 | 654 |

APPENDIX | 713 |

pound Functions and | 737 |

Functionsof a Complex Variable | 769 |

Developments and Applications | 782 |

List of Biographical Dates | 941 |

948 | |

953 | |

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### Common terms and phrases

analytic function angle arbitrary assume boundary bounded circle closed curve coefficients complex components condition constant continuous function converges corresponding curl defined denote depends determined differential equation differential form direction divergence theorem double integral dx dy dz dz dx elementary surface Euler's example Exercises expression finite number follows force formula Gauss's theorem given Green's theorem Hence independent variables integral curves integrand interior interval Jacobian Laplace's equation line integral linear mass motion neighborhood obtain oriented positively oriented surface origin parameter parametric representation particle partition of unity polar coordinates position vector positively with respect potential power series problem proof Prove radius region satisfies side simple surface solution space sphere Stokes's theorem subset surface integral tangent plane tion transformation u-plane vanish velocity Volume x-axis y-plane zero