## Mathematical analysis: a modern approach to advanced calculus |

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### Contents

THE REAL AND COMPLEX NUMBER SYsrEMs | 1 |

P11l | 19 |

ELEMENTS or Pomr SET Tnaomr | 40 |

Copyright | |

31 other sections not shown

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absolutely convergent accumulation point apply Theorem Assume that f bounded variation called chain rule closed interval complex numbers components connected set continuous functions converges absolutely countable deﬁned and bounded deﬁnition denote described differential discontinuities diverges equation example Exercise f and g f be deﬁned f deﬁned f e R(a f is continuous ﬁnd ﬁner ﬁnite number ﬁrst ﬁxed following theorem formula function f geometric given hence implies improper integrals inequality inﬁnite integral ff interior point Jacobian Jordan content Let f limit line integral Mean Value Theorem n-dimensional NOTE obtain open interval open set parametric surface partial derivatives partition polygon positively oriented power series real numbers real-valued function deﬁned rectiﬁable Jordan curve Riemann integral Riemann-Stieltjes integral satisﬁes sequence Show subinterval subset tion uniform convergence variables vector ﬁeld vector-valued function write zero