## Complex variables and applicationsThis text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserves the basic content and style of earlier editions and includes many new and relevant applications which are introduced early in the text. |

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### Contents

Complex Numbers l | 1 |

Algebraic Properties | 2 |

Moduli and Conjugates | 6 |

Copyright | |

106 other sections not shown

### Other editions - View all

Complex variables and applications, Volume 1 James Ward Brown,Ruel Vance Churchill Snippet view - 1996 |

Complex variables and applications, Volume 1 James Ward Brown,Ruel Vance Churchill Snippet view - 1996 |

### Common terms and phrases

analytic function angle antiderivative arctan Boundary Value Problems calculus Cauchy Cauchy-Goursat theorem Cauchy-Riemann equations coefficients complex variable continuous converges corresponding cosh curve defined denote differentiating Dirichlet problem disk domain of definition essential singular point evaluate EXAMPLE Exercise exists expression FIGURE finite number flow follows function f half line harmonic conjugate harmonic function Hence imaginary improper integrals inequality integral formula integrand inverse Laurent series limit line segment linear fractional transformation logz Maclaurin series mapping multiple-valued function nonzero complex number nonzero point Note obtained origin point z0 points interior pole of order polygon polynomial positive number power series quadrant real axis real numbers region residue result Riemann surface satisfies series representation shown in Fig simple closed contour sinh sinz smooth arc square strip Suppose Taylor series temperature theorem in Sec vector verify write xy plane zero