## A First Course in Complex Analysis with ApplicationsAdapted from chapters 17-20 of Advanced engineering mathematics, 2nd ed., this undergraduate textbook focuses on the calculus of functions of a complex variable, presenting only proofs of the major results in the subject. The authors (Loyola Marymount University) cover complex functions as mappings |

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pour les équipot et lignes de champ elec

### Contents

Complex Functions and Mappings | 49 |

5 | 142 |

Elementary Functions | 175 |

Integration in the Complex Plane | 235 |

Formulas | 277 |

Series and Residues | 301 |

Integrals | 354 |

Conformal Mappings | 389 |

I | 453 |

497 | |

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### Common terms and phrases

analytic function angle Answers to selected arg(w arg(z boundary conditions branch Cauchy-Goursat theorem Cauchy-Riemann equations color in Figure complex exponential function complex function complex logarithm complex mapping complex number complex power conformal mapping continuous cosh defined Definition derivative Dirichlet problem evaluate Example Exercises Figure for Problem Find the image flow follows function f(z harmonic ideal fluid integral formula iv(x Laurent series level curves line segment linear fractional transformation linear mapping loge modulus multiple-valued function nth root obtain odd-numbered problems begin one-to-one parametrization point ZQ polygonal region polynomial power series principal square root principal value proof radius of convergence Re(z real and imaginary real axis real functions real number rotation satisfies Section selected odd-numbered problems shown in black shown in color shown in Figure simple closed contour sinh Solution solve Suppose trigonometric unit circle upper half-plane vector field z-plane zero