## Functions of a Complex Variable: With Applications |

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### Contents

PREFACE p vii | 1 |

CONFORMAL REPRESENTATION p | 32 |

SOME SPECIAL TRANSFORMATIONS p | 57 |

3 other sections not shown

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### Common terms and phrases

2tri analytic angle Argand diagram bilinear transformation boundary bounded circle of centre circle of convergence closed contour complex numbers complex variable theory conformal transformation consider const constant continuous contour integral cosec cosh defined definition denote differentiable domain Eacample ellipse essential singularity finite follows function f(z given infinite number inside integral round interior point inverse isogonal Laplace's equation lemma limit point magnification many-valued function maps Möbius modulus neighbourhood obtain one-one parabola plane point at infinity pole of order polygon positive real axis power series prove radius real and imaginary real numbers real variable region regular function reið Riemann surface roots ſ f(z)dz satisfied semicircle Show Similarly simple poles singularity of f(z sinh ſº straight line strip Taylor's theorem tends to zero unit circle upper half upper half-plane w-plane corresponding write z—zo