## Functions of a complex variable: with applications |

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### Contents

FUNCTIONS OF A COMPLEX VARIABLE p | 1 |

CONFORMAL REPRESENTATION p | 32 |

SOME SPECIAL TRANSFORMATIONS p | 57 |

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angle Argand diagram bilinear transformation boundary bounded branch-point Cauchy-Riemann equations circle of centre circle of convergence closed contour complex numbers confocal conformal transformation consider const constant contour integral cosec cosh cross-ratio D.Sc defined definition denote differentiable domain ellipse essential singularity example f f(z)dz finite number follows function f(z given Hence integral round interior point inverse isogonal Jordan curve Laplace's equation lemma limit point magnification many-valued function maps Mobius modulus neighbourhood obtain one-one parabola plane point at infinity point z0 pole of order polygon positive real axis power series prove radius rational function real and imaginary real numbers real variable rectangle region regular function residue Riemann surface roots satisfied semicircle Show Similarly simple poles sinh small circle square straight line Taylor's theorem tends to zero to-plane unit circle upper half upper half-plane whole z-plane write z-plane corresponding