Functions of a Complex Variable: With Applications |
Contents
PREFACE p vii | 1 |
CONFORMAL REPRESENTATION p | 32 |
SOME SPECIAL TRANSFORMATIONS p | 57 |
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analytic angle Argand diagram b₁ bilinear transformation boundary C₁ Cauchy-Riemann equations circle of centre closed contour complex numbers conformal transformation consider const constant continuous contour integral cosec cosh D.Sc defined definition denote derivatives differentiable domain ellipse essential singularity example Ə² finite follows function f(z Hence infinite number inside integral round interior point inverse isogonal Laplace's equation lemma limit point many-valued function maps Möbius neighbourhood one-one P₁ P₂ parabola plane point at infinity pole of order polygon positive real axis power series prove radius real numbers real variable region regular function Riemann surface roots satisfied semicircle Show simple poles singularity of f(z sinh square straight line strip Taylor's theorem tends to zero u+iv unit circle upper half upper half-plane w-plane w₁ w₂ write x+iy z-plane corresponding z₁ ди მყ