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PREFACE p vii
CONFORMAL REPRESENTATION p
SOME SPECIAL TRANSFORMATIONS p
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2tri analytic angle Argand diagram bilinear transformation boundary bounded Cauchy's theorem 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 Eacample ellipse essential singularity finite number follows given Hence infinite 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 rational function real and imaginary real numbers real variable rectangle region regular function Riemann surface roots ſ f(z)dz satisfied semicircle Show Similarly simple poles singularity of f(z sinh small circle ſº square straight line strip Taylor's theorem tends to zero unit circle upper half upper half-plane w-plane write z-plane corresponding z—zo z+iy