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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angle Argand diagram b₁ bilinear transformation bounded C₁ C₂ Cauchy-Riemann equations circle of centre closed contour complex numbers complex variable theory conformal transformation consider const contour integral cosec cosh defined definition denote derivatives differentiable domain ellipse essential singularity 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 pole of order polygon positive real axis power series prove radius rational function real and imaginary real numbers real variable region regular function Riemann surface roots satisfied semicircle Show Similarly simple poles singularity of f(z sinh 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 corresponds z₁ πα Σπί ди მა