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FUNCTIONS OF A COMPLEX VARIABLE p
CONFORMAL REPRESENTATION p
SOME SPECIAL TRANSFORMATIONS p
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angle annulus Argand diagram bilinear transformation boundary bounded branch-point cardioid Cauchy-Riemann equations Cauchy's theorem circle of centre circle of convergence closed contour complex numbers complex variable theory confocal conformal transformation consider const contour integral cosec cosh cross-ratio defined definition denote differentiable domain ellipse essential singularity example finite follows given Hence infinite number 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 Riemann surface roots satisfied semicircle Show Similarly simple poles sinh small circle straight line strip Taylor's theorem tends to zero to-plane unit-circle upper half upper half-plane write x+iy z-plane corresponds