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FUNCTIONS OF A COMPLEX VARIABLE p
CONFORMAL REPRESENTATION p
SOME SPECIAL TRANSFORMATIONS p
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angle Argand diagram bilinear transformation boundary bounded branch-point Cauchy-Riemann equations Cauchy's theorem circle of centre circle of convergence closed contour complex numbers complex variable theory conformal transformation consider const constant contour integral cosec cosh defined definition denote differentiable domain ellipse essential singularity example finite number follows function f(z given Hence infinite 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 straight line strip Taylor's theorem tends to zero unit circle upper half upper half-plane w-plane corresponding write x+iy z-plane