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CHAPTER PAGE I Origin and Applications of the Theory
The usefulness of the theory
Founders of the theory
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a+ib absolute value algebraic amplitude analytic continuation analytic functions analytic throughout angle approach zero becomes infinite boundary branch branch-cut branch-point Burkhardt-Rasor Cauchy-Riemann equations Cauchy's integral theorem Chapter circle of convergence closed curve co-ordinates coefficients complex numbers complex variable conformal mapping continuous function corresponding curve integral curve segment defined definition differential equations equal essential singular point example expression finite number foregoing formula func function analytic given Goursat-Hedrick Hence indefinite integral infinite series interior Laurent's series limit linear transformation logarithmic loop lytic many-valued functions mathematical monodromic group negative obtain origin Osgood partial derivatives path Pierpont point z0 polynomial power series quotient real functions real number real variable Riemann surface root sequences of points series converges similarly simply connected simply connected region single-valued and analytic solution Taylor's series theory of functions throughout a neighborhood throughout a region tion tive uniformly convergent unit circle vanish z-plane