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what is the Physical interpretation of Cauchy's integral formula ?

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    @Naveen: start here: http://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations#Physical_interpretation2012-08-29

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I would suggest Chapter 9 of Cohen's book Conformal Mapping on Riemann Surfaces, where he relates existence theorems of Harmonic Differentials and the Cauchy-Riemann Equations to the study of Electrostatics and Hydrodynamics.