Titlebook: Complex Analysis and Applications; Hemant Kumar Pathak Textbook 2019 Springer Nature Singapore Pte Ltd. 2019 Complex number.Riemann sphere

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Complex Integrations,s and have far-ranging applications. Notice that many important properties of analytic functions are very difficult to prove without use of complex integrations. For instance, the existence of higher derivatives of analytic functions is a striking property of this type. There occur real integrals in

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Calculus of Residues and Applications to Contour Integration,., except for . inside .. If . has a removable singularity at ., then it is clear that the integral will be zero. If . is a pole or an essential singularity, then the answer is not always zero, but can be found with little difficulty. In this chapter, we show the very surprising fact that Cauchy’s r

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Bilinear Transformations and Applications, which we shall answer more abstract questions for determining whether and in what manner a given finite portion of an analytic surface could be represented on a portion of a plane. This chapter also deals with fixed points of bilinear transformations, elliptic, hyperbolic, and parabolic transformat

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Harmonic Functions and Integral Functions,etermining all regions . such that for any continuous function . there is a continuous function . such that . for . and . is harmonic in .. Alternatively, the Dirichlet problem consists in determining all regions . such that Laplace’s equation is solvable with arbitrary boundary values.

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