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Applied Mathematical Methods by Bhaskar Dasgupta

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45

Analytic Functions

As we have experienced earlier, the algebra of polynomials and matrices, even of real ones, becomes clear and freely navigable, when we operate with the algebra of complex numbers. Similarly, many profound concepts and results of pure and applied mathematics are completely appreciated, when we view them through the perspective of complex functions. In the three chapters here, we summarize the most prominent ideas of complex analysis. In the present chapter, we focus on analytic functions, conformal mappings and their applications, leaving complex integrals and singularities in the agenda for the following chapters.

Analyticity of Complex Functions

We encountered the term ‘analytic function’ earlier in this book in Chap. ...

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