Abstract
This chapter deals with functions of a complex variable. It starts with a survey of the basic properties of analytic functions, of their power series expansions (Taylor-Laurent series), and with a careful analysis of their singularities. The main attention is then addressed to the evaluation of many types of integrals by means of various complex variable methods, both in the presence of isolated singularities and of branch points and cut lines. Some typical examples of conformal mappings are finally studied, in order to solve Dirichlet Problems; the results are compared with those obtained in other chapters with different methods, with a discussion about the uniqueness of the solutions.
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Cicogna, G. (2020). Functions of a Complex Variable. In: Exercises and Problems in Mathematical Methods of Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-59472-5_2
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DOI: https://doi.org/10.1007/978-3-030-59472-5_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59471-8
Online ISBN: 978-3-030-59472-5
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