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Complex analysis

Mel'nyk, Taras.

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Complex analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Complex analysis/ by Taras Mel'nyk.
Author:	Mel'nyk, Taras.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xviii, 244 p. :ill. (chiefly color), digital ;24 cm.
[NT 15003449]:	1 Complex Numbers and Complex Plane -- 2 Analytic Functions -- 3 Elementary Analytic Functions -- 4 Integration of Functions of a Single Complex Variable -- 5 Complex Power Series -- 6 Laurent Series. Isolated Singularities of Analytic Functions -- 7 Residue Calculus -- 8 Analytic Continuations -- 9 Qualitative Properties of Analytic Functions.
Contained By:	Springer Nature eBook
Subject:	Functions of complex variables. -
Online resource:	https://doi.org/10.1007/978-3-031-39615-1
ISBN:	9783031396151

Complex analysis
Mel'nyk, Taras.

Complex analysis[electronic resource] /by Taras Mel'nyk. - Cham :Springer International Publishing :2023. - xviii, 244 p. :ill. (chiefly color), digital ;24 cm.

1 Complex Numbers and Complex Plane -- 2 Analytic Functions -- 3 Elementary Analytic Functions -- 4 Integration of Functions of a Single Complex Variable -- 5 Complex Power Series -- 6 Laurent Series. Isolated Singularities of Analytic Functions -- 7 Residue Calculus -- 8 Analytic Continuations -- 9 Qualitative Properties of Analytic Functions.

Today, the theory of complex-valued functions finds widespread applications in various areas of mathematical research, as well as in electrical and mechanical engineering, aeronautics, and other disciplines. Complex analysis has become a basic course in mathematics, physics, and select engineering departments. This concise textbook provides a thorough introduction to the function theory of one complex variable. It presents the fundamental concepts with clarity and rigor, offering concise proofs that avoid lengthy and tedious arguments commonly found in mathematics textbooks. It goes beyond traditional texts by exploring less common topics, including the different approaches to constructing analytic functions, the conformal mapping criterion, integration of analytic functions along arbitrary curves, global analytic functions and their Riemann surfaces, the general inverse function theorem, the Lagrange-Bürmann formula, and Puiseux series. Drawing from several decades of teaching experience, this book is ideally suited for one or two semester courses in complex analysis. It also serves as a valuable companion for courses in topology, approximation theory, asymptotic analysis, and functional analysis. Abundant examples and exercises make it suitable for self-study as well.

ISBN: 9783031396151

Standard No.: 10.1007/978-3-031-39615-1doiSubjects--Topical Terms:

523875
Functions of complex variables.

LC Class. No.: QA331.7

Dewey Class. No.: 515.9

Complex analysis
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100 1 $a Mel'nyk, Taras. $3 3503149
245 1 0 $a Complex analysis $h [electronic resource] / $c by Taras Mel'nyk.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xviii, 244 p. : $b ill. (chiefly color), digital ; $c 24 cm.
505 0 $a 1 Complex Numbers and Complex Plane -- 2 Analytic Functions -- 3 Elementary Analytic Functions -- 4 Integration of Functions of a Single Complex Variable -- 5 Complex Power Series -- 6 Laurent Series. Isolated Singularities of Analytic Functions -- 7 Residue Calculus -- 8 Analytic Continuations -- 9 Qualitative Properties of Analytic Functions.
520 $a Today, the theory of complex-valued functions finds widespread applications in various areas of mathematical research, as well as in electrical and mechanical engineering, aeronautics, and other disciplines. Complex analysis has become a basic course in mathematics, physics, and select engineering departments. This concise textbook provides a thorough introduction to the function theory of one complex variable. It presents the fundamental concepts with clarity and rigor, offering concise proofs that avoid lengthy and tedious arguments commonly found in mathematics textbooks. It goes beyond traditional texts by exploring less common topics, including the different approaches to constructing analytic functions, the conformal mapping criterion, integration of analytic functions along arbitrary curves, global analytic functions and their Riemann surfaces, the general inverse function theorem, the Lagrange-Bürmann formula, and Puiseux series. Drawing from several decades of teaching experience, this book is ideally suited for one or two semester courses in complex analysis. It also serves as a valuable companion for courses in topology, approximation theory, asymptotic analysis, and functional analysis. Abundant examples and exercises make it suitable for self-study as well.
650 0 $a Functions of complex variables. $3 523875
650 0 $a Mathematical analysis. $3 516833
650 1 4 $a Functions of a Complex Variable. $3 897310
650 2 4 $a Functional Analysis. $3 893943
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773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-031-39615-1
950 $a Mathematics and Statistics (SpringerNature-11649)