國立虎尾科技大學 |

Complex analysis

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Complex analysis/ by Taras Mel'nyk.
作者:	Mel'nyk, Taras.
出版者:	Cham :Springer International Publishing : : 2023.,
面頁冊數:	xviii, 244 p. :ill. (chiefly color), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Functional Analysis. -
電子資源:	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:

672166
Functional Analysis.

LC Class. No.: QA331.7

Dewey Class. No.: 515.9

Complex analysis
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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.
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