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Details
Title
Complex analysis / Taras Mel'nyk.
Author
Mel'nyk, Taras, author.
ISBN
9783031396151 (electronic bk.)
3031396154 (electronic bk.)
9783031396144
3031396146
3031396154 (electronic bk.)
9783031396144
3031396146
Published
Cham : Springer, [2023]
Copyright
©2023
Language
English
Language Note
Translated from Ukrainian.
Description
1 online resource (xviii, 244 pages) : illustrations (chiefly color)
Other Standard Identifiers
10.1007/978-3-031-39615-1 doi
Call Number
QA331.7
Dewey Decimal Classification
515/.9
Summary
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 LagrangeBrmann 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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed October 12, 2023).
Available in Other Form
Print version: 9783031396144
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Table of Contents
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.
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.