Complex Analysis
Mel'nyk, Taras
- 出版商: Springer
- 出版日期: 2024-10-06
- 售價: $2,340
- 貴賓價: 9.5 折 $2,223
- 語言: 英文
- 頁數: 244
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031396170
- ISBN-13: 9783031396175
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相關主題
商品描述
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.
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.
商品描述(中文翻譯)
今天，複變函數理論在數學研究的各個領域以及電機工程、機械工程、航空學和其他學科中得到了廣泛應用。複變分析已成為數學、物理學和部分工程系的基礎課程。
這本簡明的教科書對一個複變數的函數理論提供了徹底的介紹。它以清晰和嚴謹的方式呈現基本概念，提供簡潔的證明，避免了數學教科書中常見的冗長和乏味的論證。它超越了傳統文本，探討了較不常見的主題，包括構造解析函數的不同方法、保形映射準則、沿任意曲線的解析函數積分、全局解析函數及其黎曼面、一般反函數定理、拉格朗日-布爾曼公式以及普伊塞系列。
基於數十年的教學經驗，本書非常適合用於一或兩學期的複變分析課程。它也作為拓撲學、逼近理論、漸近分析和泛函分析課程的寶貴輔助資料。豐富的例子和練習題使其同樣適合自學。
作者簡介
Taras A. Mel'nyk is a professor of the department of mathematical physics at Taras Shevchenko National University of Kyiv. He is a fellow of the Alexander von Humboldt Foundation and a member of the American Mathematical Society. In his teaching, he has developed special courses on a range of topics such as asymptotic methods in mathematical physics, the theory of homogenization, the theory of Sobolev spaces, complex analysis and nonlinear analysis. He has published widely and has authored the monograph Multiple-Scale Analysis of Boundary-Value Problems in Thick Multi-Level Junctions of Type 3:2:2 (Springer, 2019) and two textbooks Complex Analysis (2015, in Ukrainian) and Sobolev Space Theory and Weak Solutions of Boundary Value Problems (2018, in Ukrainian). His research interests are related to asymptotic analysis of boundary-value problems, spectral problems, variational inequalities, optimal control problems, convection-diffusion problems in domains with complex micro-inhomogeneous structures (perforated materials, composite materials, thick multi-structures, domains with rapidly oscillating boundaries, domains with concentrated masses, thin domains, thin graph-like junctions).
作者簡介(中文翻譯)
Taras A. Mel'nyk 是基輔塔拉斯·舍甫琴科國立大學數學物理系的教授。他是亞歷山大·馮·洪堡基金會的研究員，也是美國數學學會的成員。在教學中，他開發了涵蓋多個主題的專門課程，例如數學物理中的漸近方法、均質化理論、Sobolev 空間理論、複變分析和非線性分析。他的出版作品廣泛，著有專著《多尺度分析在厚型 3:2:2 多層接頭邊界值問題中的應用》（Springer，2019）以及兩本教科書《複變分析》（2015，烏克蘭文）和《Sobolev 空間理論及邊界值問題的弱解》（2018，烏克蘭文）。他的研究興趣與邊界值問題的漸近分析、譜問題、變分不等式、最優控制問題、在具有複雜微不均勻結構的區域中的對流-擴散問題（如穿孔材料、複合材料、厚多結構、具有快速振盪邊界的區域、集中質量的區域、薄區域、薄圖形狀接頭）有關。
