More Explorations in Complex Functions

Beals, Richard, Wong, Roderick S. C.

More Explorations in Complex Functions
  • 出版商: Springer
  • 出版日期: 2023-07-03
  • 售價: $3,280
  • 貴賓價: 9.5 折 $3,116
  • 語言: 英文
  • 頁數: 403
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031282876
  • ISBN-13: 9783031282874

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商品描述

More Explorations in Complex Functions is something of a sequel to GTM 287, Explorations in Complex Functions. Both texts introduce a variety of topics, from core material in the mainstream of complex analysis to tools that are widely used in other areas of mathematics and applications, but there is minimal overlap between the two books. The intended readership is the same, namely graduate students and researchers in complex analysis, independent readers, seminar attendees, or instructors for a second course in complex analysis. Instructors will appreciate the many options for constructing a second course that builds on a standard first course in complex analysis. Exercises complement the results throughout. There is more material in this present text than one could expect to cover in a year's course in complex analysis. A mapping of dependence relations among chapters enables instructors and independent readers a choice of pathway to reading the text. Chapters 2,4, 5, 7, and 8 contain the function theory background for some stochastic equations of current interest, such as SLE.

The text begins with two introductory chapters to be used as a resource. Chapters 3 and 4 are stand-alone introductions to complex dynamics and to univalent function theory, including deBrange's theorem, respectively. Chapters 5--7 may be treated as a unit that leads from harmonic functions to covering surfaces to the uniformization theorem and Fuchsian groups. Chapter 8 is a stand-alone treatment of quasiconformal mapping that paves the way for Chapter 9, an introduction to Teichmüller theory. The final chapters, 10-14, are largely stand-alone introductions to topics of both theoretical and applied interest: the Bergman kernel, theta functions and Jacobi inversion, Padé approximants and continued fractions, the Riemann--Hilbert problem and integral equations, and Darboux's method for computing asymptotics.

商品描述(中文翻譯)

《更多複雜函數探索》可以說是《GTM 287 複雜函數探索》的續集。這兩本書都介紹了各種主題，從複分析的核心材料到在其他數學領域和應用中廣泛使用的工具，但兩本書之間幾乎沒有重疊。目標讀者群是相同的，即複分析的研究生和研究人員、獨立讀者、研討會參與者或複分析第二門課的教師。教師們將欣賞到有很多選擇來構建一門建立在標準複分析第一門課基礎上的第二門課。練習題與結果相輔相成。這本書的內容比一年的複分析課程所能涵蓋的要多。章節之間的相依關係對教師和獨立讀者提供了閱讀本書的不同路徑選擇。第2、4、5、7和8章包含了一些當前感興趣的隨機方程的函數理論背景，例如SLE。

本書以兩個引言章節開始，可作為資源使用。第3和第4章是獨立的複雜動力學和單射函數理論的介紹，包括deBrange的定理。第5至7章可以作為一個單元，從調和函數到覆蓋曲面，再到均一化定理和Fuchsian群。第8章是獨立的拟共形映射的研究，為第9章的Teichmüller理論介紹鋪平道路。最後的第10至14章主要是對理論和應用感興趣的主題的獨立介紹：Bergman核、theta函數和Jacobi反演、Padé逼近和連分數、Riemann-Hilbert問題和積分方程，以及Darboux的計算漸近解法。

作者簡介

Richard Beals is Professor Emeritus of Mathematics at Yale University. His research interests include ordinary and partial differential equations, operator theory, integrable systems, and transport theory. He has authored many books, including Advanced Mathematical Analysis, published in 1973 as the twelfth volume in the series Graduate Texts in Mathematics.

Roderick S. C. Wong is Professor Emeritus of Mathematics at the City University of Hong Kong. His research interests include asymptotic analysis, perturbation methods, and special functions. He has been president of the Canadian Applied Mathematics Society and the Hong Kong Mathematical Society, and received numerous professional honors, including election to the European Academy of Sciences in 2007. He has written and edited a wide variety of books, with several notable works in the area of special functions.


作者簡介(中文翻譯)

Richard Beals是耶魯大學的數學名譽教授。他的研究興趣包括常微分方程和偏微分方程、算子理論、可積系統和傳輸理論。他撰寫了許多書籍，包括1973年出版的《高等數學分析》（Advanced Mathematical Analysis），該書是《數學研究生教材系列》（Graduate Texts in Mathematics）的第12卷。

Roderick S. C. Wong是香港城市大學的數學名譽教授。他的研究興趣包括漸近分析、擾動方法和特殊函數。他曾擔任加拿大應用數學學會和香港數學學會的主席，並獲得了許多專業榮譽，包括2007年當選為歐洲科學院院士。他撰寫和編輯了各種各樣的書籍，其中在特殊函數領域有幾部重要作品。

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