More Explorations in Complex Functions
Beals, Richard, Wong, Roderick S. C.
- 出版商: Springer
- 出版日期: 2024-07-03
- 售價: $2,350
- 貴賓價: 9.5 折 $2,233
- 語言: 英文
- 頁數: 403
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031282906
- ISBN-13: 9783031282904
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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.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。
