Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces
暫譯: 狄利克雷原理、共形映射與最小曲面
Courant, Richard
- 出版商: Dover Publications
- 出版日期: 2005-11-03
- 售價: $940
- 貴賓價: 9.5 折 $893
- 語言: 英文
- 頁數: 352
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0486445526
- ISBN-13: 9780486445526
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相關分類:
工程數學 Engineering-mathematics
海外代購書籍(需單獨結帳)
商品描述
Mathematical development, the author of this text observes, comes about through specific, easily understood problems that require difficult solutions and demand the use of new methods. Richard Courant employs this instructive approach in a text that balances the individuality of mathematical objects with the generality of mathematical methods.
Beginning with a discussion of Dirichlet's principle and the boundary-value problem of potential theory, the text proceeds to examinations of conformal mapping on parallel-slit domains and Plateau's problem. Succeeding chapters explore the general problem of Douglas and conformal mapping of multiply connected domains, concluding with a survey of minimal surfaces with free boundaries and unstable minimal surfaces.
Beginning with a discussion of Dirichlet's principle and the boundary-value problem of potential theory, the text proceeds to examinations of conformal mapping on parallel-slit domains and Plateau's problem. Succeeding chapters explore the general problem of Douglas and conformal mapping of multiply connected domains, concluding with a survey of minimal surfaces with free boundaries and unstable minimal surfaces.
商品描述(中文翻譯)
數學的發展，這本書的作者觀察到，是通過特定的、易於理解的問題來實現的，這些問題需要困難的解決方案並要求使用新方法。理查德·庫朗（Richard Courant）在這本書中採用了這種教學方法，平衡了數學對象的個體性與數學方法的普遍性。
本書首先討論了狄利克雷原理（Dirichlet's principle）和潛能理論的邊界值問題，接著進入對平行狹縫區域的保形映射（conformal mapping）和普拉托問題（Plateau's problem）的研究。隨後的章節探討了道格拉斯的一般問題（Douglas problem）和多重連通區域的保形映射，最後總結了具有自由邊界的最小表面（minimal surfaces）和不穩定最小表面（unstable minimal surfaces）的概述。
