Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering
暫譯: 物理與工程模型的泛函分析、變分法與數值方法
Botelho, Fabio Silva
- 出版商: CRC
- 出版日期: 2020-11-03
- 售價: $8,050
- 貴賓價: 9.5 折 $7,648
- 語言: 英文
- 頁數: 576
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367356740
- ISBN-13: 9780367356743
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相關分類:
微積分 Calculus、物理學 Physics
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相關主題
商品描述
The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity.
The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.
商品描述(中文翻譯)
本書討論了函數分析、測度與積分理論、變分法及其對非凸性變分問題的應用的基本概念,例如超導體中的 Ginzburg-Landau 系統、形狀優化模型、微磁學的對偶變分公式等。針對這些及類似問題的數值方法,例如飛行力學中的模型和流體力學中的 Navier-Stokes 系統,已通過廣義線法發展出來,包括它們的矩陣有限維近似。最後,書中回顧了應用於量子力學和相對論的黎曼幾何的最新研究。
本書將吸引應用數學家和應用數學的研究生。物理學家、工程師及相關領域的研究人員也會發現本書在提供適用於各自專業領域的數學背景方面非常有用。
作者簡介
Fabio Silva Botelho obtained a Ph.D in Mathematics from Virginia Tech, USA in 2009. Prior to that got his undergraduate and master degrees in Aeronautical Engineering from the Technological Institute of Aeronautics, ITA, SP, Brazil, in 1992 and 1996 respectively. From 2004 to 2015 he was an Assistant Professor at the Mathematics Department of Federal University of Pelotas in Brazil. From May 2015 to the present date, he has worked as an Adjunct Professor at the Department of Mathematics of Federal University of Santa Catarina, in Florianopolis, SC, Brazil. His field of research is Functional Analysis, Calculus of Variations, Duality and Numerical Analysis applied to problems in physics and engineering. He has published two books Functional Analysis and Applied Optimization in Banach Spaces (2014) and Real Analysis and Applications (2018), both with Springer. He is also the author of a generalization of the Method of Lines, a numerical method for solving partial differential equations in which the domain of the equation in question is discretized in lines and the concerning solution is written on these lines as functions of the boundary conditions and the domain boundary shape.
作者簡介(中文翻譯)
Fabio Silva Botelho 於2009年在美國維吉尼亞理工大學獲得數學博士學位。在此之前,他於1992年和1996年分別在巴西聖保羅的航空技術學院(Technological Institute of Aeronautics, ITA)獲得航空工程的學士和碩士學位。從2004年到2015年,他擔任巴西佩洛塔斯聯邦大學數學系的助理教授。自2015年5月至今,他在巴西弗洛里亞諾波利斯的聖卡塔琳娜聯邦大學數學系擔任兼任教授。他的研究領域包括泛函分析、變分法、對偶性以及應用於物理和工程問題的數值分析。他出版了兩本書籍,分別是Functional Analysis and Applied Optimization in Banach Spaces(2014年)和Real Analysis and Applications(2018年),均由Springer出版。他也是線法(Method of Lines)的一個推廣的作者,這是一種用於解決偏微分方程的數值方法,其中相關方程的定義域被離散化為線,並且相應的解被寫在這些線上,作為邊界條件和定義域邊界形狀的函數。