Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory
暫譯: 高等微積分及其在變分量子力學與相對論中的應用
Botelho, Fabio Silva
- 出版商: CRC
- 出版日期: 2021-07-13
- 售價: $6,500
- 貴賓價: 9.5 折 $6,175
- 語言: 英文
- 頁數: 324
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 036774645X
- ISBN-13: 9780367746452
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相關分類:
微積分 Calculus、量子 Quantum
海外代購書籍(需單獨結帳)
商品描述
The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters.
The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry.
The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.
商品描述(中文翻譯)
本書的第一部分回顧了多變量高級微積分的一些關鍵主題。所提出的方法包括對 Rn 中曲面的詳細和嚴謹的研究，涵蓋了微分形式和 Rn 中斯托克斯定理的抽象版本等內容。結論部分向讀者介紹了黎曼幾何，這在後續章節中將會使用。
第二部分回顧了應用，特別是在變分量子力學和相對論理論中的應用。涵蓋了相對論性克萊因-戈登方程的變分形式，以及通過（半）黎曼幾何首次推導相對論性力學的變分形式。第二部分具有更一般的背景，包含了微分幾何的基本原理。
後面的章節通過半經典方法描述了波爾原子模型的新詮釋。本書以量子力學中輻射腔模型的經典描述作結。
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 (1992) and master (1996) degrees in Aeronautical Engineering from the Technological Institute of Aeronautics, ITA, SP, Brazil. From 2004 to 2015 he was an Assistant Professor at the Mathematics Department of Federal University of Pelotas in Brazil. Since 2015 he has worked as an Adjunct Professor at the Department of mathematics of Federal University of Santa Catarina, in Florianopolis, SC, Brazil. His fields of reserach are Functional Analysis, Calculus of Variations, Duality and Numerical Analysis applied to problems in Physics and Engineering. He has published three books, Functional Analysis and Applied Optimization in Banach Spaces (2014), Real Analysis and Applications (2018), both with Springer, and Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering (2020), published by CRC Taylor and Francis. 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年獲得巴西聖保羅航空技術學院（Technological Institute of Aeronautics, ITA）的航空工程學士學位，並於1996年獲得碩士學位。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年以來，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。他出版了三本書，分別是《Banach 空間中的泛函分析與應用優化》（2014年）、《實分析與應用》（2018年），均由Springer出版，以及《物理和工程模型的泛函分析、變分法與數值方法》（2020年），由CRC Taylor and Francis出版。他還是線法的一種推廣方法的作者，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，並且相應的解作為邊界條件和定義域邊界形狀的函數寫在這些線上。
