Understanding Mathematical Concepts in Physics: Insights from Geometrical and Numerical Approaches
Dhurandhar, Sanjeev
- 出版商: Springer
- 出版日期: 2024-07-17
- 售價: $3,780
- 貴賓價: 9.5 折 $3,591
- 語言: 英文
- 頁數: 351
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3031603931
- ISBN-13: 9783031603938
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相關分類:
物理學 Physics
海外代購書籍(需單獨結帳)
相關主題
商品描述
Modern mathematics has become an essential part of today's physicist's arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods.
Adopting a numerical approach to complex analysis it is shown that Cauchy's theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities.
Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of χ2 discriminators in terms of vector bundles.
This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching.
商品描述(中文翻譯)
現代數學已成為當今物理學家必不可少的工具，本書涵蓋了幾個相關的主題。本書的主要目標是以直觀的方式介紹關鍵的數學概念，並借助幾何和數值方法來幫助理解 - 「理解」是關鍵。並非所有的微分方程都可以用標準技巧解決。例子說明了幾何洞察力和數值方法在理解一般微分方程時的有用性，但在無法使用標準方法解決的方程中提取相關信息時則是不可或缺的。
通過採用數值方法進行複雜分析，可以通過使用Python代碼進行實際計算來驗證柯西定理、柯西積分公式、殘餘定理等。圖形闡明了極點和本質奇異點的概念。
此外，本書還涵蓋了拓撲學、希爾伯特空間、傅立葉變換（討論快速傅立葉變換的工作原理）、現代微分幾何、李群和李代數、概率和有用的概率分佈，以及信號的統計檢測。新特點包括：（i）通過實數線上的連續性概念引入拓撲學，然後自然地引導到拓撲空間。（ii）在微分幾何框架中進行數據分析，並以向量丛的形式對χ2鑑別器進行一般描述。
本書針對物理學研究生和理論（可能也是實驗）物理學家。除了研究生之外，本書對於從事研究和教學的活躍物理學家也很有用。
作者簡介
Prof. Sanjeev Dhurandhar has published over hundred papers in top international journals such as Physical Reviews, MNRAS, Classical & Quantum Gravity, and also a review article (coauthored with M. Tinto) in Living Reviews published by Springer. About three quarters of the publications are on gravitational waves, mainly on their data analysis, and the rest are on various aspects of general relativity. Recently, he has published a book (Springer) entitled General Relativity and Gravitational Waves: Essentials of theory and Practice co-authored with Prof. Sanjit Mitra. The author led
the gravitational wave group at IUCAA from 1989 to 2011 until he superannuated. He has taught the Mathematical Physics course at IUCAA at graduate level to physics students for decades and also in the mathematics & physics department of Pune University in the1980s. He has also given courses on differential geometry, probability theory etc. during his career at IUCAA. He holds a Master's degree in mathematics (he switched to physics for his Ph. D.).
The author is a recipient of several prestigious awards which include the Vijnan Bhushan Firodia Award for Outstanding Contributions to Science, the Meghnad Saha Memorial Gold Medal (The Asiatic Society, Kolkata, India) for Outstanding Contributions to Physics, Milners breakthrough prize (Milners Foundation U.S.A.) awarded for the detection of gravitational waves (shared with the Ligo Science Collaboration), etc. He is a fellow of the American Physical Society (APS), the three prestigious Indian academies: (i) Indian National Science Academy, Delhi, (ii) the Indian Academy of Sciences, Bangalore, and (iii) National Academy of Sciences India, Allahabad.
作者簡介(中文翻譯)
Prof. Sanjeev Dhurandhar教授在頂尖國際期刊，如Physical Reviews、MNRAS、Classical & Quantum Gravity等，以及Springer出版的Living Reviews（與M. Tinto合著的評論文章）上發表了超過一百篇論文。其中大約四分之三的論文是關於引力波，主要是關於其數據分析，其餘的則是關於廣義相對論的各個方面。最近，他與Sanjit Mitra教授合著了一本名為《廣義相對論和引力波：理論和實踐的基本要素》的書（Springer出版）。作者在1989年至2011年期間領導了IUCAA的引力波研究小組，直到退休。他在數十年的時間裡，在IUCAA教授了物理學研究生的數學物理課程，也在1980年代在普納大學的數學與物理學系教授過該課程。在他在IUCAA的職業生涯中，他還開設了微分幾何學、概率論等課程。他擁有數學碩士學位（他在攻讀博士學位時轉到物理學領域）。
作者獲得了多個傑出獎項，包括Vijnan Bhushan Firodia科學傑出貢獻獎、Meghnad Saha紀念金牌（印度加爾各答亞洲學會）物理學傑出貢獻獎、Milners突破獎（Milners基金會美國）（與Ligo科學合作組織共同獲得）等。他是美國物理學會（APS）以及印度三個著名學會的會士：（i）印度國家科學院，德里，（ii）印度科學院，班加羅爾，以及（iii）印度國家科學院，阿拉哈巴德。
