物理微分方程的数学之旅 A Mathematical Journey Through Differential Equations Of Physics 英文原版 Max Lein
基本信息
Format Paperback | 480 pages
Dimensions 152.4 x 228.6 x 24.38mm | 635.03g
Publication date 10 Oct 2022
Publisher World Scientific Publishing Co Pte Ltd
Publication City/Country Singapore, Singapore
Language English
ISBN10 9811227667
ISBN13 9789811227660
书籍信息仅供参考，具体以实物为准
书籍简介
数学是物理学的语言，随着时间的推移，物理学家们已经形成了自己的方言。本书的主要目的是弥合这一语言障碍，并向读者介绍数学物理学的魅力。它展示了如何结合两种方法的优势：物理学家经常在良好的直觉基础上得出有趣的猜想，这可以作为有趣数学的起点。相反，数学家可以更容易地看到非常不同的领域（如量子力学和电磁学）之间的共同点，并采用更先进的工具。该书不是专注于一个特定的主题，而是展示了不同物理理论的概念和数学的共同点。它将物理问题转化为具体的数学问题，展示如何回答这些问题，并解释如何从物理上解释答案。例如，如果两个哈密顿人很接近，为什么他们的动力学会相似？本书在以数学和物理学为中心的章节之间交替进行，并包括大量来自物理学的具体例子以及76个带有解决方案的练习。它利用了两端的读者已经熟悉一些材料的特点。以数学为中心的章节提供了必要的背景，使物理概念在数学上精确，并建立基本事实。而以物理学为中心的每一章都以对数学家更友好的方式介绍物理理论。随着书的进展，高级材料被洒入，以展示数学和物理学如何相互增强。其中一些例子是基于最近的出版物，包括其他教科书中没有涉及的材料。这是为了保持读者的兴趣。
Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine the strengths of both approaches: physicists often arrive at interesting conjectures based on good intuition, which can serve as the starting point of interesting mathematics. Conversely, mathematicians can more easily see commonalities between very different fields (such as quantum mechanics and electromagnetism), and employ more advanced tools.Rather than focusing on a particular topic, the book showcases conceptual and mathematical commonalities across different physical theories. It translates physical problems to concrete mathematical questions, shows how to answer them and explains how to interpret the answers physically. For example, if two Hamiltonians are close, why are their dynamics similar?The book alternates between mathematics- and physics-centric chapters, and includes plenty of concrete examples from physics as well as 76 exercises with solutions. It exploits that readers from either end are familiar with some of the material already. The mathematics-centric chapters provide the necessary background to make physical concepts mathematically precise and establish basic facts. And each physics-centric chapter introduces physical theories in a way that is more friendly to mathematicians.As the book progresses, advanced material is sprinkled in to showcase how mathematics and physics augment one another. Some of these examples are based on recent publications and include material which has not been covered in other textbooks. This is to keep it interesting for the readers.
作者简介
马克斯-莱恩是东北大学跨学科的WPI-高级材料研究所的副教授和数学组的成员。他在慕尼黑工业大学学习物理和数学，师从Herbert Spohn，并在多伦多大学和菲尔兹研究所做了两年的菲尔兹博士后研究。其他停留的地方包括加州大学伯克利分校、九州大学和图宾根大学。
他的专业领域是凝聚态系统的拓扑现象和经典波，以及有效动力学的推导。他的研究成就包括严格和非严格的出版物，这些出版物出现在各种数学和物理学杂志上。他与Giuseppe De Nittis合作出版了一本关于线性响应理论的新型数学方法的书。
他有丰富的教学经验，从零开始设计了几门研究生水平的课程--包括本书的基础课程。
Max Lein is an associate professor and a member of the mathematics group at the interdisciplinary WPI-Advanced Institute of Materials Research of Tohoku University. He studied physics and mathematics at Technical University of Munich under the tutelage of Herbert Spohn and spent two years as a Fields Postdoctoral Fellow at the University of Toronto and the Fields Institute. Other stays included UC Berkeley, Kyushu University and the University of Tübingen.
His area of expertise are topological phenomena in condensed matter systems and classical waves as well as the derivation of effective dynamics. His research accomplishments include rigorous and non-rigorous publications alike, which have appeared in various top-level mathematics and physics journals. He has published one book with Giuseppe De Nittis on a novel mathematical approach to linear response theory.
He has extensive teaching experience and has designed several graduate-level courses from scratch — including the one this book is based on.
