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光滑流形导论 : [英文本 🔍
(美)李著, John M. Lee著, E Le 世界图书出版公司北京公司, 2008, 2008
英语 [en] · 中文 [zh] · PDF · 29.7MB · 2008 · 📗 未知类型的图书 · 🚀/duxiu/zlibzh · Save
描述
Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under­ standing'space'in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com­ puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma­ trices, as easily as we think about the familiar 2-dimensional sphere in ]R3.
备用文件名
zlibzh/no-category/（美）李著, John M. Lee著, E Le/光滑流形导论_31168227.pdf
备选标题
Introduction to Smooth Manifolds (Graduate Texts in Mathematics)
备选作者
Lee, John M.
备用出版商
World Publishing Corporation
备用出版商
Springer-Verlag Telos
备用出版商
Springer Verlag
备用出版商
Copernicus
备用版本
Springer Nature (Textbooks & Major Reference Works), New York, NY, 2013
备用版本
Graduate texts in mathematics -- 218, New York, New York State, 2003
备用版本
Graduate texts in mathematics, 218, Reprinted ed, Beijing, 2008
备用版本
Graduate texts in mathematics, Nachdr, New York, 2006
备用版本
United States, United States of America
备用版本
China, People's Republic, China
备用版本
Ying yin ban, Beijing, 2008
备用版本
September 23, 2002
备用版本
October 1, 2002
备用版本
1, PS, 2002
元数据中的注释
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filepath:40213698.zip — md5:d11abbf3ej0d6b659c24799a924225b2 — filesize:48122445
filepath:/读秀/读秀4.0/读秀/4.0/数据库21-2/40213698.zip
filepath:第二部分/77-1/40213698.zip
元数据中的注释
Includes bibliographical references (p. [597]-599) and index.
备用描述
<p><P>This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research&#151;- smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations. The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. John M. Lee is Professor of Mathematics at the University of Washington in Seattle, where he regularly teaches graduate courses on the topology and geometry of manifolds. He was the recipient of the American Mathematical Society's Centennial Research Fellowship and he is the author of two previous Springer books, Introduction to Topological Manifolds (2000) and Riemannian Manifolds&#58; An Introduction to Curvature (1997).</p>
备用描述
"This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research - smooth structures, tangent vectors and convectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more.
The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. Along the way, the book introduces students to some of the most important examples of geometric structures that manifolds can carry, such as Riemannian metrics, symplectic structures, and foliations.
The book is aimed at students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis."--BOOK JACKET.
备用描述
This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological Manifolds(2000). While the subject is often called "differential geometry," in this book the author has decided to avoid use of this term because it applies more specifically to the study of smooth manifolds endowed with some extra structure, such as a Riemannian metric, a symplectic structure, a Lie group structure, or a foliation, and of the properties that are invariant under maps that preserve the structure. Although this text addresses these subjects, they are treated more as interesting examples to which to apply the general theory than as objects of study in their own right. A student who finishes this book should be well prepared to go on to study any of these specialized subjects in much greater depth
备用描述
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
开源日期
2024-06-13
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