Introduction to Smooth Manifolds 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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John M. Lee 作者

Springer

译者

2012-9-29 出版日期

750 页数

USD 89.95 价格

Hardcover

Graduate Texts in Mathematics 丛书系列

9781441999818 图书编码

Introduction to Smooth Manifolds 在线电子书图书标签: 数学 Manifolds 微分几何流形牛人推荐数学书籍 Topology 几何经典

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发表于2024-05-13

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Introduction to Smooth Manifolds 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Introduction to Smooth Manifolds 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

Introduction to Smooth Manifolds 在线电子书用户评价

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For physics students who study GR, manifold, differential geometry，强推Sean Carrol 写的书。写的比数学的定义intrinsic非常多。简单到根本不可能看不懂。https://douc.cc/4jbB7Y

评分☆☆☆☆☆

终于读完Diffrential Forms了，这本书是我读过最好的教科书，和小说一般精彩。我终于可以开始看毕设参考书第一行了...

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一周横扫五百面（好多定理直接跳过证明，题当然也是没做）。这书好在极其严谨，几何的东西很多感觉就那么回事，但想严密描述出来就得花一番功夫，更何况严密证明。这本书做到了这些，定义和定理非常细致精确。不可避免的缺点就是太长了——没办法啊。这本跟Spivak“纯几何”的微分几何教材很好地互补。

评分☆☆☆☆☆

嗯嗯，流形贼快乐！这个学期还是学得太匆忙了，有机会重刷。以及怀念代数几何的美好时光。

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当作课程参考看，还是希望能好好学一遍。

Introduction to Smooth Manifolds 在线电子书著者简介

Introduction to Smooth Manifolds 在线电子书图书目录

Introduction to Smooth Manifolds 在线电子书 pdf 下载 txt下载 epub 下载 mobi 在线电子书下载

Introduction to Smooth Manifolds 在线电子书图书描述

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 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. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.

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