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Introduction to Smooth Manifolds (Graduate Texts in Mathematics) de John Lee
Descripción - Críticas From the reviews of the second edition:“It starts off with five chapters covering basics on smooth manifolds up to submersions, immersions, embeddings, and of course submanifolds. … the book under review is laden with excellent exercises that significantly further the reader’s understanding of the material, and Lee takes great pains to motivate everything well all the way through … . a fine graduate-level text for differential geometers as well as people like me, fellow travelers who always wish they knew more about such a beautiful subject.” (Michael Berg, MAA Reviews, October, 2012) Reseña del editor 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. Contraportada 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. Biografía del autor 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 four previous Springer books: the first edition (2003) of Introduction to Smooth Manifolds, the first edition (2000) and second edition (2010) of Introduction to Topological Manifolds, and Riemannian Manifolds: An Introduction to Curvature (1997).
Graduate texts in mathematics springer graduate texts in mathematics bridge the gap between passive study and creative understanding, offering graduatelevel introductions to advanced topics in mathematics the volumes are carefully written as teaching aids and highlight characteristic features of the theory although these books are frequently used as textbooks in graduate courses, they are also suitable for individual study Descargar lie groups, lie algebras libros geniales this book provides an introduction to lie groups, lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics although there are already several excellent books that cover many of the same topics, this book has two distinctive features that i hope will make it a useful addition to the literature first, it treats lie groups not just lie alge bras in a Graduate texts in mathematics 218 graduate texts in mathematics bridge the gap between passive study and creative understanding, offering graduatelevel introductions to advanced topics in mathematics the volumes are carefully written as teaching aids and highlight characteristic features of the theory although these books are frequently used as textbooks
A course in functional analysis graduate texts in a course in functional analysis graduate texts in mathematics conway, john b libros en idiomas extranjeros Introduction to smooth manifolds lee, john m this book is an introductory graduatelevel 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 Introduction to smooth manifolds by john m lee it is a natural sequel to the authors last book, introduction to topological manifolds 2000 while the this book is an introductory graduatelevel 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
Detalles del Libro
- Name: Introduction to Smooth Manifolds (Graduate Texts in Mathematics)
- Autor: John Lee
- Categoria: Libros,Ciencias, tecnología y medicina,Matemáticas
- Tamaño del archivo: 12 MB
- Tipos de archivo: PDF Document
- Idioma: Español
- Archivos de estado: AVAILABLE
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