Introduction To Smooth Manifolds
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Introduction To Smooth Manifolds
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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Introduction To Smooth Manifolds written by John M. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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
Introduction To Smooth Manifolds
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Author : John Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-27
Introduction To Smooth Manifolds written by John Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Mathematics categories.
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.
Introduction To Topological Manifolds
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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Introduction To Topological Manifolds written by John M. Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Exercises in the text, especially in the first part of the book. Author states, that they have to be solved, without the solutions, the text is incomplete. Includes also problems after each chapter
An Introduction To Manifolds
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Author : Loring W. Tu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-05
An Introduction To Manifolds written by Loring W. Tu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-05 with Mathematics categories.
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
An Introduction To Smooth Manifolds
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Author : Manjusha Majumdar
language : en
Publisher: Springer Nature
Release Date : 2023-06-01
An Introduction To Smooth Manifolds written by Manjusha Majumdar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-01 with Mathematics categories.
Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.
Introduction To Topological Manifolds
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Author : John Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-25
Introduction To Topological Manifolds written by John Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-25 with Mathematics categories.
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
Introduction To Smooth Manifolds
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Author : John M. Lee
language : en
Publisher:
Release Date : 2000
Introduction To Smooth Manifolds written by John M. Lee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Introduction To Riemannian Manifolds
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Author : John M. Lee
language : en
Publisher: Springer
Release Date : 2019-01-02
Introduction To Riemannian Manifolds written by John M. Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-02 with Mathematics categories.
This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.
Smooth Manifolds And Observables
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Author : Jet Nestruev
language : en
Publisher: Springer Nature
Release Date : 2020-09-10
Smooth Manifolds And Observables written by Jet Nestruev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-10 with Mathematics categories.
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
Calculus On Manifolds
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Author : Michael Spivak
language : en
Publisher: Hachette UK
Release Date : 1971-01-22
Calculus On Manifolds written by Michael Spivak and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-01-22 with Science categories.
This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.