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An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 517/5 ( reviews)

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Book Synopsis An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised by : William Munger Boothby

Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised written by William Munger Boothby. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised has sold over 6,000 copies since publication in 1986 and this revision will make it even more useful. This is the only book available that is approachable by "beginners" in this subject. It has become an essential introduction to the subject for mathematics students, engineers, physicists, and economists who need to learn how to apply these vital methods. It is also the only book that thoroughly reviews certain areas of advanced calculus that are necessary to understand the subject. Line and surface integrals Divergence and curl of vector fields

An Introduction to Differentiable Manifolds and Riemannian Geometry

1986-04-21 Mathematics
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Release : 1986-04-21
Genre : Mathematics
Kind : eBook
Book Rating : 398/5 ( reviews)

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Book Synopsis An Introduction to Differentiable Manifolds and Riemannian Geometry by :

Download or read book An Introduction to Differentiable Manifolds and Riemannian Geometry written by . This book was released on 1986-04-21. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Differentiable Manifolds and Riemannian Geometry

Differential and Riemannian Manifolds

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 820/5 ( reviews)

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Book Synopsis Differential and Riemannian Manifolds by : Serge Lang

Download or read book Differential and Riemannian Manifolds written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This is the third version of a book on differential manifolds. The first version appeared in 1962, and was written at the very beginning of a period of great expansion of the subject. At the time, I found no satisfactory book for the foundations of the subject, for multiple reasons. I expanded the book in 1971, and I expand it still further today. Specifically, I have added three chapters on Riemannian and pseudo Riemannian geometry, that is, covariant derivatives, curvature, and some applications up to the Hopf-Rinow and Hadamard-Cartan theorems, as well as some calculus of variations and applications to volume forms. I have rewritten the sections on sprays, and I have given more examples of the use of Stokes' theorem. I have also given many more references to the literature, all of this to broaden the perspective of the book, which I hope can be used among things for a general course leading into many directions. The present book still meets the old needs, but fulfills new ones. At the most basic level, the book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.).

Differentiable Manifolds

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 842/5 ( reviews)

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Book Synopsis Differentiable Manifolds by : Lawrence Conlon

Download or read book Differentiable Manifolds written by Lawrence Conlon. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.

An Introduction to Riemannian Geometry

2014-07-26 Mathematics
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Release : 2014-07-26
Genre : Mathematics
Kind : eBook
Book Rating : 669/5 ( reviews)

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Book Synopsis An Introduction to Riemannian Geometry by : Leonor Godinho

Download or read book An Introduction to Riemannian Geometry written by Leonor Godinho. This book was released on 2014-07-26. Available in PDF, EPUB and Kindle. Book excerpt: Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.

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