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Topics in Differential Geometry

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 036/5 ( reviews)

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Book Synopsis Topics in Differential Geometry by : Peter W. Michor

Download or read book Topics in Differential Geometry written by Peter W. Michor. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: "This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.

Elementary Topics in Differential Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 538/5 ( reviews)

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Book Synopsis Elementary Topics in Differential Geometry by : J. A. Thorpe

Download or read book Elementary Topics in Differential Geometry written by J. A. Thorpe. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.

Basic Concepts of Synthetic Differential Geometry

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis Basic Concepts of Synthetic Differential Geometry by : R. Lavendhomme

Download or read book Basic Concepts of Synthetic Differential Geometry written by R. Lavendhomme. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: Starting at an introductory level, the book leads rapidly to important and often new results in synthetic differential geometry. From rudimentary analysis the book moves to such important results as: a new proof of De Rham's theorem; the synthetic view of global action, going as far as the Weil characteristic homomorphism; the systematic account of structured Lie objects, such as Riemannian, symplectic, or Poisson Lie objects; the view of global Lie algebras as Lie algebras of a Lie group in the synthetic sense; and lastly the synthetic construction of symplectic structure on the cotangent bundle in general. Thus while the book is limited to a naive point of view developing synthetic differential geometry as a theory in itself, the author nevertheless treats somewhat advanced topics, which are classic in classical differential geometry but new in the synthetic context. Audience: The book is suitable as an introduction to synthetic differential geometry for students as well as more qualified mathematicians.

Manifolds and Differential Geometry

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 151/5 ( reviews)

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Book Synopsis Manifolds and Differential Geometry by : Jeffrey Marc Lee

Download or read book Manifolds and Differential Geometry written by Jeffrey Marc Lee. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.

Fundamentals of Differential Geometry

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 417/5 ( reviews)

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Book Synopsis Fundamentals of Differential Geometry by : Serge Lang

Download or read book Fundamentals of Differential Geometry written by Serge Lang. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

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