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Smooth manifolds

Gorodski, Claudio.

Smooth manifolds

Record Type:	Electronic resources : Monograph/item
Title/Author:	Smooth manifoldsby Claudio Gorodski.
Author:	Gorodski, Claudio.
Published:	Cham :Springer International Publishing :2020.
Description:	xii, 154 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Manifolds (Mathematics)
Online resource:	https://doi.org/10.1007/978-3-030-49775-0
ISBN:	9783030497750$q(electronic bk.)

Smooth manifolds
Gorodski, Claudio.

Smooth manifolds[electronic resource] /by Claudio Gorodski. - Cham :Springer International Publishing :2020. - xii, 154 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

Preface -- Smooth manifolds -- Tensor fields and differential forms -- Lie groups -- Integration -- Appendix A: Covering manifolds -- Appendix B: Hodge Theory -- Bibliography -- Index.

This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms) It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes' theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike.

ISBN: 9783030497750$q(electronic bk.)

Standard No.: 10.1007/978-3-030-49775-0doiSubjects--Topical Terms:

198996
Manifolds (Mathematics)

LC Class. No.: QA613 / .G676 2020

Dewey Class. No.: 516.07

Smooth manifolds
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245 1 0 $a Smooth manifolds $h [electronic resource] / $c by Claudio Gorodski.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a xii, 154 p. : $b ill., digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-4568
505 0 $a Preface -- Smooth manifolds -- Tensor fields and differential forms -- Lie groups -- Integration -- Appendix A: Covering manifolds -- Appendix B: Hodge Theory -- Bibliography -- Index.
520 $a This concise and practical textbook presents the essence of the theory on smooth manifolds. A key concept in mathematics, smooth manifolds are ubiquitous: They appear as Riemannian manifolds in differential geometry; as space-times in general relativity; as phase spaces and energy levels in mechanics; as domains of definition of ODEs in dynamical systems; as Lie groups in algebra and geometry; and in many other areas. The book first presents the language of smooth manifolds, culminating with the Frobenius theorem, before discussing the language of tensors (which includes a presentation of the exterior derivative of differential forms) It then covers Lie groups and Lie algebras, briefly addressing homogeneous manifolds. Integration on manifolds, explanations of Stokes' theorem and de Rham cohomology, and rudiments of differential topology complete this work. It also includes exercises throughout the text to help readers grasp the theory, as well as more advanced problems for challenge-oriented minds at the end of each chapter. Conceived for a one-semester course on Differentiable Manifolds and Lie Groups, which is offered by many graduate programs worldwide, it is a valuable resource for students and lecturers alike.
650 0 $a Manifolds (Mathematics) $3 198996
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 273786
650 2 4 $a Topological Groups, Lie Groups. $3 273787
650 2 4 $a Differential Geometry. $3 273785
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950 $a Mathematics and Statistics (SpringerNature-11649)