國立虎尾科技大學 |

Smooth Manifolds

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Smooth Manifolds/ by Claudio Gorodski.
作者:	Gorodski, Claudio.
面頁冊數:	XII, 154 p. 11 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Differential Geometry. -
電子資源:	https://doi.org/10.1007/978-3-030-49775-0
ISBN:	9783030497750

Smooth Manifolds
Gorodski, Claudio.

Smooth Manifolds[electronic resource] /by Claudio Gorodski. - 1st ed. 2020. - XII, 154 p. 11 illus.online resource. - 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

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

671118
Differential Geometry.

LC Class. No.: QA614-614.97

Dewey Class. No.: 514.74

Smooth Manifolds
LDR:02751nam a22003975i 4500 001 1020606
003 DE-He213
005 20200801213940.0
007 cr nn 008mamaa
008 210318s2020 gw | s |||| 0|eng d
020 $a 9783030497750 $9 978-3-030-49775-0
024 7 $a 10.1007/978-3-030-49775-0 $2 doi
035 $a 978-3-030-49775-0
050 4 $a QA614-614.97
072 7 $a PBKS $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 514.74 $2 23
100 1 $a Gorodski, Claudio. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1316111
245 1 0 $a Smooth Manifolds $h [electronic resource] / $c by Claudio Gorodski.
250 $a 1st ed. 2020.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2020.
300 $a XII, 154 p. 11 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 2 4 $a Differential Geometry. $3 671118
650 2 4 $a Topological Groups, Lie Groups. $3 672074
650 1 4 $a Global Analysis and Analysis on Manifolds. $3 672519
650 0 $a Differential geometry. $3 882213
650 0 $a Lie groups. $3 527929
650 0 $a Topological groups. $3 885827
650 0 $a Manifolds (Mathematics). $3 1051266
650 0 $a Global analysis (Mathematics). $3 1255807
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030497743
776 0 8 $i Printed edition: $z 9783030497767
830 0 $a Compact Textbooks in Mathematics, $x 2296-4568 $3 1253517
856 4 0 $u https://doi.org/10.1007/978-3-030-49775-0
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)