國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁 到查詢結果 [ subject:"Differential Geometry." ]

切換: 標籤 | MARC模式 | ISBD

An introduction to differential mani...

Lafontaine, Jacques.

An introduction to differential manifolds

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	An introduction to differential manifoldsby Jacques Lafontaine.
作者:	Lafontaine, Jacques.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xix, 395 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differentiable manifolds.
電子資源:	http://dx.doi.org/10.1007/978-3-319-20735-3
ISBN:	9783319207353 (electronic bk.)

An introduction to differential manifolds
Lafontaine, Jacques.

An introduction to differential manifolds[electronic resource] /by Jacques Lafontaine. - Cham :Springer International Publishing :2015. - xix, 395 p. :ill., digital ;24 cm.

Differential Calculus -- Manifolds: The Basics -- From Local to Global -- Lie Groups -- Differential Forms -- Integration and Applications -- Cohomology and Degree Theory -- Euler-Poincare and Gauss-Bonnet.

This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of "abstract" notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux varietes differentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.

ISBN: 9783319207353 (electronic bk.)

Standard No.: 10.1007/978-3-319-20735-3doiSubjects--Topical Terms:

190948
Differentiable manifolds.

LC Class. No.: QA614.3

Dewey Class. No.: 516.36

An introduction to differential manifolds
LDR:02932nmm a2200325 a 4500 001 472804
003 DE-He213
005 20160223152109.0
006 m d
007 cr nn 008maaau
008 160316s2015 gw s 0 eng d
020 $a 9783319207353 (electronic bk.)
020 $a 9783319207346 (paper)
024 7 $a 10.1007/978-3-319-20735-3 $2 doi
035 $a 978-3-319-20735-3
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA614.3
072 7 $a PBMP $2 bicssc
072 7 $a MAT012030 $2 bisacsh
082 0 4 $a 516.36 $2 23
090 $a QA614.3 $b .L166 2015
100 1 $a Lafontaine, Jacques. $3 728098
240 1 0 $a Introduction aux varietes differentielles. $l English
245 1 3 $a An introduction to differential manifolds $h [electronic resource] / $c by Jacques Lafontaine.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xix, 395 p. : $b ill., digital ; $c 24 cm.
505 0 $a Differential Calculus -- Manifolds: The Basics -- From Local to Global -- Lie Groups -- Differential Forms -- Integration and Applications -- Cohomology and Degree Theory -- Euler-Poincare and Gauss-Bonnet.
520 $a This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fields, differential forms, Lie groups, and a few more sophisticated topics such as de Rham cohomology, degree theory and the Gauss-Bonnet theorem for surfaces. Its ambition is to give solid foundations. In particular, the introduction of "abstract" notions such as manifolds or differential forms is motivated via questions and examples from mathematics or theoretical physics. More than 150 exercises, some of them easy and classical, some others more sophisticated, will help the beginner as well as the more expert reader. Solutions are provided for most of them. The book should be of interest to various readers: undergraduate and graduate students for a first contact to differential manifolds, mathematicians from other fields and physicists who wish to acquire some feeling about this beautiful theory. The original French text Introduction aux varietes differentielles has been a best-seller in its category in France for many years. Jacques Lafontaine was successively assistant Professor at Paris Diderot University and Professor at the University of Montpellier, where he is presently emeritus. His main research interests are Riemannian and pseudo-Riemannian geometry, including some aspects of mathematical relativity. Besides his personal research articles, he was involved in several textbooks and research monographs.
650 0 $a Differentiable manifolds. $3 190948
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Differential Geometry. $3 273785
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-20735-3
950 $a Mathematics and Statistics (Springer-11649)