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Elementary topics in differential geometry / John A. Thorpe
Titre : Elementary topics in differential geometry Type de document : texte imprimé Auteurs : John A. Thorpe, Auteur Editeur : New York : Springer-Verlag Année de publication : 1994 Collection : Undergraduate texts in mathematics, ISSN 0172-6056 Importance : XIII-253 p. Présentation : ill. Format : 18X25 cm ISBN/ISSN/EAN : 978-0-387-90357-6 Note générale : Bibliogr. p. 245. IÉditeur : Springer-Verlag New York Inc.; 1st ed. 1979. Corr. 4th printing 1994 édition (27 octobre 1994)
Langue : Anglais
Relié : 256 pages
ISBN-10 : 0387903577
ISBN-13 : 978-0387903576
Poids de l'article : 1.25 kg
Dimensions : 15.6 x 1.75 x 23.39 cmndexLangues : Anglais (eng) Mots-clés : Elementary topics in differential geometry graphs and level sets vector fields the tangent space surfaces the gauss map geodesics parallel transportcurvature of plane curves convex surfaces isometries riemannien metrics Index. décimale : 516 Géométrie Résumé : This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.
SOMMAIRE:
1-GRAPHS AND LEVEL SETS
2-VECTOR FIELDS
3-THE TANGENT SPACE
4-SURFACES
5-VECTOR FIELDS ON SURFACES;ORIENTATION
6-THE GAUSS MAP
7-GEODESICS
8-PARALLEL TRANSPORT
9-THE WEINGARTEN MAP
10-CURVATURE OF PLANE CURVES
11-ARC LENGTH AND LINE INTEGRALS
12-CURVATURE OF SURFACES
13-CONVEX SURFACES
14-PARAMETRIZED SURFACES
15-LOCAL EQUIVALENCE OF SURFACES AND PARAMETRIZED
16-FOCAL POINTS
17-SURFACE AREA AND VOLUME
18-MINIMAL SURFACES
19-THE EXPONENTIAL MAP
20-SURFACES WITH BOUNDARY
21-THE GAUSS-BONNET THEOREM
22-RIGID MOTIONS AND CONGRUENCE
23-ISOMETRIES
24-RIEMANNIAN METRICSNote de contenu : lementary Topics in Differential Geometry (Anglais) Relié – 27 octobre 1994
de J.A. Thorpe (Auteur)
BIBLIOGRAPHY
NATIONAL INDEX
SUBJECT INDEXElementary topics in differential geometry [texte imprimé] / John A. Thorpe, Auteur . - New York : Springer-Verlag, 1994 . - XIII-253 p. : ill. ; 18X25 cm. - (Undergraduate texts in mathematics, ISSN 0172-6056) .
ISBN : 978-0-387-90357-6
Bibliogr. p. 245. IÉditeur : Springer-Verlag New York Inc.; 1st ed. 1979. Corr. 4th printing 1994 édition (27 octobre 1994)
Langue : Anglais
Relié : 256 pages
ISBN-10 : 0387903577
ISBN-13 : 978-0387903576
Poids de l'article : 1.25 kg
Dimensions : 15.6 x 1.75 x 23.39 cmndex
Langues : Anglais (eng)
Mots-clés : Elementary topics in differential geometry graphs and level sets vector fields the tangent space surfaces the gauss map geodesics parallel transportcurvature of plane curves convex surfaces isometries riemannien metrics Index. décimale : 516 Géométrie Résumé : This introductory text develops the geometry of n-dimensional oriented surfaces in Rn+1. By viewing such surfaces as level sets of smooth functions, the author is able to introduce global ideas early without the need for preliminary chapters developing sophisticated machinery. the calculus of vector fields is used as the primary tool in developing the theory. Coordinate patches are introduced only after preliminary discussions of geodesics, parallel transport, curvature, and convexity. Differential forms are introduced only as needed for use in integration. The text, which draws significantly on students' prior knowledge of linear algebra, multivariate calculus, and differential equations, is designed for a one-semester course at the junior/senior level.
SOMMAIRE:
1-GRAPHS AND LEVEL SETS
2-VECTOR FIELDS
3-THE TANGENT SPACE
4-SURFACES
5-VECTOR FIELDS ON SURFACES;ORIENTATION
6-THE GAUSS MAP
7-GEODESICS
8-PARALLEL TRANSPORT
9-THE WEINGARTEN MAP
10-CURVATURE OF PLANE CURVES
11-ARC LENGTH AND LINE INTEGRALS
12-CURVATURE OF SURFACES
13-CONVEX SURFACES
14-PARAMETRIZED SURFACES
15-LOCAL EQUIVALENCE OF SURFACES AND PARAMETRIZED
16-FOCAL POINTS
17-SURFACE AREA AND VOLUME
18-MINIMAL SURFACES
19-THE EXPONENTIAL MAP
20-SURFACES WITH BOUNDARY
21-THE GAUSS-BONNET THEOREM
22-RIGID MOTIONS AND CONGRUENCE
23-ISOMETRIES
24-RIEMANNIAN METRICSNote de contenu : lementary Topics in Differential Geometry (Anglais) Relié – 27 octobre 1994
de J.A. Thorpe (Auteur)
BIBLIOGRAPHY
NATIONAL INDEX
SUBJECT INDEXRéservation
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