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Titre : An Introduction to Infinite-Dimensional Differential Geometry Type de document : document électronique Auteurs : Alexander Schmeding, Auteur Editeur : Cambridge [United Kingdom] : Cambridge University Press Année de publication : 2022 Importance : 284 p. Présentation : ill. ISBN/ISSN/EAN : 978-1-00-909125-1 Langues : Anglais (eng) Catégories : Open Access Publications Tags : Geometry Differential Geometry Infinite-dimensional manifolds Frechet spaces Hilbert manifolds Banach manifolds Lie groups Diffeomorphism groups Loop spaces Tangent bundles Riemannian metrics Global analysis Index. décimale : 516 Géométrie Résumé : Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. En ligne : https://doi.org/10.1017/9781009091251 An Introduction to Infinite-Dimensional Differential Geometry [document électronique] / Alexander Schmeding, Auteur . - Cambridge (United Kingdom) : Cambridge University Press, 2022 . - 284 p. : ill.
ISBN : 978-1-00-909125-1
Langues : Anglais (eng)
Catégories : Open Access Publications Tags : Geometry Differential Geometry Infinite-dimensional manifolds Frechet spaces Hilbert manifolds Banach manifolds Lie groups Diffeomorphism groups Loop spaces Tangent bundles Riemannian metrics Global analysis Index. décimale : 516 Géométrie Résumé : Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. En ligne : https://doi.org/10.1017/9781009091251 Réservation
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Code-barres Cote Support Localisation Section Disponibilité 9781009091251 516 SCH E-Book En Ligne Mathématiques Disponible
Titre : Cours de géométrie Type de document : texte imprimé Auteurs : Marc Troyanov, Auteur Editeur : Lausanne : Presses polytechniques et universitaires romandes Année de publication : 2009 Autre Editeur : [Paris] : diff. Géodif Collection : Enseignement des mathématiques Importance : 358 p. Présentation : ill. en noir et en coul., couv. ill. en coul. Format : 24 cm ISBN/ISSN/EAN : 978-2-88074-817-3 Note générale : Bibliogr. p. 351-353. Index Langues : Français (fre) Catégories : Livres Tags : Géométrie Index. décimale : 516 Géométrie Cours de géométrie [texte imprimé] / Marc Troyanov, Auteur . - Lausanne : Presses polytechniques et universitaires romandes : [Paris] : diff. Géodif, 2009 . - 358 p. : ill. en noir et en coul., couv. ill. en coul. ; 24 cm. - (Enseignement des mathématiques) .
ISBN : 978-2-88074-817-3
Bibliogr. p. 351-353. Index
Langues : Français (fre)
Catégories : Livres Tags : Géométrie Index. décimale : 516 Géométrie Réservation
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Code-barres Cote Support Localisation Section Disponibilité C1-13159/11 516 TRO C1 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Exclu du prêt C2-13160/11 516 TRO C2 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Disponible
Titre : Differential Geometry Type de document : texte imprimé Auteurs : Victor V Prasolov, Auteur Editeur : Cham [Switzerland] : Springer International Publishing Année de publication : 2022 Collection : Moscow Lectures, ISSN 2522-0322 num. 8 Importance : 271 p. Format : 23 cm ISBN/ISSN/EAN : 978-3-030-92251-1 Langues : Anglais (eng) Catégories : Livres Tags : Differential Geometry Geometry, Differential Index. décimale : 516 Géométrie Résumé : This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces. The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups Differential Geometry [texte imprimé] / Victor V Prasolov, Auteur . - Cham (Switzerland) : Springer International Publishing, 2022 . - 271 p. ; 23 cm. - (Moscow Lectures, ISSN 2522-0322; 8) .
ISBN : 978-3-030-92251-1
Langues : Anglais (eng)
Catégories : Livres Tags : Differential Geometry Geometry, Differential Index. décimale : 516 Géométrie Résumé : This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces. The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups Réservation
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Code-barres Cote Support Localisation Section Disponibilité C1-043/23 516 PRA C1 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Exclu du prêt C2-044/23 516 PRA C2 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Disponible
Titre : Differential Geometry of Curves and Surfaces Type de document : texte imprimé Auteurs : Thomas F. Banchoff, Auteur ; Stephen Lovett, Traducteur Mention d'édition : Third edition Editeur : Boca Raton [USA] : CRC press Année de publication : 2023 Importance : 368 p. Format : 23 cm ISBN/ISSN/EAN : 978-1-03-228109-4 Langues : Anglais (eng) Catégories : Livres Tags : Differential Geometry Analysis Manifolds and Cell Complexes Geometry, Differential Mathematical analysis Manifolds (Mathematics) Index. décimale : 516 Géométrie Résumé : Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces.
Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player.
The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research.
At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises.
This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.Differential Geometry of Curves and Surfaces [texte imprimé] / Thomas F. Banchoff, Auteur ; Stephen Lovett, Traducteur . - Third edition . - Boca Raton (USA) : CRC press, 2023 . - 368 p. ; 23 cm.
ISBN : 978-1-03-228109-4
Langues : Anglais (eng)
Catégories : Livres Tags : Differential Geometry Analysis Manifolds and Cell Complexes Geometry, Differential Mathematical analysis Manifolds (Mathematics) Index. décimale : 516 Géométrie Résumé : Through two previous editions, the third edition of this popular and intriguing text takes both an analytical/theoretical approach and a visual/intuitive approach to the local and global properties of curves and surfaces.
Requiring only multivariable calculus and linear algebra, it develops students’ geometric intuition through interactive graphics applets. Applets are presented in Maple workbook format, which readers can access using the free Maple Player.
The book explains the reasons for various definitions while the interactive applets offer motivation for definitions, allowing students to explore examples further, and give a visual explanation of complicated theorems. The ability to change parametric curves and parametrized surfaces in an applet lets students probe the concepts far beyond what static text permits. Investigative project ideas promote student research.
At users of the previous editions' request, this third edition offers a broader list of exercises. More elementary exercises are added and some challenging problems are moved later in exercise sets to assure more graduated progress. The authors also add hints to motivate students grappling with the more difficult exercises.
This student-friendly and readable approach offers additional examples, well-placed to assist student comprehension. In the presentation of the Gauss-Bonnet Theorem, the authors provide more intuition and stepping-stones to help students grasp phenomena behind it. Also, the concept of a homeomorphism is new to students even though it is a key theoretical component of the definition of a regular surface. Providing more examples show students how to prove certain functions are homeomorphisms.Réservation
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Code-barres Cote Support Localisation Section Disponibilité C1-045/23 516 BAN C1 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Exclu du prêt C2-046/23 516 BAN C2 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Disponible
Titre : éléments de géométrie : niveau M1 Type de document : texte imprimé Auteurs : Alain Hénaut (1945-....), Auteur ; Alain Yger, Auteur Editeur : Paris : Ellipses Année de publication : 2004 Collection : Mathématiques à l'université Importance : 371 p. Présentation : ill., couv. ill. Format : 26 cm ISBN/ISSN/EAN : 978-2-7298-1996-5 Note générale : Bibliogr. p. 363-364. Index Langues : Français (fre) Catégories : Livres Tags : Géométrie différentielle Manuels d'enseignement supérieur Géométrie algébrique Index. décimale : 516 Géométrie éléments de géométrie : niveau M1 [texte imprimé] / Alain Hénaut (1945-....), Auteur ; Alain Yger, Auteur . - Paris : Ellipses, 2004 . - 371 p. : ill., couv. ill. ; 26 cm. - (Mathématiques à l'université) .
ISBN : 978-2-7298-1996-5
Bibliogr. p. 363-364. Index
Langues : Français (fre)
Catégories : Livres Tags : Géométrie différentielle Manuels d'enseignement supérieur Géométrie algébrique Index. décimale : 516 Géométrie Réservation
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Code-barres Cote Support Localisation Section Disponibilité C1-8839/10 516 HEN C1 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Exclu du prêt C2-8840/10 516 HEN C2 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Disponible C3-8841/10 516 HEN C3 Livre 1er Cycle.(Salle 2ème Étage) Mathématiques Disponible PermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalinkPermalink
