Analysis and algebra on differentiable manifolds: a workbook for students and teachers / Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk

Auteur: Gadea, Pedro Martínez - AuteurCo-auteur: Muñoz Masqué, Jaime - Auteur ; Mykytiuk, Igor Vladimirovich - AuteurType de document: Livre numérique Collection: Problem books in mathematics Langue: anglaisÉditeur: New York : Springer, cop. 2013 ISBN: 9789400759510 Note: Publisher's description: "This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. "The exercises range from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. "A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. "In this second edition: ∙ 76 new problems ∙ a section devoted to a generalization of Gauss's Lemma ∙ a short novel section dealing with some properties of the energy of Hopf vector fields ∙ an expanded collection of formulae and tables ∙ an extended bibliography "Audience: This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.'' Sujets MSC: 00A07 General -- General and miscellaneous specific topics -- Problem books
53-01 Differential geometry -- Instructional exposition (textbooks, tutorial papers, etc.)
58-01 Global analysis, analysis on manifolds -- Instructional exposition (textbooks, tutorial papers, etc.)
En-ligne: Springerlink | Zentralblatt

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Publisher's description: "This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds.
"The exercises range from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear.
"A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics.
"In this second edition:


76 new problems

a section devoted to a generalization of Gauss's Lemma

a short novel section dealing with some properties of the energy of Hopf vector fields

an expanded collection of formulae and tables

an extended bibliography


"Audience: This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.''

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