Analysis and algebra on differentiable Manifolds : a workbook for students and teachers / Pedro M. Gadea, Ihor V. Mykytyuk, Jaime Muñoz Masqué. – 2nd ed. – London [etc.] : Springer, 2013. – XXV, ... więcej

Analysis and algebra on differentiable Manifolds : a workbook for students and teachers / Pedro M. Gadea, Ihor V. Mykytyuk, Jaime Muñoz Masqué. – 2nd ed. – London [etc.] : Springer, 2013. – XXV, [1], 617 s. : il. (w tym kolor.). – (Problem Books in Mathematics, ISSN 0941-3502). – Bibliogr. przy rozdz. – doi: 10.1007/978-94-007-5952-7. – ISBN 978-007-5951-0. – ISBN 978-94-007-5952-7 (eBook)

This is the second edition of the problem book for students. It contains over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises ... więcej

This is the second edition of the problem book for students. It contains over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go 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 2nd edition there are: 76 new problems, a section devoted to a generalization of Gauss’ 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. 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.