Analysis and Algebra on Differentiable Manifolds - A Workbook for Students and Teachers (Relié)

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 generalisation 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.