Gadea, Pedro M., Muñoz Masqué, Jaime, Mykytyuk, Ihor V.
2nd ed. 2013, XXV, 617 p. 68 illus., 38 illus. in color.
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Exercises range from rudimentary to challenging, so will benefit the beginner as well as advanced students
Over 400 completely solved exercises
56-page index of formulae
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 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: • 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.