This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers int...

Ausführliche Beschreibung

Bibliographische Detailangaben

1. Verfasser:	Torres del Castillo, Gerardo F. 1956- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cham Birkhäuser [2020]
Ausgabe:	Second Edition
Schlagworte:	bicssc bisacsh Differential geometry Physics Topological groups Lie groups Mechanics Mathematics Differentialgeometrie Lie-Gruppe Hamilton-Formalismus Differenzierbare Mannigfaltigkeit Mathematische Physik Hardcover, Softcover / Mathematik/Geometrie
Zusammenfassung:	This textbook delves into the theory behind differentiable manifolds while exploring various physics applications along the way. Included throughout the book are a collection of exercises of varying degrees of difficulty. Differentiable Manifolds is intended for graduate students and researchers interested in a theoretical physics approach to the subject. Prerequisites include multivariable calculus, linear algebra, and differential equations and a basic knowledge of analytical mechanics
Beschreibung:	This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics.The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations, connections, Riemannian manifolds, Lie groups, and Hamiltonian mechanics. Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics.This second edition greatly expands upon the first by including more examples, additional exercises, and new topics, such as the moment map and fiber bundles. Detailed solutions to every exercise are also provided.Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and a basic knowledge of analytical mechanicsReview of the first edition:This book presents an introduction to differential geometry and the calculus on manifolds with a view on some of its applications in physics. … The present author has succeeded in writing a book which has its own flavor and its own emphasis, which makes it certainly a valuable addition to the literature on the subject. Frans Cantrijn, Mathematical Reviews Preface.-1 Manifolds.- 2 Lie Derivatives.- 3 Differential Forms.- 4 Integral Manifolds.- 5 Connections.- 6. Riemannian Manifolds.- 7 Lie Groups.- 8 Hamiltonian Classical Mechanics.- References.-Index.
Beschreibung:	x, 444 Seiten Illustrationen 235 mm
ISBN:	9783030451929