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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie Differentiable Manifolds
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Differentiable Manifolds
Gerardo F. Torres del Castillo (Broschiert, Englisch)
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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 mechanics Review 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 Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
24.06.2021
Sprache
Englisch
EAN
9783030451950
Herausgeber
Springer International Publishing
Sonderedition
Nein
Autor
Gerardo F. Torres del Castillo
Seitenanzahl
444
Auflage
2
Einbandart
Broschiert
Buch Untertitel
A Theoretical Physics Approach
Schlagwörter
differentiable manifolds, Differentiable manifolds physics, differential forms algebra, Riemannian manifolds, metric tensor, Lie groups physics and geometry, Hamiltonian classical mechanics, Lie algebras physics, Fiber bundles physics, Euler equations, Lie derivatives, time-dependent formalism, Vector field, Tensor field, Lie derivatives
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PHU - Mathematische Physik
PBG - Gruppen und Gruppentheorie
PHD - Klassische Mechanik
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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