Manifolds, Tensor Analysis, and Applications - Taschenbuch

EAN (ISBN-13): 9781461269908
ISBN (ISBN-10): 1461269903
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2012
Herausgeber: Springer

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ISBN/EAN: 1461269903

ISBN - alternative Schreibweisen:
1-4612-6990-3, 978-1-4612-6990-8
Alternative Schreibweisen und verwandte Suchbegriffe:
Autor des Buches: jerrold marsden, tudor, abraham ralph, marsden ratiu
Titel des Buches: tens, brief tensor analysis, manifolds tensor analysis and applications, manifold

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Daten vom Verlag:

Autor/in: Ralph Abraham; Jerrold E. Marsden; Tudor Ratiu
Titel: Applied Mathematical Sciences; Manifolds, Tensor Analysis, and Applications
Verlag: Springer; Springer US
656 Seiten
Erscheinungsjahr: 2012-10-17
New York; NY; US
Gedruckt / Hergestellt in Niederlande.
Sprache: Englisch
139,09 € (DE)
142,99 € (AT)
153,50 CHF (CH)
POD
XI, 656 p.

BC; Hardcover, Softcover / Mathematik/Geometrie; Topologie; Verstehen; Derivative; Electromagnetism; Hodge star operator; Implicit function; Riemannian geometry; calculus; compactness; exterior derivative; manifold; Manifolds and Cell Complexes; Analysis; Theoretical, Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimization; Mathematische Analysis, allgemein; Mathematische Physik; Kybernetik und Systemtheorie; Optimierung; BB; EA

1 Topology.- 1.1 Topological Spaces.- 1.2 Metric Spaces.- 1.3 Continuity.- 1.4 Subspaces, Products, and Quotients.- 1.5 Compactness.- 1.6 Connectedness.- 1.7 Baire Spaces.- 2 Banach Spaces and Differential Calculus.- 2.1 Banach Spaces.- 2.2 Linear and Multilinear Mappings.- 2.3 The Derivative.- 2.4 Properties of the Derivative.- 2.5 The Inverse and Implicit Function Theorems.- 3 Manifolds and Vector Bundles.- 3.1 Manifolds.- 3.2 Submanifolds, Products, and Mappings.- 3.3 The Tangent Bundle.- 3.4 Vector Bundles.- 3.5 Submersions, Immersions and Transversality.- 4 Vector Fields and Dynamical Systems.- 4.1 Vector Fields and Flows.- 4.2 Vector Fields as Differential Operators.- 4.3 An Introduction to Dynamical Systems.- 4.4 Frobenius’ Theorem and Foliations.- 5 Tensors.- 5.1 Tensors in Linear Spaces.- 5.2 Tensor Bundles and Tensor Fields.- 5.3 The Lie Derivative: Algebraic Approach.- 5.4 The Lie Derivative: Dynamic Approach.- 5.5 Partitions of Unity.- 6 Differential Forms.- 6. I Exterior Algebra.- 6.2 Determinants, Volumes, and the Hodge Star Operator.- 6.3 Differential Forms.- 6.4 The Exterior Derivative, Interior Product, and Lie Derivative.- 6.5 Orientation, Volume Elements, and the Codifferential.- 7 Integration on Manifolds.- 7.1 The Definition of the Integral.- 7.2 Stokes’ Theorem.- 7.3 The Classical Theorems of Green, Gauss, and Stokes.- 7.4 Induced Flows on Function Spaces and Ergodicity.- 7.5 Introduction to Hodge-deRham Theory and Topological Applications of Differential Forms.- 8 Applications.- 8.1 Hamiltonian Mechanics.- 8.2 Fluid Mechanics.- 8.3 Electromagnetism.- 8.3 The Lie-Poisson Bracket in Continuum Mechanics and Plasma Physics.- 8.4 Constraints and Control.- References.