UID:
almafu_9960119316502883
Umfang:
1 online resource (xvii, 414 pages) :
,
digital, PDF file(s).
Ausgabe:
1st ed.
ISBN:
1-316-04283-9
,
1-139-17178-X
Inhalt:
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Frontmatter -- Contents -- Preface -- Glossary of notation -- Introduction -- Tensors in linear spaces -- 1 Linear and affine spaces -- 2 Differential calculus -- 3 Tensor algebra -- 4 Alternating products -- 5 Special relativity -- 6 The uses of covariance -- Manifolds -- 7 Manifolds -- 8 Tangent vectors and 1-forms -- 9 Lie bracket -- 10 Tensors on manifolds -- 11 Mappings -- 12 Cotangent bundle -- 13 Tangent bundle -- 14 Vector fields and dynamical systems -- 15 Contact bundles -- 16 The geometry of thermodynamics -- Transformations -- 17 Lie groups -- 18 Lie derivative -- 19 Holonomy -- 20 Contact transformations -- 21 Symmetries -- The calculus of differential forms -- 22 Differential forms -- 23 Exterior calculus -- 24 The ✶ operator -- 25 Metric symmetries -- 26 Normal forms -- 27 Index notation -- 28 Twisted differential forms -- 29 Integration -- 30 Cohomology -- Applications of the exterior calculus -- 31 Diffusion equations -- 32 First-order partial differential equations -- 33 Conservation laws -- 34 Calculus of variations -- 35 Constrained variations -- 36 Variations of multiple integrals -- 37 Holonomy and thermodynamics -- 38 Exterior differential systems -- 39 Symmetries and similarity solutions -- 40 Variational principles and conservation laws -- 41 When not to use forms -- Classical electrodynamics -- 42 Electrodynamics and differential forms -- 43 Electrodynamics in spacetime -- 44 Laws of conservation and balance -- 45 Macroscopic electrodynamics -- 46 Electrodynamics of moving bodies -- Dynamics of particles and fields -- 47 Lagrangian mechanics of conservative systems -- 48 Lagrange's equations for general systems -- 49 Lagrangian field theory -- 50 Hamiltonian systems -- 51 Symplectic geometry -- 52 Hamiltonian optics -- 53 Dynamics of wave packets -- Calculus on fiber bundles -- 54 Connections.
,
55 Parallel transport -- 56 Curvature and torsion -- 57 Covariant differentiation -- 58 Metric connections -- Gravitation -- 59 General relativity -- 60 Geodesies -- 61 Geodesic deviation -- 62 Symmetries and conserved quantities -- 63 Schwarzschild orbit problem -- 64 Light deflection -- 65 Gravitational lenses -- 66 Moving frames -- Bibliography -- Index.
,
English
Weitere Ausg.:
ISBN 0-521-26929-6
Weitere Ausg.:
ISBN 0-521-26317-4
Sprache:
Englisch
URL:
https://doi.org/10.1017/CBO9781139171786
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