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Willi-hans Steeb

Problems And Solutions In Differential Geometry, Lie Series, Differential Forms, Relativity And Applications

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Differential Forms
Differential Geometry
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Language_English
Lie Algebras
Lie Series
Manifolds
Matrix-valued Differential Forms
Metric Tensor Fields
Ordinary Differential Equations
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Problem Solving
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Relativity
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Surface
Vector Fields

Product details

  • ISBN 9789813232969
  • Publication Date: 18 Dec 2017
  • Publisher: World Scientific Publishing Co Pte Ltd
  • Publication City/Country: SG
  • Product Form: Paperback
  • Language: English
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Description
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.