Differential Geometry and Relativity Theories vol. 1 : Tangent vectors, derivatives, paths, 1-forms, vector fields

David Carfì

ISBN 10: 3330028858 / ISBN 13: 9783330028852

Published by LAP LAMBERT Academic Publishing, 2017

About this Item

nach der Bestellung gedruckt Neuware - Printed after ordering - In this book, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic topics, for instance definition of tangent vectors, change of coordinate system in the definition of tangent vectors, action of tangent vectors on coordinate systems, structure of tangent spaces, geometric interpretation of tangent vectors, canonical tangent vectors determined by local charts, tangent frames determined by local charts, change of local frames, tangent vectors and contravariant vectors, covariant vectors, the gradient of a real function, invariant scalars, tangent applications, local Jacobian matrices, basic properties of the tangent map, chain rule, diffeomorphisms and derivatives, transformation of tangent bases under derivatives, paths on a manifold, vector derivative of a path with respect to a re-parametrization, tangent derivative versus calculus derivative, vector derivative of a path in local coordinates, existence of a path with a given initial tangent vector and other topics.

Seller Inventory # 9783330028852

Bibliographic Details

• Title: Differential Geometry and Relativity Theories vol. 1 : Tangent vectors, derivatives, paths, 1-forms, vector fields
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2017
• Language: English
• ISBN 10: 3330028858
• ISBN 13: 9783330028852
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 11D millimeters 220 millimeters width by 150 millimeters height by 11 millimeters depth
• Weight: 274 grams

About this title

Synopsis

In this book, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic topics, for instance definition of tangent vectors, change of coordinate system in the definition of tangent vectors, action of tangent vectors on coordinate systems, structure of tangent spaces, geometric interpretation of tangent vectors, canonical tangent vectors determined by local charts, tangent frames determined by local charts, change of local frames, tangent vectors and contravariant vectors, covariant vectors, the gradient of a real function, invariant scalars, tangent applications, local Jacobian matrices, basic properties of the tangent map, chain rule, diffeomorphisms and derivatives, transformation of tangent bases under derivatives, paths on a manifold, vector derivative of a path with respect to a re-parametrization, tangent derivative versus calculus derivative, vector derivative of a path in local coordinates, existence of a path with a given initial tangent vector and other topics.

About the Author

PhD, Professor of Mathematics in Economics and Physics, Research Scholar in USA. Invited speaker in USA, India, Russia, Romania, Canada, France, Germany, Uzbekistan, Belgium, for Game Theory inEconomics and Differential Geometry in Physics and Finance. Expert of Game Theory, Relativity Theory, Quant. Finance in international scientific committees.