Titlebook: Differentiable Manifolds; A Theoretical Physic Gerardo F. Torres del Castillo Textbook 2020Latest edition Springer Nature Switzerland AG 20

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se are also provided..Differentiable Manifolds. is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, dif978-3-030-45195-0978-3-030-45193-6

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Manifolds, possess the structure of a normed vector space. Recall that the differentiability of a function of . to . means that around each interior point of its domain the function can be approximated by a linear transformation, but this requires the notions of linearity and distance, which are not present i

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Lie Derivatives,ntiable manifold, there is a one-to-one relation between vector fields and families of transformations of the manifold onto itself. This relation is essential in the study of various symmetries, as shown in Chaps. 4, 6 and 8, and in the relationship of a Lie group with its Lie algebra, treated in Ch

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Differential Forms,useful and versatile tool. They are employed in some areas of physics, mainly in thermodynamics and classical mechanics, and of mathematics, such as differential equations, differential geometry, Lie groups, and differential topology.

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Integral Manifolds,ield acquires its simplest expression. Just as a vector field defines a family of curves such that through each point of the manifold there passes one of these curves, it is shown that under certain conditions, a set of vector fields (or of 1-forms) defines a family of submanifolds of a fixed dimens

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