| 书目名称 | Differentiable Manifolds | | 副标题 | A Theoretical Physic | | 编辑 | Gerardo F. Torres del Castillo | | 视频video | | | 概述 | Introduces differentiable manifolds using a theoretical physics approach.Includes applications to differential geometry and general relativity.Expands on the first edition with additional examples, mo | | 图书封面 |  | | 描述 | .This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics..The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations, connections, Riemannian manifolds, Lie groups, and Hamiltonian mechanics. Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics..This second edition greatly expands upon the first by including more examples, additional exercises, and new topics, such as the moment map and fiber bundles. Detailed solutions to every exercise are also provided..Differentiable Manifolds. is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, dif | | 出版日期 | Textbook 2020Latest edition | | 关键词 | differentiable manifolds; Differentiable manifolds physics; differential forms algebra; Riemannian mani | | 版次 | 2 | | doi | https://doi.org/10.1007/978-3-030-45193-6 | | isbn_softcover | 978-3-030-45195-0 | | isbn_ebook | 978-3-030-45193-6 | | copyright | Springer Nature Switzerland AG 2020 |
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发表于 2025-3-21 17:19:30
