| 书目名称 | Smooth Functions and Maps | | 编辑 | Boris M. Makarov,Anatolii N. Podkorytov | | 视频video | | | 概述 | Contains a consistent theory of smooth functions.Deals with critical values of smooth mappings.Uses a new technical approach that allows to clarify some of the technically difficult proofs while maint | | 丛书名称 | Moscow Lectures | | 图书封面 |  | | 描述 | .The book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus...The scope of notions includes, among others, Lagrange inequality, Taylor’s formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings...In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor’s formula in a nonconvex area (Chapter I, §8), Whitney‘s extension theorem for smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem (Chapter II, §5), results on sets of critical values of smooth mappin | | 出版日期 | Textbook 2021 | | 关键词 | Euclidean space; interior point; limit; partial derivative; differentiability; tangent space; gradient of | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-79438-5 | | isbn_softcover | 978-3-030-79440-8 | | isbn_ebook | 978-3-030-79438-5Series ISSN 2522-0314 Series E-ISSN 2522-0322 | | issn_series | 2522-0314 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 16:29:55
