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Smooth functions and maps

Makarov, Boris M.

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Smooth functions and maps

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Smooth functions and maps/ by Boris M. Makarov, Anatolii N. Podkorytov.
作者:	Makarov, Boris M.
其他作者:	Podkorytov, Anatolii N.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	xl, 244 p. :ill., digital ;24 cm.
內容註:	Introduction -- Differentiable functions -- Smooth maps -- Implicit function theorem and some its applications -- Critical values of smooth maps -- Appendix -- References -- Names Index -- Subject Index.
Contained By:	Springer Nature eBook
標題:	Smoothness of functions. -
電子資源:	https://doi.org/10.1007/978-3-030-79438-5
ISBN:	9783030794385

Smooth functions and maps
Makarov, Boris M.

Smooth functions and maps[electronic resource] /by Boris M. Makarov, Anatolii N. Podkorytov. - Cham :Springer International Publishing :2021. - xl, 244 p. :ill., digital ;24 cm. - Moscow lectures,v.72522-0314 ;. - Moscow lectures ;v.7..

Introduction -- Differentiable functions -- Smooth maps -- Implicit function theorem and some its applications -- Critical values of smooth maps -- Appendix -- References -- Names Index -- Subject Index.

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 mappings and the related Whitney example (Chapter IV) The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.

ISBN: 9783030794385

Standard No.: 10.1007/978-3-030-79438-5doiSubjects--Topical Terms:

662446
Smoothness of functions.

LC Class. No.: QA355

Dewey Class. No.: 515

Smooth functions and maps
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520 $a 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 mappings and the related Whitney example (Chapter IV) The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus.
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