000			02653 a2200313 4500
003			NISER
005			20260128143834.0
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020			_a9783030794408 _qPaperback
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082	0	4	_a515.16 _bMAK-S
100	1		_aMakarov, Boris M.
245	1	0	_aSmooth functions and maps
260			_aCham : _bSpringer, _c2021.
300			_axix, 284 pages : _billustrations ; _c23 cm.
490			_aMoscow lectures ; _vv. 7.
504			_aIncludes bibliographical references and indexes.
520			_aThe 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.
650		0	_aAnalysis
650		0	_aGlobal analysis _xMathematics
650		0	_aManifolds (Mathematics)
650		0	_aLagrange function
650		0	_aTaylor’s formula
650		0	_aLagrange inequality
700	1		_aPodkorytov, Anatolii N.
856	4	1	_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-3-030-79438-5/1
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/58135711-smooth-functions-and-maps?ac=1&from_search=true&qid=LoNDH9xd4u&rank=1#CommunityReviews
942			_cBK _2udc
999			_c36793 _d36793