LEADER 03532nam 22006015 450 001 9910495214403321 005 20251204105118.0 010 $a3-030-79438-5 024 7 $a10.1007/978-3-030-79438-5 035 $a(CKB)4100000011989977 035 $a(MiAaPQ)EBC6683115 035 $a(Au-PeEL)EBL6683115 035 $a(OCoLC)1261878499 035 $a(PPN)269150056 035 $a(BIP)81015828 035 $a(BIP)80380434 035 $a(DE-He213)978-3-030-79438-5 035 $a(EXLCZ)994100000011989977 100 $a20210724d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSmooth Functions and Maps /$fby Boris M. Makarov, Anatolii N. Podkorytov 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (296 pages) 225 1 $aMoscow Lectures,$x2522-0322 ;$v7 311 08$a3-030-79437-7 327 $aIntroduction -- Differentiable functions -- Smooth maps -- Implicit function theorem and some its applications -- Critical values of smooth maps -- Appendix -- References -- Names Index -- Subject Index. . 330 $aThe book contains a consistent and sufficiently comprehensive theory of smooth functions and maps insofar as it is connected with differential calculus. The scope of notions includes, among others, Lagrange inequality, Taylor?s formula, finding absolute and relative extrema, theorems on smoothness of the inverse map and on conditions of local invertibility, implicit function theorem, dependence and independence of functions, classification of smooth functions up to diffeomorphism. The concluding chapter deals with a more specific issue of critical values of smooth mappings. In several chapters, a relatively new technical approach is used that allows the authors to clarify and simplify some of the technically difficult proofs while maintaining full integrity. Besides, the book includes complete proofs of some important results which until now have only been published in scholarly literature or scientific journals (remainder estimates of Taylor?s formula in a nonconvex area (Chapter I, §8), Whitney's extension theorem for smooth function (Chapter I, §11) and some of its corollaries, global diffeomorphism theorem (Chapter II, §5), results on sets of critical values of smooth mappings and the related Whitney example (Chapter IV). The text features multiple examples illustrating the results obtained and demonstrating their accuracy. Moreover, the book contains over 150 problems and 19 illustrations. Perusal of the book equips the reader to further explore any literature basing upon multivariable calculus. 410 0$aMoscow Lectures,$x2522-0322 ;$v7 606 $aMathematical analysis 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aAnalysis 606 $aGlobal Analysis and Analysis on Manifolds 615 0$aMathematical analysis. 615 0$aGlobal analysis (Mathematics). 615 0$aManifolds (Mathematics). 615 14$aAnalysis. 615 24$aGlobal Analysis and Analysis on Manifolds. 676 $a511.4 700 $aMakarov$b B. M.$0521456 702 $aPodkorytov$b Anatolii 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910495214403321 996 $aSmooth functions and maps$92834298 997 $aUNINA