LEADER 03235nam 2200565 a 450 001 9910438145003321 005 20200520144314.0 010 $a1-283-90886-7 010 $a1-4614-5981-8 024 7 $a10.1007/978-1-4614-5981-1 035 $a(CKB)2670000000278624 035 $a(EBL)1082052 035 $a(OCoLC)820204665 035 $a(SSID)ssj0000798787 035 $a(PQKBManifestationID)11430342 035 $a(PQKBTitleCode)TC0000798787 035 $a(PQKBWorkID)10755369 035 $a(PQKB)11678288 035 $a(DE-He213)978-1-4614-5981-1 035 $a(MiAaPQ)EBC1082052 035 $a(PPN)168304406 035 $a(EXLCZ)992670000000278624 100 $a20121022d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe implicit function theorem $ehistory, theory, and applications /$fSteven G. Krantz, Harold R. Parks 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2013 215 $a1 online resource (172 p.) 225 0$aModern Birkhauser classics 300 $a"Reprint of the 2003 edition." 311 $a1-4614-5980-X 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction to the Implicit Function Theorem -- History -- Basic Ideas -- Applications -- Variations and Generalizations -- Advanced Implicit Function Theorems -- Glossary -- Bibliography -- Index. 330 $aThe implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis.   There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth functions, and (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash?Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present uncorrected reprint of this classic monograph. Originally published in 2002, The Implicit Function Theorem is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas. 410 0$aModern Birkhäuser Classics,$x2197-1803 606 $aImplicit functions 615 0$aImplicit functions. 676 $a515.8 700 $aKrantz$b Steven G$055961 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438145003321 996 $aThe Implicit Function Theorem$92516807 997 $aUNINA