LEADER 03919nam 22006495 450 001 9910254309403321 005 20200704152458.0 010 $a3-319-51744-9 024 7 $a10.1007/978-3-319-51744-5 035 $a(CKB)3710000001127296 035 $a(DE-He213)978-3-319-51744-5 035 $a(MiAaPQ)EBC5596196 035 $a(PPN)199766975 035 $a(EXLCZ)993710000001127296 100 $a20170328d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to Complex Theory of Differential Equations /$fby Anton Savin, Boris Sternin 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (IX, 138 p. 43 illus.) 225 1 $aFrontiers in Mathematics,$x1660-8046 311 $a3-319-51743-0 327 $aLeray residues -- Ramied integrals -- Asymptotics of ramied integrals -- Ramied Fourier transform -- Properties of ramied Fourier transform -- The Cauchy problem for equations with constant coefficients -- Singularities of the solution of Cauchy problem -- The Cauchy problem for equations with variable coefficients. Leray's uniformization -- Balayage inwards problem -- Mother body problem -- Hints for exercises. 330 $aThis book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds. Although the theory of differential equations on real manifolds is well known ? it is described in thousands of papers and its usefulness requires no comments or explanations ? to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincaré balayage problem and the mother body problem in geophysics. The monograph does not require readers to be familiar with advanced notions in complex analysis, differential equations, or topology. With its numerous examples and exercises, it appeals to advanced undergraduate and graduate students, and also to researchers wanting to familiarize themselves with the subject. 410 0$aFrontiers in Mathematics,$x1660-8046 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aDifferential equations, Partial 606 $aFunctions of complex variables 606 $aGeophysics 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aGeophysics/Geodesy$3https://scigraph.springernature.com/ontologies/product-market-codes/G18009 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aDifferential equations, Partial. 615 0$aFunctions of complex variables. 615 0$aGeophysics. 615 14$aGlobal Analysis and Analysis on Manifolds. 615 24$aPartial Differential Equations. 615 24$aSeveral Complex Variables and Analytic Spaces. 615 24$aGeophysics/Geodesy. 676 $a550 700 $aSavin$b Anton$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767156 702 $aSternin$b Boris$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254309403321 996 $aIntroduction to Complex Theory of Differential Equations$92129524 997 $aUNINA