LEADER 04053nam 22007095 450 001 9910300245303321 005 20200629140702.0 010 $a3-319-23715-2 024 7 $a10.1007/978-3-319-23715-2 035 $a(CKB)3810000000022099 035 $a(SSID)ssj0001585498 035 $a(PQKBManifestationID)16264040 035 $a(PQKBTitleCode)TC0001585498 035 $a(PQKBWorkID)14865512 035 $a(PQKB)11625654 035 $a(DE-He213)978-3-319-23715-2 035 $a(MiAaPQ)EBC6315797 035 $a(MiAaPQ)EBC5595538 035 $a(Au-PeEL)EBL5595538 035 $a(OCoLC)1076264652 035 $a(PPN)190532270 035 $a(EXLCZ)993810000000022099 100 $a20151014d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Real and the Complex: A History of Analysis in the 19th Century /$fby Jeremy Gray 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVI, 350 p. 71 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-23714-4 320 $aIncludes bibliographical references and index. 327 $aLagrange and foundations for the calculus -- Joseph Fourier -- Legendre -- Cauchy and continuity -- Cauchy: differentiation and integration -- Cauchy and complex functions to 1830 -- Abel -- Jacobi -- Gauss -- Cauchy and complex function theory, 1830-1857 -- Complex functions and elliptic integrals -- Revision -- Gauss, Green, and potential theory -- Dirichlet, potential theory, and Fourier series -- Riemann -- Riemann and complex function theory -- Riemann's later complex function theory -- Responses to Riemann's work -- Weierstrass -- Weierstrass's foundational results -- Revision { and assessment -- Uniform Convergence -- Integration and trigonometric series -- The fundamental theorem of the calculus -- The construction of the real numbers -- Implicit functions -- Towards Lebesgue's theory of integration -- Cantor, set theory, and foundations -- Topology -- Assessment. 330 $aThis book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass. This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in keeping with how they were seen at the time. It is suitable as a course in the history of mathematics for students who have studied an introductory course in analysis, and will enrich any course in undergraduate real or complex analysis. 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aFunctions of complex variables 606 $aFunctions of real variables 606 $aMathematics 606 $aHistory 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 615 0$aFunctions of complex variables. 615 0$aFunctions of real variables. 615 0$aMathematics. 615 0$aHistory. 615 14$aFunctions of a Complex Variable. 615 24$aReal Functions. 615 24$aHistory of Mathematical Sciences. 676 $a515.9 700 $aGray$b Jeremy$4aut$4http://id.loc.gov/vocabulary/relators/aut$053883 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300245303321 996 $aThe Real and the Complex: A History of Analysis in the 19th Century$92541511 997 $aUNINA