LEADER 03659nam 22005775 450 001 9910299970903321 005 20200707031343.0 010 $a3-319-11511-1 024 7 $a10.1007/978-3-319-11511-5 035 $a(CKB)3710000000277612 035 $a(EBL)1965366 035 $a(OCoLC)899249097 035 $a(SSID)ssj0001386581 035 $a(PQKBManifestationID)11994473 035 $a(PQKBTitleCode)TC0001386581 035 $a(PQKBWorkID)11374404 035 $a(PQKB)10229810 035 $a(MiAaPQ)EBC1965366 035 $a(DE-He213)978-3-319-11511-5 035 $z(PPN)258869186 035 $a(PPN)183089448 035 $a(EXLCZ)993710000000277612 100 $a20141107d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Several Complex Variables /$fby Paul M. Gauthier 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (110 p.) 300 $aDescription based upon print version of record. 311 $a3-319-11510-3 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Basics -- Cauchy Integral Formula -- Sequences of Holomorphic Functions -- Series -- Zero Sets of Holomorphic Functions -- Holomorphic Mappings -- Plurisubharmonic Functions -- The Dirichlet Problem -- Uniform Approximation -- Complex Manifolds -- Examples of Manifolds -- Holomorphic Continuation -- The Tangent Space -- Meromorphic Functions and Subvarieties. 330 $aThis monograph provides a concise, accessible snapshot of key topics in several complex variables, including the Cauchy Integral Formula, sequences of holomorphic functions, plurisubharmonic functions, the Dirichlet problem, and meromorphic functions.  Based on a course given at Université de Montréal, this brief introduction covers areas of contemporary importance that are not mentioned in most treatments of the subject, such as modular forms, which are essential for Wiles' theorem and the unification of quantum theory and general relativity.   Also covered is the Riemann manifold of a function, which generalizes the Riemann surface of a function of a single complex variable and is a topic that is well-known in one complex variable, but rarely treated in several variables.  Many details, which are intentionally left out, as well as many theorems are stated as problems, providing students with carefully structured instructive exercises.   Prerequisites for use of this book are functions of one complex variable, functions of several real variables, and topology, all at the undergraduate level.  Lectures on Several Complex Variables will be of interest to advanced undergraduate and beginning undergraduate students, as well as mathematical researchers and professors. 606 $aFunctions of complex variables 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aFunctions of complex variables. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aFunctions of a Complex Variable. 676 $a510 676 $a515.9 676 $a515.94 700 $aGauthier$b Paul M$4aut$4http://id.loc.gov/vocabulary/relators/aut$056864 906 $aBOOK 912 $a9910299970903321 996 $aLectures on several complex variables$91409936 997 $aUNINA