LEADER 01485nas 2200493- 450 001 9910367606303321 005 20240515213015.0 011 $a2628-491X 035 $a(OCoLC)1117852391 035 $a(CKB)4100000010105892 035 $a(CONSER)--2022229026 035 $a(DE-599)ZDB2967900-X 035 $a(EXLCZ)994100000010105892 100 $a20190830a20209999 o-- - 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aAdvances in laboratory medicine 210 1$aBerlin, Germany :$cDe Gruyter,$d[2020]- 215 $a1 online resource 300 $aRefereed/Peer-reviewed 517 3 $aAvances en medicina de laboratorio 531 10$aAdv Lab Med 606 $aDiagnosis, Laboratory$vPeriodicals 606 $aClinical Laboratory Techniques 606 $aBiochemistry 606 $aBiomedical Technology 606 $aDiagnosis, Laboratory$2fast$3(OCoLC)fst00892307 608 $aPeriodical. 608 $aPeriodicals.$2fast 608 $aPeriodicals.$2lcgft 615 0$aDiagnosis, Laboratory 615 12$aClinical Laboratory Techniques. 615 22$aBiochemistry. 615 22$aBiomedical Technology. 615 7$aDiagnosis, Laboratory. 676 $a610 712 02$aSociedad Espaņola de Medicina de Laboratorio, 906 $aJOURNAL 912 $a9910367606303321 996 $aAdvances in Laboratory Medicine$92106274 997 $aUNINA LEADER 03900nam 22006975 450 001 9910299977403321 005 20200706073316.0 010 $a1-4471-6422-9 024 7 $a10.1007/978-1-4471-6422-7 035 $a(CKB)3710000000106724 035 $a(EBL)1698288 035 $a(SSID)ssj0001205023 035 $a(PQKBManifestationID)11788712 035 $a(PQKBTitleCode)TC0001205023 035 $a(PQKBWorkID)11191862 035 $a(PQKB)10045774 035 $a(DE-He213)978-1-4471-6422-7 035 $a(MiAaPQ)EBC6315268 035 $a(MiAaPQ)EBC1698288 035 $a(Au-PeEL)EBL1698288 035 $a(CaPaEBR)ebr10983348 035 $a(OCoLC)876832821 035 $a(PPN)178320900 035 $a(EXLCZ)993710000000106724 100 $a20140410d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPotential Theory /$fby Lester L. Helms 205 $a2nd ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (494 p.) 225 1 $aUniversitext,$x0172-5939 300 $aDescription based upon print version of record. 311 $a1-4471-6421-0 327 $aPreliminaries -- Laplace?s Equation -- The Dirichlet Problem -- Green Functions -- Negligible Sets -- Dirichlet Problem for Unbounded Regions -- Energy -- Interpolation and Monotonicity -- Newtonian Potential -- Elliptic Operators -- Apriori Bounds -- Oblique Derivative Problem -- Application to Diffusion Processes. 330 $aPotential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics, and engineering. 410 0$aUniversitext,$x0172-5939 606 $aDifferential equations, Partial 606 $aPotential theory (Mathematics) 606 $aProbabilities 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aDifferential equations, Partial. 615 0$aPotential theory (Mathematics) 615 0$aProbabilities. 615 14$aPartial Differential Equations. 615 24$aPotential Theory. 615 24$aProbability Theory and Stochastic Processes. 676 $a515.7 700 $aHelms$b Lester L$4aut$4http://id.loc.gov/vocabulary/relators/aut$0524785 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299977403321 996 $aPotential theory$9820733 997 $aUNINA