03935nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118040002500153050001600178072001700194072002300211072001600234082001500250245007400265264003800339300004200377336002600419337002600445338003600471347002400507490002900531505028400560520166400844650003602508650002602544650001702570650003702587650001702624650009302641650010802734650009702842650010702939650010403046700007803150710003403228773002003262776003603282776003603318830002903354856004603383978-1-84882-319-8DE-He21320181204133146.0cr nn 008mamaa100301s2009 xxk| s |||| 0|eng d a97818488231987 a10.1007/978-1-84882-319-82doi aISI Library, Kolkata 4aQA404.7-405 7aPBWL2bicssc 7aMAT0330002bisacsh 7aPBWL2thema04a515.9622310aPotential Theoryh[electronic resource] /cedited by Lester L. Helms. 1aLondon :bSpringer London,c2009. aXI, 441 p. 2 illus.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUniversitext,x0172-59390 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. aAimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem of the calculus, the author develops methods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic partial differential equations involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary. 0aPotential theory (Mathematics). 0aMathematical physics. 0aEngineering. 0aDifferential equations, partial. 0aMathematics.14aPotential Theory.0http://scigraph.springernature.com/things/product-market-codes/M1216324aMathematical Methods in Physics.0http://scigraph.springernature.com/things/product-market-codes/P1901324aEngineering, general.0http://scigraph.springernature.com/things/product-market-codes/T0000424aPartial Differential Equations.0http://scigraph.springernature.com/things/product-market-codes/M1215524aApplications of Mathematics.0http://scigraph.springernature.com/things/product-market-codes/M130031 aHelms, Lester L.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978184882318108iPrinted edition:z9781848823204 0aUniversitext,x0172-593940uhttps://doi.org/10.1007/978-1-84882-319-8