000			03149nam a22004935i 4500
001			978-1-4471-6422-7
003			DE-He213
005			20180115171511.0
007			cr nn 008mamaa
008			140410s2014 xxk| s |||| 0|eng d
020			_a9781447164227 _9978-1-4471-6422-7
024	7		_a10.1007/978-1-4471-6422-7 _2doi
050		4	_aQA370-380
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.353 _223
100	1		_aHelms, Lester L. _eauthor.
245	1	0	_aPotential Theory _h[electronic resource] / _cby Lester L. Helms.
250			_a2nd ed. 2014.
264		1	_aLondon : _bSpringer London : _bImprint: Springer, _c2014.
300			_aXIV, 485 p. 2 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aUniversitext, _x0172-5939
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aPartial differential equations.
650		0	_aPotential theory (Mathematics).
650		0	_aProbabilities.
650	1	4	_aMathematics.
650	2	4	_aPartial Differential Equations.
650	2	4	_aPotential Theory.
650	2	4	_aProbability Theory and Stochastic Processes.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781447164210
830		0	_aUniversitext, _x0172-5939
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4471-6422-7
912			_aZDB-2-SMA
999			_c370445 _d370445