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978-1-84882-319-8
DE-He213
20181204133146.0
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100301s2009 xxk| s |||| 0|eng d
9781848823198
978-1-84882-319-8
10.1007/978-1-84882-319-8
doi
ISI Library, Kolkata
QA404.7-405
PBWL
bicssc
MAT033000
bisacsh
PBWL
thema
515.96
23
Potential Theory
[electronic resource] /
edited by Lester L. Helms.
London :
Springer London,
2009.
XI, 441 p. 2 illus.
online resource.
text
txt
rdacontent
computer
c
rdamedia
online resource
cr
rdacarrier
text file
PDF
rda
Universitext,
0172-5939
Preliminaries -- 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.
Aimed 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.
Potential theory (Mathematics).
Mathematical physics.
Engineering.
Differential equations, partial.
Mathematics.
Potential Theory.
http://scigraph.springernature.com/things/product-market-codes/M12163
Mathematical Methods in Physics.
http://scigraph.springernature.com/things/product-market-codes/P19013
Engineering, general.
http://scigraph.springernature.com/things/product-market-codes/T00004
Partial Differential Equations.
http://scigraph.springernature.com/things/product-market-codes/M12155
Applications of Mathematics.
http://scigraph.springernature.com/things/product-market-codes/M13003
Helms, Lester L.
editor.
edt
http://id.loc.gov/vocabulary/relators/edt
SpringerLink (Online service)
Springer eBooks
Printed edition:
9781848823181
Printed edition:
9781848823204
Universitext,
0172-5939
https://doi.org/10.1007/978-1-84882-319-8
ZDB-2-SMA
EB
Mathematics and Statistics (Springer-11649)
426165
426165