Partial Differential Equations in Classical Mathematical Physics

Name: Partial Differential Equations in Classical Mathematical Physics
Price: 86.03 USD
Availability: InStock
ISBN: 9780521558464

ISBN-10: 0521558468

ISBN-13: 9780521558464

Edition: 1998

Authors: Isaak Rubinstein, Lev Rubinstein

List price: $114.99

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Description:

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical…

Book details

List price: $114.99
Copyright year: 1998
Publisher: Cambridge University Press
Publication date: 4/28/1998
Binding: Paperback
Pages: 696
Size: 7.25" wide x 10.00" long x 1.25" tall
Weight: 2.640
Language: English



Preface



Introduction



Typical equations of mathematical physics


Boundary conditions



Cauchy problem for first-order partial differential equations



Classification of second-order partial differential equations with linear principal part


Elements of the theory of characteristics



Cauchy and mixed problems for the wave equation in R1


Method of travelling waves



Cauchy and Goursat problems for a second-order linear hyperbolic equation with two independent variables


Riemannï¿½ï¿½ï¿½s method



Cauchy problem for a 2-dimensional wave equation


The Volterra-D'Adhemar solution



Cauchy problem for the wave equation in R3


Methods of averaging and descent


Huygens's principle



Basic properties of harmonic functions



Greenï¿½ï¿½ï¿½s functions



Sequences of harmonic functions


Perron's theorem


Schwarz alternating method



Outer boundary-value problems


Elements of potential theory



Cauchy problem for heat-conduction equation



Maximum principle for parabolic equations



Application of Greenï¿½ï¿½ï¿½s formulas


Fundamental identity


Green's functions for Fourier equation



Heat potentials



Volterra integral equations and their application to solution of boundary-value problems in heat-conduction theory



Sequences of parabolic functions



Fourier method for bounded regions



Integral transform method in unbounded regions



Asymptotic expansions


Asymptotic solution of boundary-value problems



Elements of vector analysis



Elements of theory of Bessel functions



Fourier's method and Sturm-Liouville equations



Fourier integral



Examples of solution of nontrivial engineering and physical problems


References


Index