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Partial Differential Equations in Classical Mathematical Physics - Isaak Rubinstein

Partial Differential Equations in Classical Mathematical Physics

Paperback

Published: 7th September 1998
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This book considers the theory of partial differential equations as the language of continuous processes in mathematical physics. This is an interdisciplinary area in which the mathematical phenomena are reflections of their physical counterparts. The authors trace 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 counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by students and researchers in applied mathematics and mathematical physics.

'There is no doubt that this is a work of considerable and thorough erudition.' Times Higher Education Supplement

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
RiemannâÇÖs 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
GreenâÇÖs 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 GreenâÇÖs 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
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521558464
ISBN-10: 0521558468
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 696
Published: 7th September 1998
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 25.4 x 18.42  x 3.18
Weight (kg): 1.2