Partial Differential Equations in Classical Mathematical Physics

By: Isaak Rubenstein, Rubinstein, Isaak Rubinstein

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Paperback | 7 September 1998

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696 Pages

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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 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 both students and researchers alike.

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

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Non-Fiction Science Physics Mathematical Physics Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics

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.

Partial Differential Equations in Classical Mathematical Physics

At a Glance

Paperback

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