经典数学物理中的偏微分方程

出版时间:2000-6   出版时间:世界图书出版公司   作者:I.Rubinstein,L.Rubinstein 著   页数:677  
封面图片

经典数学物理中的偏微分方程
内容概要

The unique characteristic of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is to say, 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 interrelation is traced through study of the asymptotics of the solutions of the respective initial boundaryvalue problems both with respect to time and the governing parameters of the problem. 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 graduate students and researchers alike.
书籍目录

PrefaceChapter
1.IntroductionChapter
2.
Typical
equations
of
mathematical
physics.
Boundary
conditionsChapter
3.
Cauchy
problem
for
first-order
partial
differential
equationsChapter
4.
Classification
of
second-order
partial
differential
equations
with
linear
principal
part.Elements
of
the
theory
of
characteristics
Chapter
5.
Cauchy
and
mixed
problems
for
the
wave
equation
in
R1.
Method
of
traveling
wavesChapter
6.
Cauchy
and
Goursat
problems
for
a
second-order
linear
hyperbolic
equation
withtwo
independent
variables.
Riemann''s
methodChapter
7.
Cauchy
problem
for
a
2-dimensional
wave
equation.
The
Volterra-D''AdhemarsolutionChapter
8.
Cauchy
problem
for
the
wave
equation
in
Rs.
Methods
of
averaging
and
descent.Huygens''s
principleChapter
9.
Basic
properties
of
harmonic
functionsChapter
10.
Green''s
functionsChapter
11.
Sequences
of
harmonic
functions.
Perron''s
theorem.
Schwarzalternating
methodChapter
12.
Outer
boundary-value
problems.
Elements
of
potential
theoryChapter
13.
Cauchy
problem
for
heat-conduction
equationChapter
14.
Maximum
principle
for
parabolic
equationsChapter
15.
Application
of
Green''s
formulas.
Fundamental
identity.
Green''s
functions
forFourier
equationChapter
16.
Heat
potentialsChapter
17.
Volterra
integral
equations
and
their
application
to
solution
of
boundary-value
problems
in
heat-conduction
theoryChapter
18.
Sequences
of
parabolic
functionsChapter
19.
Fourier
method
for
bounded
regionsChapter
20.
Integral
transform
method
in
unbounded
regionsChapter
21.
Asymptotic
expansions.
Asymptotic
solution
of
boundary-value
problemsAppendix
ReferencesIndex
图书标签Tags

数学,经典
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