经典数学物理中的偏微分方程

经典数学物理中的偏微分方程

图书基本信息
出版时间:2000-6
出版社:世界图书出版公司
作者:I.Rubinstein,L.Rubinstein 著
页数:677
书名:经典数学物理中的偏微分方程
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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评论与打分
  •     像系统的学习一下。,很实用
  •      一直有买,小孩看了
  •     就是和教材配套的。特实在的有用,就是对非数学专业来说有点难
  •     跟教材同步配套,理工科必备宝典啊
  •     希望对他上学前有帮助。,超赞
  •     老师给推荐的教材,答案书很好
  •     内容不错。适合入门。,过得去吧
  •     辅助你实现编程,当初买的时候很庆幸
  •     自我提高,对这本书很满意
  •     书很早就收到了,竞赛的时候看到原题啦!
  •     相当好的一本书,不过还没开始正式学习
  •     关注很久了。上次5折没买,题目跟上一版有变化
  •     适合拔高训练。,还是比电子书好啊
  •     浏览了一遍觉得还可以,不过重要的是内容
  •     看了以后感觉比Ross的概率论基础教程视角更高,数字现在写得很漂亮了!这本书不错哦!
  •     光盘里是课件。课本知识挺详尽的,各方面知识很全面~
  •     竞赛真题评析,要上中学后才能看明白
  •     但里面的数学,这本书从另一个角度讲解数学
  •     宝贝蛮喜欢,书比较皱
  •     矩阵计算很经典的一本书,对照英文版