连续力学中的数学模型

所属分类:力学  
出版时间:2003-9   出版时间:北京世图   作者:R.Temam,A.Miranville   页数:288  
Tag标签:数学  

内容概要

At a time when mathematical modeling is pervading many areas of science and master's degree programs in industrial mathematics are being initiated in many universities, this book is intended as an introduction to continuum mechanics and mathematical modeling. One of the aims of the book is to reduce the gap slightly between mathematics and this area of natural science - a gap that is usually due to the language barrier and to the differences in thinking and reasoning. This book is written in a style suitable for mathematicians and adapted to their training. We have tried to remain very close to physics and to mathematics at the same time by making, in particular, a clear separation between what is assumed and what is proved. As it is, the book may appeal as well to a broader audience, such as engineers who would like to have a different perspective on the field, relying less on physical intuition, and advanced researchers who would like an introduction to a field new to them.

书籍目录

IntroductionA
Few
Words
About
NotationsPART
ONE.
FUNDAMENTAL
CONCEPTS
IN
CONTINUUM
MECHANICS 1
Describing
the
Motion
of
a
System:
Geometry
and
Kinematics 
1.1
Deformations  1.2
Motion
and
Its
Observation
Kinematics  1.3
Description
of
the
Motion
of
a
System:
Eulerian
and
Lagrangian
Derivatives  1.4
Velocity
Field
of
a
Rigid
Body:
Helicoidal
Vector
Fields  1.5
Differentiation
of
a
Volume
Integral
Depending
on
a
Parameter 2
The
Fundamental
Law
of
Dynamics  2.1
The
Concept
of
Mass  2.2
Forces  2.3
The
Fundamental
Law
of
Dynamics
and
Its
First
Consequences  2.4
Application
to
Systems
of
Material
Points
and
to
Rigid
Bodies  2.5
Galilean
Frames:
The
Fundamental
Law
of
Dynamics
Expressed
in
a
Non-Galilean
Frame 3
The
Cauchy
Stress
Tensor
-
Applications 
3.1
Hypotheses
on
the
Cohesion
Forces  3.2
The
Cauchy
Stress
Tensor  3.3
General
Equations
of
Motion  3.4
Symmetry
of
the
Stress
Tensor 4
Real
and
Virtual
Powers  4.1
Study
of
a
System
of
Material
Points  4.2
General
Material
Systems:
Rigidifying
Velocities  4.3
Virtual
Power
of
the
Cohesion
Forces:
The
General
Case  4.4
Real
Power:
The
Kinetic
Energy
Theorem 5
Deformation
Tensor,
Deformation
Rate
Tensor,Constitutive
Laws  5.1
Further
Properties
of
Deformations  5.2
The
Deformation
Rate
Tensor  5.3
Introduction
to
Rheology:
The
Constitutive
Laws 6
Energy
Equations
and
Shock
Equations  6.1
Heat
and
Energy  6.2
Shocks
and
the
Rankine-Hugoniot
RelationsPART
TWO.
PHYSICS
OF
FLUIDS 7
General
Properties
of
Newtonian
Fluids  7.1
General
Equations
of
Fluid
Mechanics  7.2
Statics
of
Fluids  7.3
Remark
on
the
Energy
of
a
Fluid 8
Flows
of
Inviscid
Fluids  8.1
GeneralTheorems  8.2
Plane
Irrotational
Flows  8.3
Transsonic
Flows  8.4
Linear
Acoustics 9
Viscous
Fluids
and
Thermohydraulics  9.1
Equations
of
Viscous
Incompressible
Fluids  9.2
Simple
Flows
of
Viscous
Incompressible
Fluids  9.3
Thermohydraulics  9.4
Equations
in
Nondimensional
Form:
Similarities  9.5
Notions
of
Stability
and
Turbulence  9.6
Notion
of
Boundary
Layer 10
Magnetohydrodynamics
and
Inertial
Confinement
of
Plasmas  10.1
The
Maxwell
Equations
and
Electromagnetism  10.2
Magnetohydrodynamics  10.3
The
Tokamak
Machine 11
Combustion  11.1
Equations
for
Mixtures
of
Fluids  11.2
Equations
of
Chemical
Kinetics  11.3
The
Equations
of
Combustion  11.4
Stefan-Maxwell
Equations  11.5
A
Simplified
Problem:
The
Two-Species
Model 12
Equations
of
the
Atmosphere
and
of
the
Ocean  12.1
Preliminaries  12.2
Primitive
Equations
of
the
Atmosphere  12.3
Primitive
Equations
of
the
Ocean  12.4
Chemistry
of
the
Atmosphere
and
the
Ocean  Appendix:
The
Differential
Operators
in
Spherical
CoordinatesPART
THREE.
SOLID
MECHANICS 13
The
General
Equations
of
Linear
Elasticity  13.1
Back
to
the
Stress-Strain
Law
of
Linear
Elasticity:  The
Elasticity
Coefficients
of
a
Material  13.2
Boundary
Value
Problems
in
Linear
Elasticity:The
Linearization
Principle  13.3
Other
Equations  13.4
The
Limit
of
Elasticity
Criteria 14
Classical
Problems
of
Elastostatics  14.1
Longitudinal
Traction-Compression
of
a
Cylindrical
Bar  14.2
Uniform
Compression
of
an
Arbitrary
Body……15
Energy
Theorems
-
Duality:
Variational
Formulations16
Introduction
to
Nonlinear
Constitutive
Laws
and
to
Homogenization17
Linear
Wave
Equations
in
Mechanics18
The
Soliton
Equation:
The
Korteweg-de
Vries
Equation19
The
Nonlinear
Schrodinger
EquationAppendix
The
Partial
Differential
Equations
of
MechanicsReferencesIndex

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图书标签Tags

数学


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用户评论 (总计20条)

 
 

  •     发货速度快 我侄女很喜欢,题不是很难
  •     不过有点难懂,有些担心一套只有3本
  •     但是发现很难。高中以上的孩子看,要是表明每道题的答案具体在哪页就更好了
  •     能让我看到了一些平时没有看到的东西。我看了将近两遍。,方便使用。
  •     还有c++代码实现,不要买
  •     推荐此书,虽然很厚
  •     内容过于老套!!!,只做了一点点
  •     要很下功夫呀。,家长可以看看
  •     欧美经典,不朽的经典
  •     我完全看不下去!十分的浪费啊!!!哥德巴赫猜想不过是里面的一小篇。。。,适合每一个数学老师
  •     这书质量很好!感觉不错,用着还行
  •     正在学习SPss软件,开拓思维
  •     我做了这本练习册,不值得!
  •     对于数学这样枯燥的东西,这本书蛮好的
  •     读后很有启发。,看了三分之一才被吸引过去·~~
  •     就是比较适合有基础的人看,适合第二阶段复习~~~
  •     东西非常好,概率论考试中给了我很多帮助!把她形容成功夫熊猫里的神龙秘籍也不为过!
  •     故事形式启蒙数学知识,很不错的引进教材
  •     比如蒙特卡罗方法的初步和马尔可夫性质这些都没有讲不过总体还是物有所值的,实物如图一样
  •     看了一小部分,没有什么可说的
 

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