力学中的偏微分方程第1卷

所属分类:力学  
出版时间:2004-4   出版时间:世界图书出版公司   作者:A.P.S.Selvadurai   页数:595  
Tag标签:science,物理  

内容概要

The material presented in these monographs is the outcome of the author's long-standing interest in the analytical modelling of problems in mechanics by appeal to the theory of partial differential equations. The impetus for writing these volumes was the opportunity to teach the subject matter to both undergraduate and graduate students in engineering at several universities. The approach is distinctly different to that which would adopted should such a course be given to students in pure mathematics; in this sense, the teaching of partial differential equations within an engineering curriculum should be viewed in the broader perspective of "The Modelling of Problems in Engineering" . An engineering student should be given the opportunity to appreciate how the various combination of balance laws, conservation equations, kinematic constraints, constitutive responses, thermodynamic restrictions, etc., culminates in the development of a partial differential equation, or sets of partial differential equations, with potential for applications to engineering problems. This ability to distill all the diverse information about a physical or mechanical process into partial differential equations is a particular attraction of the subject area.

书籍目录

1.
Mathematical
preliminaries
 1.1
Components
of
a
vector
 1.2
Dot
or
scalar
product
 1.3
Cross
or
vector
product
 1.4
Derivative
of
a
vector
 1.5
Results
involving
derivatives
 1.6
Partial
derivatives
of
vectors
  1.6.1
The
gradient
of
a
scalar
field
  1.6.2
The
divergence
of
a
vector
field
  1.6.3
The
Laplacian
of
a
scalar
or
vector
field
  1.6.4
The
curl
of
a
vector
field
  1.6.5
Other
formulae
involving
 1.7
Divergence
of
a
vector
field:
an
application
 1.8
Divergence
or
Green‘s
theorem
 1.9
Green‘s
theorem
in
two
dimensions
 1.10
Orthogonal
curvilinear
coordinates
 1.11
Gradient
and
Laplacian
in
orthogonal
curvilinear
coordinates
 1.12
Integral
transforms
  1.12.1
Laplace
transform
  1.12.2
Fourier
transforms
  1.12.3ccHankelctransforms 1.13
PROBLEM
SET
12.
General
concepts
in
partial
differential
equations 2.1
Fundamental
concepts  2.1.1
The
order
of
a
partial
differential
equation  2.1.2
The
linearity
of
a
partial
differential
equation  2.1.3
Homogeneity
of
a
partial
differential
equation 2.2
Well-posed
problems  2.2.1
Boundary
conditions  2.2.2
Initial
conditions  2.2.3
Well-posed
problems 2.3
PROBLEM
SET
23.Partial
differential
equations
of
the
first-order 3.1
General
concepts 3.2
Examples
involving
first-order
equations 3.3
Advective
transport
in
reactor
column  3.3.1
Governing
equation
-
one
dimensional
case  3.3.2
Governing
equation
-
generalized
formulation 3.4
A
heat
exchanger
problem 3.5
PROBLEM
SET
34.Partial
differential
equations
of
the
second-order 4.1
Classification
of
second-order
partial
differential
equations 4.2
Reduction
to
canonical
forms 4.3
Applications
of
the
procedures 4.4
Classification
of
second-order
pdes for
n
independent
variables 4.5
PROBLEM
SET
45.Laplace's
equation 5.1
Derivation
of
Laplace's
equation  5.1.1
Irrotational
flow
in
fluid
mechani
s  5.1.2
Flow
of
fluids
in
porous
media 5.2
Boundary
conditions  5.2.1
Boundary
conditions
for
fluid
flow  5.2.2
Boundary
conditions
for
porous
media
flow  5.2.3
Boundary
conditions
for
heat
conduction 5.3
Generalized
results 5.4
Methods
of
solution
of
Laplace's
equation  5.4.1
Direct
solution
procedure  5.4.2
Separation
of
variables
method
Cartesian
coordinates  5.4.3
Separation
of
variables
method
plane
polar
coordinates 5.5
Integral
transform
solution
of
Laplace's
equation 5.6
Line
source
within
a
half-plane
region 5.7
Uniqueness
theorem 5.8
A
maximum
principle 5.9
PROBLEM
SET
56.The
diffusion
equation7.The
wave
equationBibliographyIndex

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图书标签Tags

science,物理


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用户评论 (总计21条)

 
 

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