mathematical methods in science and engineering bayin pdf
Mathematical Methods in Science and Engineering by Selcuk Bayin Jul 18, 2006 pptx
Ngày tải lên :
27/06/2014, 05:20
...
(2.27)
MATHEMATICAL
METHODS
IN
SCIENCE
AND ENGINEERING
PREFACE
xviii
encountered special functions in science and engineering. This is also very
timely, because during the first year
of ... part
of the learning process.
In a vast area like mathematical methods in science and engineering, there
is
always room for new approaches,
new
applications, and new topics. In fact,
the number ... naturally comes from the inner
efficiency of our brain. Research on subjects like brain stimulators, hard
wiring of our brain, and mind reading machines are all aiming at
a
faster and
much more efficient...
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MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING docx
Ngày tải lên :
22/03/2014, 13:20
... MATHEMATICAL
METHODS
IN
SCIENCE
AND ENGINEERING
MATHEMATICS AND MIND
5
1.3
MATHEMATICS AND
MIND
Almost, everywhere mathematics is
a
very useful and powerful language in
expressing ... part
of the learning process.
In a vast area like mathematical methods in science and engineering, there
is
always room for new approaches,
new
applications, and new topics. In fact,
the number ... naturally comes from the inner
efficiency of our brain. Research on subjects like brain stimulators, hard
wiring of our brain, and mind reading machines are all aiming at
a
faster and
much more efficient...
- 709
- 403
- 0
MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING ppt
Ngày tải lên :
27/06/2014, 18:20
... relevant links of interest to readers.
S.
BAYIN
OD
TU
Ankam/TURKE
Y
April
2006
MATHEMATICAL
METHODS
IN
SCIENCE
AND ENGINEERING
Preface
Courses on mathematical methods of physics ... in physics, which
are
also offered by most engineering
departments. Considering that the audience in these coumes comes from all
subdisciplines
of
physics and engineering, the content and ... the growing in-
terest in interdisciplinary studies has brought scientists together from physics,
chemistry, biology, economy, and finance and has increased the demand for
these courses in which...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 2 pdf
Ngày tải lên :
13/08/2014, 09:21
... part
of the learning process.
In a vast area like mathematical methods in science and engineering, there
is
always room for new approaches,
new
applications, and new topics. In fact,
the number ... write
x
=
fl
in the generating function
Equation
(2.65)
we find
(2.85)
Expanding the left-hand side by using the binomial formula and comparing
equal powers oft, we obtain
9
(1)
=
1 ... and
for
meticulously reading Chapters
1
and
9
with
14
and
20.
I
also
thank Prof.
N.
K.
Pak
for many interesting and stimulating discussions, encouragement, and
critical reading...
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- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 7 pdf
Ngày tải lên :
13/08/2014, 09:21
...
Groups with infinite number of elements like
R(n)
are called
infinite groups.
A
group with finite number of elements is
called a
finite group,
where the number of elements in a finite group ...
be expressed in terms of the poten-
tials
-A'
and
4
as
In the Lorentz gauge
2
and
4
satisfy
and
(10.373)
(10.374)
(10.375)
(10.376)
(10.377)
respectively. Defining
a
four-potential ...
+ae
d
(TaB)
r2sinOaW
+a
(WE)]
After simplifying, the Laplacian
is
obtained as
r2sin6
dr
34
r2sin28
a4
'
(10.239)
Here we have obtained
a
well-known formula in
a
rather straightfor-...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 1 potx
Ngày tải lên :
13/08/2014, 09:21
... definition, 429
Cauchy integral formula, 390
Griinwald definition
differintegrals, 385
Laplace transforms, 396
484
Fractional derivatives
MATHEMATICAL
METHODS
IN
SCIENCE
AND ENGINEERING ...
and
Engineering
424
14.7.2
Fractional Fokker-Planck Equations
427
Problems
429
14.7.1 Continuous Time Random Walk (CTRW)
424
15 INFINITE SERIES 431
15.1 Convergence
of
Infinite ...
Mathematical Methods: for Students of Physics and Related
Fields,
Springer Verlag, 2000.
Hassani,
S.,
Mathematical Physics,
Springer Verlag, second edition, 2002.
Hildebrand, F.B.,
Methods...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 3 docx
Ngày tải lên :
13/08/2014, 09:21
... that the value of the integral in Equation
(3.38)
can
be
obtained
by expanding
in powers
of
t
and
s
and then by comparing the equal powers
of
tnsm
with
the left-hand side of Equation ...
(4.52)
'I
A
This Page Intentionally Left Blank
ORTHOGONALiTY
OF
LAGUERRE POLYNOMlALS
49
Interchanging the integral and the summation signs and integrating with
re-
spect
to
x
gives ... are very useful in cosmology and quantum
field
theory in
curved backgrounds. Both the spherical harmonics and the Gegenbauer poly-
nomials are combinations of sines and cosines. Chebyshev...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 4 pptx
Ngày tải lên :
13/08/2014, 09:21
... second
kind. Note that
N,(z)
and
Jm(z)
are linearly independent even
for
the
integer values
of
m.
Hence it is common practice to take
N,(z)
and
Jm(z)
as
the two linearly independent ...
can obtain the following
recursion relations
and
First by adding and then by subtracting these equations we also obtain the
relations
m
Jm-l(X)
=
-Jm(IL.)
+
J:,(X)
(6.52)
X
and
(6.53) ... equations in
physics and engineering can be solved by the method of separation
of
variables.
This method helps us to reduce a second-order partial differential equation
into
a
set of ordinary...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 5 ppsx
Ngày tải lên :
13/08/2014, 09:21
... exists
a
minimum value,
mmin,
thus determining
X
as
X
=
mmin
(9.143)
To
find
mmin
we equate the two expressions
[Eqs.
(9.141)
and
(9.143)]
for
X
to obtain
(9.144)
mmin
=
-1. ...
Cancelling
m
on both sides and noting that
(9.166)
(9.167)
and using Equation (9.164) we finally write
Similarly
We now define the ladder operators
L+
and
L-
for
the
m
index
of ...
m=O
which converges absolutely and uniformly in all subintervals free of
points
of
discontinuity. At the points of discontinuity this series rep
resents
(as
in the Fourier series) the arithmetic...
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MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 6 pps
Ngày tải lên :
13/08/2014, 09:21
...
axn
and
Adding the first two equations and subtracting the last one from the result
and after some rearrangement
of
indices we obtain
(10.197)
I0
COORDINATES
and
TENSORS
Starting with ... choosing three mutually orthogonal straight lines.
A
point is
defined by giving its coordinates,
(q,z2,q),
or by using the position vector
163
188
COORDINATES AND TENSORS
Hence
aa
and ...
1
0
-
sin
$
cosCp sin4cos$
cosdsin+ -sin4 cos~cos$
(10.93)
Reversing the order we get
cos
$
(10.94)
sin
$
sin
Cp
-
sin
$
cos
Cp
R2R1
=
0
cos
Cp
sin
4
[
sin
$
-
cos...
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- 0
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 8 pps
Ngày tải lên :
13/08/2014, 09:21
...
properties that remain invariant under similarity transformations. One such
254
CONTINUOUS GROUPS AND REPRESENTATIONS
Y’
Fig.
11.6
(z,y,z)
and the
(z‘,y’,z‘)
coordinates
we obtain (Fig. 11.6) ... 240
CONTINUOUS GROUPS AND REPRESENTATIONS
induces the following change in
a
function
f(v1,
~2):
-
f(V)
=
f
Mff,
P,
Y)VI'
(1 1.126)
Taking
the
active view we define an operator ...
the physical point
of
view a very important part of the group theory is
representing each element
of
the group with
a
linear transformation acting in
a
vector space. We now introduce the...
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