MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 17 doc
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 17 doc
...
(19.216)
(19. 217)
This
is
also the integral equation version of the time-independent Shrdinger
equation for bound states.
CaseII:
X>O:
In this case the denominator in the definition
[Eq. ... surface enclosing the volume
V
with the outward unit
normal
ii,
we obtain
Interchanging the primed and the unprimed variables and assuming that the
Green’s function is symmetri...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 3 docx
... 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...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 12 doc
...
DIFFERINTEGRALS IN SCIENCE AND ENGINEERING
427
Fig.
14.7
Probability distribution in random walk and
CTRW
An important area of application for fractional derivatives is that the ex-
traordinary ... definition
[Eq.
(14 .178 )],
which is given
as
an integral, and the Griinwald definition
[Eq.
(14.39)]
which
is given
as
an infinite series.
14.5 DIFFERINTEGRALS O...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 14 doc
... for the above
integral
is
an infinite straight line passing through the point
y
and parallel
to the imaginary axis in the complex s-plane.
y
is chosen such that all the
singularities of ... function in the infinite interval
(-CO,CO).
We now consider
a
nonperiodic function in the infinite interval
(-o,co).
Physically this corresponds to expressing an arbitrary signal in...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 18 doc
... also leads to many interesting applications in
field theory. In this Chapter we introduce the basic features of this technique,
which has many interesting existing applications and tremendous potential ... this method by evaluating the path integral
of
a
functional
F[x(T)]
=
z(T),
in the interval
[O,t]
via the unpinned Wiener measure. Let
7
be any time in the interval...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 1 potx
... definition, 429
Cauchy integral formula, 390
Griinwald definition
differintegrals, 385
Laplace transforms, 396
484
Fractional derivatives
MATHEMATICAL
METHODS
IN
SCIENCE
AND ENGINEERING ...
V(x)
in
the Bloch Equation
20.6 Methods
of
Calculating Path Integrals
20.6.1 Method
of
Time Slices
20.6.2 Evaluating Path Integrals with the ESKC
20.6.3 Path Integrals
by
t...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 2 pdf
... 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, w...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 4 pptx
... 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 ... 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 lin...
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 5 ppsx
...
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 ...
(9.141)
and
(9.143)]
for
X
to obtain
(9.144)
mmin
=
-1.
(9.146)
Since
m
changes by integer amounts, we could write
hin
=
mmax
-
integer
-1
=
1
-
integer
21
=
integer....
MATHEMATICAL METHOD IN SCIENCE AND ENGINEERING Episode 6 pps
...
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
a...
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