... (4. 42), (4. 44) , and (4. 49), we get the other expression for
y(t(n + 1)), correct to second order in (∆t):
(4. 50)
Now, comparing Eqs. (4. 48) and (4. 50), we obtain the following equalities:
(4. 51)
ytn ... we have:
(4. 46)
(4. 47)
Combining Eqs. (4. 45) to (4. 47), it follows that to second order in (∆t):
(4. 48)
Next, let us Taylor expand k
2
to second order in (∆t). This re...
... entropy:
a. N = 32 and for all i
b. N = 8 and
c. N = 4 and
d. N = 4 and
HX px px
ii
i
N
( ) ( )log ( ( ))=−
=
∑
2
1
px
i
()=
1
32
p =
1
2
1
4
1
8
1
16
1
64
1
64
1
64
1
64
,,,,,,,
p =
1
2
1
4
1
8
1
8
,,,
p ... Mouse-controlling command to read off coordinates of a
point in a graph.
global Allows variables to share their values in multiple pr...
... farray=funname(array)
x=array(1);
y=array(2);
farray(1)=7-sqrt(25+x.^2+y.^2);
farray(2)= 4- 2 *x -4 * y;
3. Use the approximate value found in step 1 as the value for the
guess array; for example:
xyguess= [4 -1 ];
4. Finally, use the fsolve command to ... creating a file for the negative of this function (call it n-funname)
and entering the following commands in the command wind...
... that is non-zero and such
that the location of this non-zero element is different for each of these basis
vectors. This basis is not unique.
For example, in 4- D space, the canonical four-unit orthonormal ... respec-
tively by:
(7 .44 )
and
(7 .45 )
Question: Can you derive a similar theorem for capacitors all in series and all
in parallel? (Remember that the equivalent capacitan...
... (10.37)], we
can write:
(10 .43 )
Again, using Eqs. (10.37) and (10 .43 ), we have:
(10 .44 )
Now, substituting Eq. (10 .41 ) in the denominator of Eq. (10 .44 ), we obtain Eq.
(10 .42 ).
Example 10.10
A digital ... 2001 by CRC Press LLC
and the hyperbolic sine function is defined by:
(S .42 )
Using the above definitions, it is straightforward to derive the following
relations:
(S .43 )...