... different transformations thus far dis-
cussed are now multiplicative and take the following forms:
(9. 19)
(9. 20)
(9. 21)
(9. 22)
(9. 23)
(9. 24)
The composite matrix of any two transformations can ... transformations, in 2-D, are
respectively:
(9. 8)
(9. 9)
In-Class Exercises
Pb. 9. 12 Find the transformation matrix for simultaneously compressing
the x-coordinate by a factor...
... equations for D(k) and D2(k), as given respec-
tively by Eqs. (4.16) and (4.30), and with the initial conditions for the function
and its derivative. The first elements for the y, D, and D2 arrays ...
(2*a(k)*y(k-1)/dt+a(k)D(k-1)+u(k));
D(k)=(2/dt)*(y(k)-y(k-1))-D(k-1);
end
plot(t,y,t,u,' ')
In-Class Exercise
Pb. 4.37 Plot the amplitude of y, and its dephasing from...
... creating a file for the negative of this function (call it n-funname)
and entering the following commands in the command window:
xmax=fmin('n-funname',xi,xf)
fmax =-1 *feval('n-funname',xmax)
Homework ... discuss the
use of the MATLAB command roots for finding all roots of a polynomial.
Following this, we consider the Golden Section method and the fmin and
fmin...
... Different Elementary Numerical Integrating Methods
Number of Sampling Points in a Period R
T
R
MP
R
S
100 0 .99 97 1.0002 1.0000
50 0 .99 86 1.0007 1.0000
40 0 .99 78 1.0011 1.0000
30 0 .99 61 1.0020 ... representing the com-
plex numbers: z
1
= 1, z
2
= j, z
3
= –1.
Solution: Enter and execute the following commands in the command
window:
z1=1;
z2=j;
z3 =-1 ;
plot(z1,'*')...
... Press LLC
(7 .94 )
and
(7 .95 )
Adding Eqs. (7 .94 ) and (7 .95 ), we obtain the more symmetric formula:
(7 .96 )
Replacing l by l – 1 in Eq. (7 .94 ) and eliminating from Eq.
(7 .95 ), we find that:
(7 .97 )
Differentiating ... find that:
(7 .97 )
Differentiating Eq. (7 .97 ) and using Eq. (7 .95 ), we obtain:
(7 .98 a)
which can be written in the equivalent form:
(7 .98 b)
which is...