Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 4 docx

... (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 k2 to second order in (∆t). This results in: (4. 49)Combining ... 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 .4. a=0. 24; b=0.9708;FIGURE 2.3Plot of the Mira curve for a = 0.7. The starting point coordinates are (0, 12.1). Top panel: b= 1, bottom panel: b = 0.9998. -2 0 -1 5 -1 0 -5 0 5 10 15 -1 5 -1 0 -5 051015a=0.7 ... LLC for n=1:1500 for m=1 :40 x(1,m) =-0 .99+2*rx(m);y(1,m) =-0 .99+2*ry(m);x(n+1,m)=a*x(n,m)-b*(y(n,m )-( x(n,m))^2);y(n+1,m)=b*x(n,m)+a*(y(n,m )-( x(n,m))^2);endendplot(x,y,'r.')axis( [-1 ... 15 -1 5 -1 0 -5 051015a=0.7 b=1 -2 0 -1 5 -1 0 -5 0 5 10 15 20 -1 5 -1 0 -5 051015a=0.7 b=0.9998xk axk byk xkyk bxk ayk xk() ()(()(()))() ()(()(()))+= +− −+= ++ −111122aba≤=−112 .and © 2001 by CRC...

... entropy:a. N = 32 and for all ib. N = 8 and c. N = 4 and d. N = 4 and HX px pxiiiN( ) ( )log ( ( ))=−=∑21pxi()=132p =121 4 181161 64 1 64 1 64 1 64 ,,,,,,,p =121 4 1818,,,p ... Mouse-controlling command to read off coordinates of apoint in a graph.global Allows variables to share their values in multiple programs.zoom Zooms in and out on a 2-D plot. 0-8 49 3-? ?? ?-? /00/$0.00+$.50© ... 0 48 1 1 50 for forelsewhere© 2001 by CRC Press LLCIn-Class ExercisePb. 3.19 In a measurement of two power values, P1 and P2, it was deter-mined that:G1 = 9 dB and G2 = –11 dBUsing...

... 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 theguess 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 window:xmax=fmin('n-funname',xi,xf)fmax =-1 *feval('n-funname',xmax)Homework ... discuss theuse of the MATLAB command roots for finding all roots of a polynomial.Following this, we consider the Golden Section method and the fmin and fmins MATLAB commands for optimizing (finding...

... following script M-file.N=720;z=exp(j*2*pi*[1:N]./N);plot(z)axis squareIn-Class ExercisesPb. 6.20 Using the exponential form of the n-roots of unity, and the expres-sion for the sum of a ... m=1 :41 ;z1=cos(k*x-w*t(m));z2=cos(k*x+w*t(m));z=z1+z2;plot(x,z,'r');axis([0 5 -3 3]);T =2πω,© 2001 by CRC Press LLC and (6 .41 )from which we can deduce Euler’s equations:(6 .42 ) and (6 .43 )Example 6.3Use MATLAB to generate the graph of ... equation, and the solution of this algebraic equation then reduces to finding the rootsof the polynomial:(6 .47 )We learned in Chapter 5 the MATLAB command for finding these roots,when needed. Now, using...

... that is non-zero and suchthat the location of this non-zero element is different for each of these basisvectors. 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 allin parallel? (Remember that the equivalent capacitance law is different for capacitors ... of these vectors, and the volume of the parallelepi-ped formed by the three vectors.Solution: Type, execute, and interpret at each step, each of the following com-mands, using the above definitions:u=[2...