Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 6 pdf

... Press LLC and where (6. 68)Preparatory ExercisePb. 6. 35 Write the analytical expression for Atot. and φtot. in Eq. (6. 68) as func-tions of the amplitudes and phases of signals 1 and 2.The ... 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 ... each of the vec-tors, and similarly for the y-component. Therefore:If: z1 = a1 + jb1 (6. 2) and z2 = a2 + jb2 (6. 3)Then: z1 + z2 = (a1 + a2) + j(b1 + b2) (6. 4)The addition...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 2 pot

... 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 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 ... Find the iterates of the logistic equation for the following values ofr: 3.1, 3.2 360 68, 3.3, 3.498 561 699, 3. 566 667 , and 3. 569 9 46, assuming the follow-ing three initial conditions:y(1) = 0.2, ... Press LLCx1(1)=0. 569 6;y1(1)=0. 162 2;x2(1)=0. 565 0;y2(1)=0. 165 0; for n=1:120x1(n+1)=a*x1(n)-b*(y1(n )-( x1(n))^2);y1(n+1)=b*x1(n)+a*(y1(n )-( x1(n))^2);x2(n+1)=a*x2(n)-b*(y2(n )-( x2(n))^2);y2(n+1)=b*x2(n)+a*(y2(n )-( x2(n))^2);endplot(x1,y1,'ro',x2,y2,'bx')2.8.2.1...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 3 docx

... FFaFF===−−−−−101010 10391215 18 (milli-Farad); F = 10 (micro-Farad); (nano-Farad); pF = 10 (pico-Farad);fF = (femto-Farad); (atto-Farad); 6 µDaba,Take0εε= 26 © 2001 by CRC Press LLCPb. ... that, for arbi-trary a, the product of the roots is and their sum is In-Class ExercisesPb. 3.11 Develop a function M-ﬁle that inputs the two real roots of a second-degree equation and returns ... I2plot(V,I1,V,I2,&apos ;-& apos;) %plot the two curvesIn-Class ExercisePb. 3 .6 In the above script M-ﬁle, we used arrays and the plot command.Rewrite this script ﬁle such that you make use of the fplot command.Further...

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

... 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);endplot(t,y,t,u,' ')In-Class ExercisePb. 4.37 Plot the amplitude of y, and its dephasing from u, as a function ofa for large t.Example 4.9Find the ﬁrst-order ... LLCdt=(tfin-tin)/(N-1);u=sin(t);a=(1/(2*pi))*ones(1,N);b=ones(1,N);y(1)=0;D(1)=(1/a(1))*(u(1)-b(1)*y(1)); for k=2:Ny(k)=((2*a(k)/dt+b(k))^ (-1 ))* (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);endplot(t,y,t,u,'...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 5 potx

... 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 ... LLCnot be found analytically. MATLAB has a built-in command that ﬁnds all theroots (real and complex) for any polynomial equation. As previously noted,the MATLAB command for ﬁnding the polynomial...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 7 pot

... θ. Find the value of θ that maxi-mizes this quantity.)7 .6 Vector Valued FunctionsAs you may recall, in Chapter 1 we described curves in 2-D and 3-D by para-metric equations. Essentially, ... 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 ... 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...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 8 pdf

... 0.4983 0. 960 1 0. 267 90.9901 0.2140 0.7 266 0.43990.7889 0 .64 35 0.4120 0.93340.4387 0.3200 0.74 46 0 .68 330.9708 0.4983 0. 960 1 0. 267 90 0.2140 0.7 266 0.43990 0 0.4120 0.93340 0 0 0 .68 33© 2001 ... 0;1 -1 0 -5 0 0 0;0 1 -1 0 -1 00 0; 0 1 0 0 0 -3 00;0 0 1 0 -RL 0;0 0 0 1 -1 -1 ];Vs=[5;0;0;0;0;0];VI=M\Vs;ilamp=VI(5);Then, from the command window, we proceed by calling this function and plotting ... V are the eigen-vectors and D is a diagonal matrix whose elements are the eigenvalues. Enter-ing the matrix M and the eigensystem commands gives:V = -0 .9701 -0 .8944 -0 .2425 -0 .4472D =1 00...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 9 ppt

... direc-tion as the positive x-axis and where the x-axis direction continuously coin-FIGURE 9.2Scrambled image of Pb. 9. 16. © 2001 by CRC Press LLCtechniques commonly employed in the handling and ... from the complexnumbers chapter (Chapter 6) . Recall that every point in a 2-D plane repre-sents a complex number, and multiplication by a complex number of modu-lus 1 and argument θ results ... (9.15)3. (9. 16) and the ﬁnal result can be written as:(9.17)We can implement the above sequence of transformations through the fol-lowing script M-ﬁle:plot (-5 ,5,'*')hold onG=[2 6 5 3...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab - Chapter 10 docx

... the roll of two dice consists of 36 elementary elements (6 × 6) , only one of which results in a snake-eyes conﬁguration; therefore:p = 1/ 36; k = 3; n = 10 and In-Class ExercisesPb. 10.15 Assuming ... })=∩=== 46 34 56 2 6 4 6 12PEB PE() ().=PED()PEDPE DPDPP()()()({ , })({ , , })=∩=== 46 4 56 2 6 3 6 23PED PE()();≠PPP(((Blue ball first and Red ball ... systems. The random arrival time of certain inputs to asystem cannot be predetermined; for example, the log-on and thelog-off times of terminals and workstations connected to a com-puter network,...

Product Design for the Environment: A Life Cycle Approach - Chapter 6 pdf

... 2722_C0 06_ r02.indd 1 462 722_C0 06_ r02.indd 1 46 11/30/2005 1:48:52 PM11/30/2005 1:48:52 PM© 20 06 by Taylor & Francis Group, LLCdiscussed in Chapter 5 (Section 5.2), and in particular (Fabrycky and ... Cycle 149 Vogtlander, J.G., Brezet, H.C., and Hendriks, C.F., The Virtual Eco-costs ’99: A single LCA-based indicator for sustainability and the Eco-costs/Value Ratio (EVR) model for economic ... nition, assessment and allocation of environmental costs and expenditures for the purpose of cost and resource management, compliance reporting, and capi-tal budgeting, planning, and operational...

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