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

... Press LLC and where (6. 68) Preparatory Exercise Pb. 6. 35 Write the analytical expression for A tot. and φ tot. 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 square In-Class Exercises Pb. 6. 20 Using the exponential form of the n-roots of unity, and the expres- sion...

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... 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 0 5 10 15 a=0.7 b=1 -2 0 -1 5 -1 0 -5 0 5 10 15 20 -1 5 -1 0 -5 0 5 10 15 a=0.7 b=0.9998 xk axk byk xk yk bxk ayk ... Find the iterates of the logistic equation for the following values of r: 3.1, 3.2 360 68, 3.3, 3.498 561 699, 3. 566 667 , and 3. 569 9...

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... F FaFF = = = − −− −− 10 10 10 10 3 912 15 18 (milli-Farad); F = 10 (micro-Farad); (nano-Farad); pF = 10 (pico-Farad); fF = (femto-Farad); (atto-Farad); 6 µ D a b a , Take 0 ε ε =       26 © 2001 by CRC Press LLC Pb. ... that, for arbi- trary a, the product of the roots is and their sum is In-Class Exercises Pb. 3.11 Develop a function M-file that inputs the two real roots of...

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... 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 fro...

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... 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...

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... θ. Find the value of θ that maxi- mizes this quantity.) 7 .6 Vector Valued Functions As 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 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-u...

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... 0.4983 0. 960 1 0. 267 9 0.9901 0.2140 0.7 266 0.4399 0.7889 0 .64 35 0.4120 0.9334 0.4387 0.3200 0.74 46 0 .68 33 0.9708 0.4983 0. 960 1 0. 267 9 0 0.2140 0.7 266 0.4399 0 0 0.4120 0.9334 0 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...

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... direc- tion as the positive x-axis and where the x-axis direction continuously coin- FIGURE 9.2 Scrambled image of Pb. 9. 16. © 2001 by CRC Press LLC techniques commonly employed in the handling and ... from the complex numbers 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 argu...

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... 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 Exercises Pb. 10.15 Assuming ... }) = ∩ ==         = 46 34 56 2 6 4 6 1 2 PEB PE() ().= PED() PED PE D PD P P () () () ({ , }) ({ , , }) = ∩ ==         = 46 4 56 2 6 3 6 2 3 PED PE()();≠...

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... 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, LLC discussed 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...

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