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

... LLC L=length(p); v=x.^[(L-1) :-1 :0]; y=sum(p.*v); In-Class Exercises Pb. 3. 13 Show that, for the polynomial p defined by Eq. (3. 9), the product of the roots is and the sum of the roots is Pb. 3. 14 Find graphically ... s=<2*pi y=0; else y=0 end In-Class Exercises Pb. 3. 30 In the above definition of all the special shape functions, we used the if-else-end form. Write each of th...

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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. 236 068, 3. 3, 3. 498561699, 3. 566667, and 3. 5...

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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 f...

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... com- mand is poly. poly(r) In-Class Exercise Pb. 5.14 Find the roots of the polynomial p = [ 132 1 03] , and com- pute their sum and product. Pb. 5.15 Consider the two polynomials: p 1 = [ 132 1 03] andp 2 ... cast in the form: x = F(x) (5.1) zxy zxy 1 22 2 725 42 4 =− + + =− − © 2001 by CRC Press LLC [xmin,ymin]=goldensection('cos' ,3, 3.5,10^ (-4 )) 5 .3. 3 MATLAB fmin...

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... (P 1 , P 2 , P 3 ) 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,'*') axis( [-2 ... plane: the x-component of the sum of two vectors is the sum of the x-components of each of the vec- tors, and similarly for the y-component. Therefore: If: z 1 = a...

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... )212 12 3and AB C(, ,), (,,), ( ,,)011 31 0 202− and r rr uv w== =(,,) (,,), (,,)120 030 1 23, xyz x yz+−= − +−= 031 0and x y z− = + = −1 3 1 1 2 2 r rr uv w, , and r rr uvw===(,,); (, ,); (, , ) 235 281 ... lati- tude of (P 1 , P 2 , P 3 ) is θ, while their longitudes are (0, 2π /3, –2π /3) , respec- tively. (3) The area of the tetrahedron is the sum of the areas of the four trian...

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... vw 11 22 33 1 1 2 2 3 3 1 2 11 2 2 22 3 2 33 1212 2121 131 3 31 31 233 2 3 3 23 2 vw vw+σ σ ) ()()()σσσ 1 2 11 2 2 22 3 2 33 11 22 33 vw vw vw vw vw vw v w++ =++=⋅II rr ()()σσ σσ σ 1212 212 1 3 12 21 vw ... 0.49 83 0.9601 0.2679 0.9901 0.2140 0.7266 0. 439 9 0.7889 0.6 435 0.4120 0. 933 4 0. 438 7 0 .32 00 0.7446 0.6 833 0.9708 0.49 83 0.9601 0.2679 0 0.2140 0.7266 0. 439...

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... 1 t t x y © 2001 by CRC Press LLC (9 .32 ) (9 .33 ) (9 .34 ) Dividing Eqs. (9 .32 ) and (9 .33 ) by Eq. (9 .34 ), we obtain: (9 .35 ) (9 .36 ) From this we can deduce the magnitude and direction of the velocity of ... 1]; G2=R*G1; plot(G2(1,:),G2(2,:),'g') G3=inv(T)*G2; plot(G3(1,:),G3(2,:),'k') axis( [-1 2 12 -1 2 12]) axis square hold off 9 .3 Manipulation of 2...

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... = − p = 1 6 PCpq( ! !! .2 5 23 1 6 5 6 0 16075 2 525 23 successes in 5 trials) = =         = PCpq( ! !! .3 successes in 10 trials) = 3 10 3 7 37 10 37 1 36 35 36 0 00211=         = © ... 0: In-Class Exercises Pb. 10. 13 Show that when two events A and B are independent, the addi- tion law for probability becomes: POH PZH POH PZH () () () () 11 00 3 5 2...

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