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

... =111 122 123 3 123 211 22 2 22 2 22 2 2 22 2 222 22 AkkkBkkk() ()=−+=+11 2 and lkkkk()!()!()+=+=+1111vkjjjCjCkkkCjkjk()()()()( )+=+++= +=+++==∑∑111 12 16 2 1 2 1© ... n=1: 120 00a =-0 .99;b1=1;b2=0.98;x1(1)=4;y1(1)=0;x2(1)=4;y2(1)=0;x1(n+1)=b1*y1(n)+a*x1(n) +2* (1-a)*(x1(n)) ^2/ (1+(x1(n) ^2) );y1(n+1)=-x1(n)+a*x1(n+1) +2* (1-a)*(x1(n+1) ^2) /(1+(x1(n+1) ^2) );x2(n+1)=b2*y2(n)+a*x2(n) +2* (1-a)*(x2(n)) ^2/ (1+(x2(n) ^2) );y2(n+1)=-x2(n)+a*x2(n+1) +2* (1-a)*(x2(n+1) ^2) /(1+(x2(n+1) ^2) );endsubplot (2, 1,1); plot(x1,y1,'.')title('a =-0 .99 b=1')subplot (2, 1 ,2) ; ... 1© 20 01 by CRC Press LLCx1(1)=0.5696;y1(1)=0.1 622 ;x2(1)=0.5650;y2(1)=0.1650; for n=1: 120 x1(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...

... )=+=+−∞∫ 2 22 πππ ττyxxx xxx x() . . .=++ −≤<−−−<< 2 244 2 10 16 0 48 1 1 50 for forelsewhere© 20 01 by CRC Press LLCIn-Class ExercisePb. 3.19 In ... FFaFF===−−−−−101010 1039 12 15 18 (milli-Farad); F = 10 (micro-Farad); (nano-Farad); pF = 10 (pico-Farad);fF = (femto-Farad); (atto-Farad);–6µDaba,Take0εε= 26 © 20 01 by CRC Press ... ExercisesPb. 3 .20 In each of the following cases, find the entropy:a. N = 32 and for all ib. N = 8 and c. N = 4 and d. N = 4 and HX px pxiiiN( ) ( )log ( ( ))=−=∑ 2 1pxi()=1 32 p =1 2 1418116164164164164,,,,,,,p...

... system gov-erned by the difference equation:wxwww() () () ( )20 1 2 210 22 2== + +…∆etc.wx 2 0 2 ()=∆wixii 2 41 123 () ( ) , , ,=− = …∆ for bx0 2 2()=∆bx1 2 2()=−∆a1 2 1()=Dktyk ... signal.()()(/)(/)////ax b dxbababa 2 32 12 12 12 43+=−−−−∫bbaba(( /) )(),/// 2 2 12 32 12 −=−© 20 01 by CRC Press LLCFIGURE 4 .2 A parabolic segment and its circumscribed parallelogram.FIGURE ... +1 12 © 20 01 by CRC Press 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,'...

... can-zxyzxy13 2 22 023 034== + −== + −zxyyxzxy1 32 2 2 22 027 40331== + + −−== + −sin ( ) /zxyzxy1 32 2 2 03 12 09== + − −==+−/()zxyzxy1 2 200414== ... that:(5 .25 )(5 .26 )(5 .27 )Now, replacing the values of a (2) and b (2) from Eqs. (5 .26 ) and (5 .27 ) into Eq.(5 .25 ), we are led to a second-degree equation in r:r 2 – 3r + 1 = 0 (5 .28 )The desired ... 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,...

... ba 12 12 12 12 12 ()()zz z z 12 1 2 2 2 ,,zjz j 12 31==−;zjzj 12 46 23 =+ =−;zjzj 12 13 24 1 2 15=+ =−(); ()zjzj 12 13 24 1 2 15=− =+(); ()( )2 1 2 2 2 ++jj© 20 01 ... )]1 22 zzzz=−+a. b c 34 25 313 12 233 2 +++−+−+−+jjjjjjjjj()()zz zzzz zzzz zzzz zzzz 12 12 12 12 12 12 12 12 +=+−=−===(/) /© 20 01 by ... cos ( ) 2 20 2 20 22 0114 42 1 0ΩΩΩΩΩ−++−−− + =rrrrrrr a br ar a b r ar a br865 4 32 81 422 8 10+− − + − − − +− +=() ( ) ()a =+(cos( ) cos( ))ΩΩ 12 2© 20 01 by...

... v v ucos( ) ( )θ1 2 2 2 2rruv u u v v v u v u uv uv⋅= +++− − − − = +1 2 1 2 2 2 1 2 2 2 11 2 22 211 22 (()()rruv uv uv uvnn⋅= + +…+11 22 rrruuuuu un 2 1 2 2 22 =⋅= + +…+rurvrru ... n=++…+ 12 111 1 12 RRR Rparalleln=++…+uv u v+≤ +uv uvuv uv uv vvuuvvu uvv+=++= + +=+ +≤+ + 2 222 2 2 22 uv u uv v u v+≤ + + =+() 22 2 2 2 © 20 01 by CRC Press LLC(7 .21 )In 2- D or 3-D, these ... ()()()000ruuu 2 1 2 2 2 =+ruêuuuuu=+11 2 2 2 12 (, )êuu uuu uunn=++……11 2 2 22 12 (, , , )© 20 01 by CRC Press LLCu = [1537]andv = [24 68]Solution: Type and execute each...