Date post: | 10-Jan-2016 |
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Graficas
Listado 2.1>> x = 0:0.05:10;>> y=sin(x).*exp(-0.4*x);>> plot(x,y)>> xlabel('x'); ylabel('y')
Listado 2.2>> y = sin(x).*exp(-0.4*x);>> x = (0:0.05:10)';>> y = sin(x).*exp(-0.4*x);>> plot(x,y)>> xlabel('x');ylabel('y')
Listado 2.3>> p=0: 0.05: 8*pi;>> z=(cos(p)+i*sin(2*p)).*exp(-0.05*p)+0.01*p;>> plot(real(z),imag(z))>> xlabel('Re(z)');ylabel('Im(z)')
Listado 2.4>> x=(0:0.4:10)';>> y=sin(x).*exp(-0.4*x);>> plot(x,y,'+')>> xlabel('x');ylabel('y')
Listado 2.5>> x=(0:0.2:10);>> y=sin(x).*exp(-0.4*x);>> plot(x,y)>> grid on>> xlabel('x'), ylabel('y')
Listado 2.6>> t=0:0.5:pi+.01;>> y=sin(3*t).*exp(-0.3*t);>> polar(t,y)>> title('Grafica polar')>> grid
Listado 2.7>> xlabel('x');ylabel('y')>> t=.1:.1:3;>> x=exp(t);>> y=exp(t.*sinh(t));>> loglog(x,y)>> grid>> xlabel('x');ylabel('y')
Listado 2.8>> t= .1:.1:3;>> semilogy(t,exp(t.*t)');>> grid>> xlabel('t'); ylabel('exp(t.*t)');
Listado 2.9>> t=.1:1:3;>> semilogx(t,exp(t.*t)');>> grid>> xlabel('t'); ylabel('exp(t.*t)');
Listado 2.10>> x=0:0.05:5;>> y=sin(x);>> z=cos(x);>> plot(x,y,x,z)
Listado 2.11>> x=0:0.05:5;>> y(1,:)=sin(x);>> y(2,:)=cos(x);>> plot(x,y)
Listado 2.12>> x=(0:0.05:5)';>> y(:,1)=sin(x);>> x(:,2)=cos(x);>> plot(x,y)
Listado 2.13>> x=0:0.05:5;>> y=sin(x);>> plot(x,y);>> hold on>> z=cos(x);>> plot(x,z,'--')>> xlabel('x'); ylabel('y(-), z(--)');
Listado 2.14clear; clf; hold off>> x=0:0.05:5;>> y=sin(x);>> plot(x,y)>> hold on>> z=cos(x)
z =
Columns 1 through 9
1.0000 0.9988 0.9950 0.9888 0.9801 0.9689 0.9553 0.9394 0.9211
Columns 10 through 18
0.9004 0.8776 0.8525 0.8253 0.7961 0.7648 0.7317 0.6967 0.6600
Columns 19 through 27
0.6216 0.5817 0.5403 0.4976 0.4536 0.4085 0.3624 0.3153 0.2675
Columns 28 through 36
0.2190 0.1700 0.1205 0.0707 0.0208 -0.0292 -0.0791 -0.1288 -0.1782
Columns 37 through 45
-0.2272 -0.2756 -0.3233 -0.3702 -0.4161 -0.4611 -0.5048 -0.5474 -0.5885
Columns 46 through 54
-0.6282 -0.6663 -0.7027 -0.7374 -0.7702 -0.8011 -0.8301 -0.8569 -0.8816
Columns 55 through 63
-0.9041 -0.9243 -0.9422 -0.9578 -0.9710 -0.9817 -0.9900 -0.9958 -0.9991
Columns 64 through 72
-1.0000 -0.9983 -0.9941 -0.9875 -0.9784 -0.9668 -0.9528 -0.9365 -0.9178
Columns 73 through 81
-0.8968 -0.8735 -0.8481 -0.8206 -0.7910 -0.7594 -0.7259 -0.6907 -0.6536
Columns 82 through 90
-0.6150 -0.5748 -0.5332 -0.4903 -0.4461 -0.4008 -0.3545 -0.3073 -0.2594
Columns 91 through 99
-0.2108 -0.1617 -0.1122 -0.0623 -0.0124 0.0376 0.0875 0.1372 0.1865
Columns 100 through 101
0.2354 0.2837
>> hold off
Listado 2.15A>> M= [0: 0.01: 1]'; k=1.4;>> p0_entre_p = (1 + (k-1)/2+M.^2).^(k/(k-1));>> plot(M,p0_entre_p)>> xlabel('M, numero de Mach')>> ylabel('p0/p')>> title('Relacion de presion, p(estancamiento)/p(esttica)')
Listado 2.15B>> clear>> %Relacion de presin vs. nmero de Mach>> clear; clf; hold off;>> M= [0:0.01:1]';>> k=1.4;>> p0_entre_p = (1 + (k-1)/2+M.^2).^(k/(k-1));>> hold on>> axis('square'); % hace que la grafica sea cuadrada>> plot(M,p0_entre_p)>> xlabel('M, numero de Mach')>> ylabel('p0/p')>> title('Relacin de presion, p(estancamiento)/p(estatica)')>> text(0.45, 1.55, 'comprensible')>> Mb=[0: 0.01: 0.7]';>> p0_entre_pb = 1 + k/2*Mb.^2;>> plot(Mb,p0_entre_pb, '--')>> text(0.5, 1.1, 'Incomprensible')
Anlisis Numrico/Races de EcuacionesEnunciadoencuentre una aproximacin a una raz de la ecuacin cos(x) 3x = 0SolucinGrafica de : cos(x) y 3x>> clear>> x=-2:0.05:2;>> y=cos(x);>> z=3*x;>> t=zeros(size(x));>> plot(x,y)>> axis([-2 2 -6 6])>> hold on>> plot(x,z)>> plot(x,t)>> grid on>> plot(x,t)>> clear>> x=-2:0.05:2;>> y=cos(x);>> z=3*x;>> t=zeros(size(x));>> plot(x,y)>> axis([-2 2 -6 6])>> hold on>> plot(x,z) >> plot(x,t)>> grid on
De la grafica, el valor cercano a la raz es (/2)/4=/8
Forma a)>> format long >> x0=pi/8;>> for i=1:5x= cos(x0)-2*x0;f=abs(cos(x0)-3*x0);disp([x0,x,f])x0=x;end 0.392699081698724 0.138481369113838 0.254217712584886
0.138481369113838 0.713464030549820 0.574982661435982
0.713464030549820 -0.670828702669616 1.384292733219437
-0.670828702669616 2.124964189389722 2.795792892059338
2.124964189389722 -4.776164262675708 6.901128452065429
Forma b)>> format long>> x0=pi/8;>> for i=1:5x= cos(x0)/3;f=abs(cos(x0)-3*x0);disp([x0,x,f])x0=x;end 0.392699081698724 0.307959844170429 0.254217712584886
0.307959844170429 0.317651318230573 0.029074422180432
0.317651318230573 0.316657205338012 0.002982338677682
0.316657205338012 0.316760548013117 0.000310028025313
0. 316760548013117 0.316749819637578 0.000032185126616
Calcule una raz real de la ecuacin empleando como valor inicial x0=1SolucinProceso iterativo>> format long>> x0=1;>> for i=1:9x=20/(x0^2+2*x0+10);dist=abs(x-x0);
dg=abs(-20*(2*x+2)/(x^2+2*x+10)^2);disp([x,dist,dg])x0=x;end 1.538461538461539 0.538461538461539 0.425718941295636
1.295019157088122 0.243442381373416 0.450997473075934
1.401825309448600 0.106806152360478 0.440466677944288
1.354209390404292 0.047615919044308 0.445285721129186
1.375298092487380 0.021088702083087 0.443174611254047
1.365929788170655 0.009368304316725 0.444117116666538
1.370086003401819 0.004156215231164 0.443699889746150
1.368241023612835 0.001844979788984 0.443885280917360
1.369059812007482 0.000818788394647 0.443803041176408Usando races de polinomio en Matlab
>> pol=[1,2,10,-20]; roots(pol)
ans =
-1.684404053910685 + 3.431331350197691i -1.684404053910685 - 3.431331350197691i 1.368808107821373 + 0.000000000000000i
Calcule una raz real de la ecuacin mediante el mtodo de Newton- Raphson, con Xo=1 y = 10-3 aplicado a
>> x=1;Eps=0.001;dist=1;>> while dist > Epsf=x^3+2*x^2+10*x-20;d=3*x^2+4*x+10;x1=x-f/d;dist=abs(x1-x);x=x1;disp([x1,dist]);end 1.411764705882353 0.411764705882353
1.369336470588235 0.042428235294118
1.368808188617532 0.000528281970703
Utilize el mtodo de la secante para obtener una raz del polinomio f(x)= >> f0=x0^3+2*x0^2+10*x0-20;>> f1=x1^3+2*x1^2+10*x1-20;>> clear>> format short>> x0=0;x1=1;>> for i=1:4f0=x0^3+2*x0^2+10*x0-20;f1=x1^3+2*x1^2+10*x1-20;x2=x1-(x1-x0)*f1/(f1-f0);dist=abs(x2-x1);disp([x2,dist])x0=x1;x1=x2;end 1.5385 0.5385
1.3503 0.1882
1.3679 0.0176
1.3688 0.0009