grÁficas fourier

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ECUACIÓN DE CALOR PROBLEMA 1 clear close all syms n x t l=1; k=5; h=(-x^2)+2*x Bn = (2/l)*(int(h*(sin((n*pi*x)/l)))); Arm = 20; for n=1:Arm f(n,:) = sum (exp (k*((-t)*pi^2*n^2))* sin(n*pi*x) *Bn) ; end disp (sum(f)) x = linspace(0, 0.1, 2); t = linspace(0, 0.1, 1); [x,t] = meshgrid(x,t); Ut= subs(sum(f),'x',x); disp (Ut); Usubt = (sum(Ut)); subplot(2,2,4),ezplot(Usubt,[0,0.04,]); title ('x vs f(t)'); Ux= subs(sum(f),'t',t); disp (Ux); Usubx = (sum(Ux)); subplot(2,2,2),ezplot(Usubx,[0,1]); title ('t vs f(x)'); U = simple(sum(f)); subplot(2,2,[1 3]), ezsurf(U,[0 ,0.05,0.2,0.5]); title ('Diagrama U(x,t) '); hold on;

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tonalidades de las graficas de ejercicios de fourier

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Page 1: GRÁFICAS FOURIER

ECUACIÓN DE CALOR

PROBLEMA 1

clearclose allsyms n x t l=1;k=5;h=(-x^2)+2*xBn = (2/l)*(int(h*(sin((n*pi*x)/l)))); Arm = 20;for n=1:Arm f(n,:) = sum (exp (k*((-t)*pi^2*n^2))* sin(n*pi*x) *Bn) ;enddisp (sum(f))x = linspace(0, 0.1, 2);t = linspace(0, 0.1, 1);[x,t] = meshgrid(x,t);Ut= subs(sum(f),'x',x);disp (Ut);Usubt = (sum(Ut));subplot(2,2,4),ezplot(Usubt,[0,0.04,]);title ('x vs f(t)');Ux= subs(sum(f),'t',t);disp (Ux);Usubx = (sum(Ux));subplot(2,2,2),ezplot(Usubx,[0,1]);title ('t vs f(x)');U = simple(sum(f));subplot(2,2,[1 3]), ezsurf(U,[0 ,0.05,0.2,0.5]);title ('Diagrama U(x,t) ');hold on;

Page 2: GRÁFICAS FOURIER

PROBLEMA 2

clcclearclose allsyms n x t h= x^2+2*xl=1;A0 = (1/l)(int(h,x,0,l));An = ((sin(n*pi/2)/(n*pi))-(2/((n^2)*pi^2))+(2*(-1^n)/(n^2*pi^2)));K= 1;Bn = 0;long = 10;for n=1:long f(n,:) = (sum (((sin(n*pi/2)/(n*pi))-(2/((n^2)*pi^2))+(2*(-1^n)/(n^2*pi^2))) *exp(-2*t*pi^2*n^2)* cos(n*pi*x) ) ) ;enddisp (sum(f))x = linspace(0, 0.5, 1);t = linspace(0,0.1, 1);%[x,t] = meshgrid(x,t);Ut= subs(sum(f),'x',x);disp (Ut)Usubt = (sum(Ut));subplot(2,2,4),ezplot(Usubt,[0,0.1]);title ('X vs f(t)');Ux= subs(sum(f),'t',t);disp (Ux)Usubx = (sum(Ux));subplot(2,2,2),ezplot(Usubx,[0,2]);title ('t vs f(x)');U = simple(sum(f));subplot(2,2,[1 3]), ezsurf(U,[0 ,0.01,0.25,0.5]);title ('diagrama expansion');hold on;

Page 3: GRÁFICAS FOURIER

PROBLEMA 3

close allsyms n x t k=1;a=1;h=x^2+2*xA0 = 0;An = ((4*sin(n*pi/2)-n*pi*cos(n*pi/2)+n*pi*(-1^n))/((pi^2)*n^2) );l=1;Bn = ((-2*(-1^n))/(n*pi));a=1;long = 10;for n=1:long f(n,:) = sum ((((4*sin(n*pi/2)-n*pi*cos(n*pi/2)+n*pi*(-1^n))/((pi^2)*n^2) )*cos(n*pi*t)+((-2*(-1^n))/(n*pi))*sin(n*pi*t))*sin(n*pi*x)) ;enddisp (sum(f))x = linspace(0, 0.1, 1);t = linspace(0, 1, 10);%[x,t] = meshgrid(x,t);Ut= subs(sum(f),'x',x);disp (Ut);Usubt = (sum(Ut));subplot(2,2,4),ezplot(Usubt,[0.04,0.45]);title ('x vs f(t)');Ux= subs(sum(f),'t',t);disp (Ux);Usubx = (sum(Ux));subplot(2,2,2),ezplot(Usubx,[0,1]);title ('t vs f(x)');U = simple(sum(f));subplot(2,2,[1 3]), ezsurf(U,[0 ,0.4,0.35,1]);title ('diagrama');hold on;

Page 4: GRÁFICAS FOURIER

PROBLEMA 4

clcclearclose allsyms n x t k=1;a=1;qn=(B^2-n^2)^1/2An = 2/pi((2*sin(n*pi/2)-n*pi*cos(n*pi/2)+n*pi*(-1^n))/((pi^2)*n^2) );l=1;B = ((-2*(-1^n))/(n*pi));a=1;long = 10;for n=1:long f(n,:) = sum ((((4*sin(n*pi/2)-n*pi*cos(n*pi/2)+n*pi*(-1^n))/((pi^2)*n^2) )*cos(n*pi*t)+((-2*(-1^n))/(n*pi))*sin(n*pi*t))*sin(n*pi*x)) ;enddisp (sum(f))x = linspace(0, 0.1, 1);t = linspace(0, 1, 10);%[x,t] = meshgrid(x,t);Ut= subs(sum(f),'x',x);disp (Ut);Usubt = (sum(Ut));subplot(2,2,4),ezplot(Usubt,[0.04,0.45]);title ('x vs f(t)');Ux= subs(sum(f),'t',t);disp (Ux);Usubx = (sum(Ux));subplot(2,2,2),ezplot(Usubx,[0,1]);title ('t vs f(x)');U = simple(sum(f));subplot(2,2,[1 3]), ezsurf(U,[0 ,0.4,0.35,1]);title ('diagrama');hold on;

Page 5: GRÁFICAS FOURIER

PROBLEMA 5

clcclearclose allsyms n x ya= 2;b=2;n=10hh= (4*x)+3;A0 = 1/(a*b)*int(hh,0,a) ;An = (2/(a*sinh((n*pi*b)/a)))*int(hh*cos(n*pi*x/a),0,a);B= 1;l=pi;Bn = 0;long = 10; for n=1:long f(n,:) = A0*y + sum(An*sinh(n*pi*y/a)*cos(n*pi*x/a)) ; end disp (f) x = linspace(0,0.1,5); y = linspace(0.8,1,5); for h=1:length(y) Fx = sum(subs(f, 'y', y(h)));subplot(2, 2, 4),plot(x, subs(Fx, 'x', x), 'Color', rand(1,3), 'Linewidth', 2); hold on; legend(num2str(y)); end hold on; grid on; box on xlabel('x'); title('En funcion de "x" para distintos "y"') for h=1:length(x) Fy = sum(subs(f, 'x', x(h))); subplot(2,2,2),plot(y, subs(Fy, 'y', y), 'Color', rand(1, 3), 'Linewidth', 2); hold on; legend(num2str(x)); end hold on; grid on; box on

Page 6: GRÁFICAS FOURIER

title('En funcion de "y" para distintos "x"') xlabel('y'); U = simple(sum(f)); subplot(2,2,[1 3]), ezsurf(U,[0,0.15,0,0.1]); title ('diagrama'); hold on;

PROBLEMA 6

clcclearclose all

Page 7: GRÁFICAS FOURIER

syms n x ya= 2;b=2;n=10hh= (4*x)+3;A0 = 1/(a*b)*int(hh,0,a) ;An = (2/(a*sinh((n*pi*b)/a)))*int(hh*cos(n*pi*x/a),0,a);B= 1;l=pi;Bn = 0;long = 10; for n=1:long f(n,:) = A0*y + sum(An*sinh(n*pi*y/a)*cos(n*pi*x/a)) ; end disp (f) x = linspace(0,0.1,5); y = linspace(0.8,1,5); for h=1:length(y) Fx = sum(subs(f, 'y', y(h)));subplot(2, 2, 4),plot(x, subs(Fx, 'x', x), 'Color', rand(1,3), 'Linewidth', 2); hold on; legend(num2str(y)); end hold on; grid on; box on xlabel('x'); title('En funcion de "x" para distintos "y"') for h=1:length(x) Fy = sum(subs(f, 'x', x(h))); subplot(2,2,2),plot(y, subs(Fy, 'y', y), 'Color', rand(1, 3), 'Linewidth', 2); hold on; legend(num2str(x)); end hold on; grid on; box on title('En funcion de "y" para distintos "x"') xlabel('y');

Page 8: GRÁFICAS FOURIER

U = simple(sum(f)); subplot(2,2,[1 3]), ezsurf(U,[0,0.15,0,0.1]); title ('diagrama'); hold on;