Contents

Ejercicio 2

A=[4 -2 -10; 2 10 -12; -4 -6 16]
b=[-10, 32, -16]'
x=A\b %x=[2 4 1]'
z=A*x %Comprobacion de la solucion

A =

     4    -2   -10
     2    10   -12
    -4    -6    16


b =

   -10
    32
   -16


x =

    2.0000
    4.0000
    1.0000


z =

  -10.0000
   32.0000
  -16.0000

Ejercicio 4

B=[0 1 -1; -6 -11 6; -6 -11 5]
[V D]=eig(B)
%V matriz de autovectores en columna
%D matriz diagonal con los autovalores (-1 -2 -3)

B =

     0     1    -1
    -6   -11     6
    -6   -11     5


V =

    0.7071   -0.2182   -0.0921
    0.0000   -0.4364   -0.5523
    0.7071   -0.8729   -0.8285


D =

   -1.0000         0         0
         0   -2.0000         0
         0         0   -3.0000

Ejercicio 5

C=[1.5+2j -0.35+1.2j; -0.35+1.2j 0.9-1.6j]
d=[30+40j; 20+15j]
r=C\d  %Tensiones V1=19.5229 - 6.0393i y V2=10.2354 + 6.4838i

C =

   1.5000 + 2.0000i  -0.3500 + 1.2000i
  -0.3500 + 1.2000i   0.9000 - 1.6000i


d =

  30.0000 +40.0000i
  20.0000 +15.0000i


r =

  19.5229 - 6.0393i
  10.2354 + 6.4838i

Ejercicio 6

Torres de Hanoi uso: hanoi(N, Tini, Taux, Tdes) donde N = numero de discos (entero >0) Tini = torre inicial (caracter i.e. 'a') Taux = torre auxiliar (caracter i.e. 'b') Tdes = torre destino (caracter i.e. 'c')

%function hanoi(n, i, a, f)
%if n > 0
%  hanoi(n-1, i, f, a);
%  fprintf('mover disco %d de %c a %c\n', n, i, f);
%  hanoi(n-1, a, i, f);
%end
hanoi(5,'a','b','c')

mover disco 1 de a a c
mover disco 2 de a a b
mover disco 1 de c a b
mover disco 3 de a a c
mover disco 1 de b a a
mover disco 2 de b a c
mover disco 1 de a a c
mover disco 4 de a a b
mover disco 1 de c a b
mover disco 2 de c a a
mover disco 1 de b a a
mover disco 3 de c a b
mover disco 1 de a a c
mover disco 2 de a a b
mover disco 1 de c a b
mover disco 5 de a a c
mover disco 1 de b a a
mover disco 2 de b a c
mover disco 1 de a a c
mover disco 3 de b a a
mover disco 1 de c a b
mover disco 2 de c a a
mover disco 1 de b a a
mover disco 4 de b a c
mover disco 1 de a a c
mover disco 2 de a a b
mover disco 1 de c a b
mover disco 3 de a a c
mover disco 1 de b a a
mover disco 2 de b a c
mover disco 1 de a a c

Ejercicio 7

x=(0:0.5:5) %Vector x de 0 a 5 cada 0.5
y=[10 10 16 24 30 38 52 68 82 96 123]   %Vector y
P=polyfit(x,y,2)    %P=4.0233 x^2 + 2.0107 x + 9.6783
plot(x,y,'b-x','LineWidth',1) %Dibujar x-y, azul, puntos x, grosor linea 1
title('Grafico XY') %Titulo
xlabel('vector x')  %Etiqueta eje x
ylabel('vector y')  %Etiqueta eje y
legend('puntos')    %Leyenda

x =

  Columns 1 through 7

         0    0.5000    1.0000    1.5000    2.0000    2.5000    3.0000

  Columns 8 through 11

    3.5000    4.0000    4.5000    5.0000


y =

    10    10    16    24    30    38    52    68    82    96   123


P =

    4.0233    2.0107    9.6783

Ejercicio 8

%a
figure
wt=(0:0.05:3*pi);
v=120*sin(wt);
i=100*sin(wt-pi/4);
subplot(2, 2, 1)
plot(wt,v,wt,i)

%b
p=v.*i;
subplot(2, 2, 2)
plot(wt,p)

%c
fm=3
fa=fm*sin(wt);
fb=fm*sin(wt-2*pi/3);
fc=fm*sin(wt-4*pi/3);
subplot(2, 2, 3)
plot(wt,fa,wt,fb,wt,fc)

%d
fr=3
theta=linspace(0,2*pi);
x=fr*cos(theta);
y=fr*sin(theta);
subplot(2, 2, 4)
plot(x,y)

fm =

     3


fr =

     3

Ejercicio 11

f=[1 0 -35 50 24]   %Vector con los coeficientes de la ecuacion
roots(f)    %Raices de la ecuacion

%Solucion: -6.491 , 4.8706, 2, -0.3796
%%Ejercicio 12
%function ode
%[t, yy] = ode45(@HalfSine, [0 35], [1 0], [ ], 0.15);
%plot(t, yy(:,1))
%function y = HalfSine(t, y, z)
%h = sin(pi*t/5).*(t<=5);
%y = [y(2); -2*z*y(2)-y(1)+h];

ejemploode

f =

     1     0   -35    50    24


ans =

   -6.4910
    4.8706
    2.0000
   -0.3796

Ejercicio 13

%a
k = 5;   m = 10;   fo = 10;   Bo = 2.5;
N = 2^m;   T = 2^k/fo;
ts = (0:N-1)*T/N;
df = (0:N/2-1)/T;
SampledSignal = Bo*sin(2*pi*fo*ts)+Bo/2*sin(2*pi*fo*2*ts);
An = abs(fft(SampledSignal, N))/N;
figure
plot(df, 2*An(1:N/2))

%b
k = 5;   m = 10;   fo = 10;
N = 2^m;   T = 2^k/fo;
ts = (0:N-1)*T/N;
df = (0:N/2-1)/T;
SampledSignal = exp(-2*ts).*sin(2*pi*fo*ts);
An = abs(fft(SampledSignal, N))/N;
figure
plot(df, 2*An(1:N/2))

%c
k = 5;   m = 10;   fo = 10;
N = 2^m;   T = 2^k/fo;
ts = (0:N-1)*T/N;
df = (0:N/2-1)/T;
SampledSignal = sin(2*pi*fo*ts+5*sin(2*pi*(fo/10)*ts));
An = abs(fft(SampledSignal, N))/N;
figure
plot(df, 2*An(1:N/2))

%d

k = 5;   m = 10;   fo = 10;
N = 2^m;   T = 2^k/fo;
ts = (0:N-1)*T/N;
df = (0:N/2-1)/T;
SampledSignal = sin(2*pi*fo*ts-5*exp(-2*ts));
An = abs(fft(SampledSignal, N))/N;
figure
plot(df, 2*An(1:N/2))

Ejercicio 14

A = imread('WindTunnel.jpg', 'jpeg');
image(A)
figure
row=200
red = A(row, :, 1);
gr = A(row, :, 2);
bl = A(row, :, 3);
plot(red, 'r');
hold on
plot(gr, 'g');
plot(bl, 'b');
hold off

row =

   200

Published with MATLAB® R2015a