Contents

1. feladat

g=9.80665;
a=16;
f=@(t,y)[y(2);g*(1-a*y(1).^3)];
[t,y]=ode45(f,[0,2],[0.1,0]);
plot(t,y(:,1))
ampl=(max(y(:,1))-min(y(:,1)))/2

merules=@(ido)interp1(t,y(:,1),ido)-0.3;
periodus=fzero(merules,1)-fzero(merules,0.2)

ampl =
      0.24694
periodus =
      0.81697

2. feladat

g=9.80665;
L=0.5;
k=40;
m=0.25;
f=@(t,y)[y(2);y(1).*y(4).^2+g*cos(y(3))-k/m*(y(1)-L);y(4);(-2*y(2)*y(4)-g*sin(y(3)))/y(1)];
[t,y]=ode45(f,[0,2],[L,0,pi/3,0]);
figure(1)
plot(t,y(:,1))
title('Hossz')
figure(2)
plot(t,y(:,3))
title('Szög')
szog=@(ido)interp1(t,y(:,3),ido);
leeresido=fzero(szog,0.4)
hossz=interp1(t,y(:,1),leeresido)

leeresido =
      0.44017
hossz =
      0.61646

3. feladat

f=@(t)exp(-t.^2/2)/sqrt(2*pi);
fprintf('   x         G(x)\n')
for x=0.1:0.1:3
fprintf('  %3.1f         %8.7f\n',x,quad(f,0,x));
end

   x         G(x)
  0.1         0.0398278
  0.2         0.0792597
  0.3         0.1179114
  0.4         0.1554217
  0.5         0.1914625
  0.6         0.2257469
  0.7         0.2580363
  0.8         0.2881446
  0.9         0.3159399
  1.0         0.3413447
  1.1         0.3643339
  1.2         0.3849303
  1.3         0.4031995
  1.4         0.4192434
  1.5         0.4331929
  1.6         0.4452008
  1.7         0.4554345
  1.8         0.4640697
  1.9         0.4712834
  2.0         0.4772499
  2.1         0.4821356
  2.2         0.4860966
  2.3         0.4892759
  2.4         0.4918025
  2.5         0.4937904
  2.6         0.4953388
  2.7         0.4965329
  2.8         0.4974448
  2.9         0.4981341
  3.0         0.4986500

4. feladat

f=@(x)x.*(x-1).*exp(x);
ezplot(f,[0,1])
h=0.1;
x=0:h:1;
y=f(x);
int=h*(y(1)/2+y(end)/2+sum(y(2:end-1)))
quad(f,0,1)

z=polyfit(x,y,10);

zint=polyint(z);

polyval(zint,1)-polyval(zint,0)

int =
     -0.27862
ans =
     -0.28172
ans =
     -0.28172

5. feladat

f=@(x)sin(x).^2.*(x.^3-x.^2+3*x)-5;
ezplot(f,[0,6])

% x=input('Honnét indítsuk a módszert? ')
x=3.8
h=0.0001;

if f(x)*(f(x-h)-2*f(x)+f(x+h))>0
   der=(f(x+h)-f(x-h))/2/h;
   for i=1:20
       x=x-f(x)/der
   end
else
    disp('Nem tudunk semmit sem garantálni.')
end

x =
          3.8
x =
       3.5772
x =
       3.5342
x =
       3.5159
x =
       3.5071
x =
       3.5027
x =
       3.5005
x =
       3.4993
x =
       3.4987
x =
       3.4984
x =
       3.4982
x =
       3.4981
x =
       3.4981
x =
       3.4981
x =
       3.4981
x =
       3.4981
x =
       3.4981
x =
       3.4981
x =
        3.498
x =
        3.498
x =
        3.498

6. feladat

%{
function ider=irany(f,x,v)
vhossz=norm(v);
t=0.00001;
ider=(f(x(1)+t*v(1)/vhossz,x(2)+t*v(2)/vhossz)-f(x(1),x(2)))/t;
ezsurf(f,[x(1)-1,x(1)+1],[x(2)-1,x(2)+1])
%}

Published with MATLAB® 7.6