function x=bisekcja(a,b)

edop=10^-12;

nmax=100;

e=1;

n=0;

a=1;

b=10;

t = a:0.01:b;

y = F(t);

E = zeros(nmax,1);

while e>edop & n<=nmax

x=(a+b)/2;

if F(a)*F(x)<0

b=x;

else

a=x;

end

e=abs(F(x));

n=n+1;

E(n) = e;

disp([n x e])

end

e

n

subplot(2,1,1);

plot(t,y,'r-','LineWidth',2);

hold on

grid on

plot(x,F(x),'bo');

subplot(2,1,2);

plot(1:n,log10(E(1:n)),'bs-','LineWidth',2);

hold on

grid on

plot([1 n],log10([edop edop]),'k-','LineWidth',2);

function y=F(x)

y=x.^2+3*x-5 + sin(8*x);

-----------------------------------------------------------------------

function x=gauss(A,b)

n=length(A);

m=zeros(n,n);

for k=1:n-1

for i=k+1:n

m(i,k)=(A(i,k))/(A(k,k));

b(i)=(b(i)-m(i,k)*b(k));

for j=1:n

A(i,j)=A(i,j)-(m(i,k)*A(k,j));

end

end

end

for k=n:-1:2

for i=k-1:-1:1

m(i,k)=(A(i,k))/(A(k,k));

b(i)=(b(i)-m(i,k)*b(k));

for j=1:n

A(i,j)=A(i,j)-(m(i,k)*A(k,j));

end

end

end

x=zeros(n,1);

for i=1:n

x(i)=b(i)/A(i,i);

end

-----------------------------------------------

function metodasiecznych

eps = 1e-16;%błąd dopuszczalny

nmax = 11; %maksymalna liczba iteracji+1, minimalnie 2, żeby nie było błędu

n = 1;

xpp = -1; %punkt startowy x0

xp = 5; %punkt startowy x1

e = abs(xp-xpp)/abs(xp);

while (e>eps && n<nmax)

x=xp-F(xp)*(xp-xpp)/(F(xp)-F(xpp));

n = n + 1;

e = abs(x-xp)/abs(x);

xpp=xp;

xp=x;

end

%współrzędne punktu końcowego

wynik=[x F(x)]

%wyznaczanie i rysowanie tej funkcji

t = -10:0.01:10;

y = F(t);

plot(t,y);

hold on

grid on

%rysowanie punktu

plot (x,F(x),'ro');

end

%funkcja której miejsce zerowe wyliczamy

function [z] = F(x)

z = sin(x)+x+1;

end

-------------------------------------------

function aproksymacja

close all

X = [1 2 3 5 8 10];

Y = [1.2 1.7 1.9 5.1 8.2 -10.5];

m=4;

plot(X,Y,'ro');

hold on

grid on

n=size(X,2);

A = zeros(n,m);

b = zeros(n,1);

for i=1:n

% A(i,:)=[X(i)^2 X(i) 1];

for j=1:m

A(i,j)=X(i)^(m-j);

end

b(i)=Y(i);

end

A

b

W=eye(n,n);

W(4,4)=10000;

C = A'*W*A;

d = A'*W*b;

C

d

a=C^-1*d;

x=min(X):0.01:max(X);

% y=a(1)*x.^2+a(2)*x+ a(3);

y=zeros(1,length(x));

for j=1:m

y=y+a(j)*x.^(m-j);

end

plot(x,y,'b-');

--------------------------------------------

function lagrange

X=-5:0.5:4;

Y=sin(X);

n=length(X);

plot(X,Y,'bo','MarkerFaceColor','b')

hold on

x=min(X):0.01:max(X);

m=length(x);

y=zeros(1,m);

for k=1:m

y(k)=p(x(k),n,Y,X);

end

plot(x,y,'r-')

function y=L(x,i,n,X)

a=1;

b=1;

for j=1:n

if j~=i

a=a*(x-X(j));

b=b*(X(i)-X(j));

end

end

y=a/b;

function y=p(x,n,Y,X)

y=0;

for i=1:n

y=y+Y(i)*L(x,i,n,X);

end

--------------------------------------

function Newton

clc

x0=6;

edop=10^-6;

nmax=1000;

n=1;

e=1;

r=1;

X=zeros(nmax,1);

X(1)=x0;

while n<nmax & max([e r])>edop

X(n+1)=X(n) - F(X(n))/Fprim(X(n));

if abs(X(n+1))>edop

e=abs((X(n+1)-X(n))/X(n+1));

else

e=abs(X(n+1)-X(n));

end

r=abs(F(X(n+1))/F(x0));

n=n+1;

disp([n X(n) e r])

end

x=-10:0.01:10;

y=F(x);

plot(x,y,'r-')

hold on

grid on

plot(X(n),F(X(n)),'bo')

function y=F(x)

y=x.*sin(x)-x.^2+5;

function y=Fprim(x)

dx = 0.01;

y = (F(x + dx) - F(x - dx))/(2*dx);

---------------------------------------------

function x = Jacobi(A,b)

n = length(A);

edop = 10^-12;

kmax = 1000;

e = 1;

k = 0;

x0 = ones(n,1);

xp = x0;

xn = zeros(n,1);

while (e>edop & k<=kmax)

for i=1:n

s = 0;

for j=1:n

if i~=j

s = s + A(i,j)*xp(j);

end

end

xn(i) = (b(i) - s)/A(i,i);

end

e = norm(xn - xp)/norm(xn);

k = k + 1;

xp = xn;

k

e

xn

pause

end

x = xn;

e

k

--------------------------------------

function mpotegowa(A)

n=size(A,2);

edop=10^-12;

kmax=1000;

x0=ones(n,1);

xp=x0;

e=1;

k=0;

while e>edop & k<=kmax;

vp=xp/norm(xp);

xn=A*vp;

Lamn=xn'*vp;

if k>0

e=abs((Lamn-Lamp)/Lamn);

end

k=k+1;

Lamp=Lamn;

xp=xn;

end

Lamn

vp

k

e

----------------------------------------

function P = zes1zad2(X,Y)

X=[1 6 9];

Y=[0 -4 7];

plot([X X(1)],[Y Y(1)],'r-','LineWidth',2);

hold on

grid on

a = sqrt( (X(2) - X(1))^2 + (Y(2) - Y(1))^2 );

b = sqrt( (X(3) - X(1))^2 + (Y(3) - Y(1))^2 );

c = sqrt( (X(3) - X(2))^2 + (Y(3) - Y(2))^2 );

p = 0.5*(a+b+c);

P = sqrt(p*(p-a)*(p-b)*(p-c));

------------------------------------------

function katmax = zes3zad2(x0,y0,x1,y1,x2,y2)

plot([x0 x1 x2 x0],[y0 y1 y2 y0],'k-','LineWidth',2);

hold on

grid on

a = sqrt( (x1-x0)^2 + (y1-y0)^2 );

b = sqrt( (x2-x1)^2 + (y2-y1)^2 );

c = sqrt( (x2-x0)^2 + (y2-y0)^2 );

eps = 10^-12;

if abs(a-b)<eps | abs(b-c)<eps | abs(a-c)<eps

if abs(a-b)<eps & abs(b-c)<eps & abs(a-c)<eps

'trójkąt równoboczny'

else

'trójkąt równoramienny'

end

end

if abs(a^2+b^2-c^2)<eps | abs(a^2+c^2-b^2)<eps | abs(b^2+c^2-a^2)<eps

'trójkąt prostokątny'

end

cos1 = (b^2 + c^2 - a^2)/(2*b*c);

cos2 = (a^2 + c^2 - b^2)/(2*a*c);

cos3 = (a^2 + b^2 - c^2)/(2*a*b);

kat1 = acos(cos1)*180/pi;

kat2 = acos(cos2)*180/pi;

kat3 = acos(cos3)*180/pi;

a

b

c

kat1

kat2

kat3

katmax = kat1;

if kat2>katmax

katmax = kat2;

end

if kat3>katmax

katmax = kat3;

end

---------------------------------------

clc

close all

clear all

a=-4;

b=3;

c=0;

x=[];

if a~=0

delta=b^2-4*a*c;

if delta>0

k=2;

x(1)=(-b-sqrt(delta))/(2*a);

x(2)=(-b+sqrt(delta))/(2*a);

elseif delta==0

k=1;

x(1)=-b/(2*a);

else

k=0;

end

else

if b~=0

k=1;

x(1)=-c/b;

else

if c==0

k=0;

disp('nieskonczenie wiele rozwiazan')

else

k=0;

end

end

end

disp('rozwiazania')

x

k

t=-10:0.01:10;

y=a*t.^2+b*t+c;

plot(t,y,'b-','LineWidth',2)

hold on

grid on

for i=1:k

plot(x(i),0,'ro','MarkerFaceColor','r')

end

-------------------------------------------------

opcja = 1;

while opcja~=4

opcja = menu('TYTUL MENU','POLE 1','POLE 2','POLE 3','WYJSCIE');

switch opcja

case 1

'rysunek sinus'

case 2

'rysunek cosinus'

end

end

------------------------------------------------

file = input('Enter name of wave file as a string: ');


[x,fs,bits] = wavread(file);


%


fprintf('Srednia: %.4f \n',mean(x))


fprintf('Odchylenie standardowe: %.4f \n', std(x))


fprintf('Wariancja: %.4f \n', var(x))

---