Example

clc
clear
rr=1;
L=2*pi*rr;
M=100;
dtheta=L/M;
a=1;
theta(1)=-dtheta;
for i=1:M+1;
    theta(i+1)=theta(i)+dtheta;
    x(i)=2*a*(1+cos(theta(i+1)))*cos(theta(i+1));
    y(i)=2*a*(1+cos(theta(i+1)))*sin(theta(i+1));
end

plot(x(1:M+1),y(1:M+1))
axis equal
grid on

---

Example

clc
clear
rr=1;
L=2*pi*rr;
M=100;
dtheta=L/M;
a=1;
theta(1)=-dtheta;
for i=1:M+1;
    theta(i+1)=theta(i)+dtheta;
    x(i)=a*cos(theta(i+1))*cos(3*(theta(i+1)));
    y(i)=a*cos(3*(theta(i+1)))*(sin(theta(i+1)));
end
plot(x(1:M+1),y(1:M+1))
axis equal
grid on

---

Example

clc
clear
rr=1;
L=5*pi*rr;
M=200;
dtheta=L/M;
a=1;
theta(1)=-dtheta;
for i=1:M+1;
theta(i+1)=theta(i)+dtheta;
x(i)=a*cos(theta(i+1))*theta(i+1);
y(i)=a*theta(i+1)*(sin(theta(i+1)));
end
plot(x(1:M+1),y(1:M+1))
axis equal
grid on

---

Example

clc
clear
a=0;
b=0;
c=0;
d=0;
for i=1:12;
    %odd even selection criterial on off relation
    a=a+1;
    x(a)=randn(1,1);
    t(a)=rem(a,2);
    if (t(a)==1)
    b=b+1;
    z(b)=x(a);
    elseif (t(a)==0)
    c=c+1;
    zz(b)=x(a);
    end
    % This sees that the condition is atisfied and then changes the value
    % of the orignal matrix and stores the value that was changed in an
    % endependent matrix
    if (x(a)>0.2)
    d=d+1;
    zzz(d)=x(a);
    x(a)=0;
    end
end
z';
x';
t';
zz';
d
zzz'
x'
y=[1:1:12];
rank(z);
plot(y,t)

---

Fourier Analysis Plots

clc
clear
x0=0;
x00=1;
y0=0;
m=1;
N=120;
dx=(x00-x0)/N;

for i=1:N;
    x(i)=i*dx;
    c(i)=y0-m*x0;
    y(i)=m*x(i)+c(i);
end
plot(y,x)
xlabel('X')
ylabel('Y')
grid on
axis equal
hold on

x0=-1;
x00=0;
y0=0;
m=1;
N=120;
dx=(x00-x0)/N;

for i=1:N;
    x(i)=i*dx;
    c(i)=y0-m*x0;
    y(i)=m*x(i)+c(i);
end
plot(y,x)
hold on

x0=-2;
x00=-1;
y0=0;
m=1;
N=120;
dx=(x00-x0)/N;

for i=1:N;
    x(i)=i*dx;
    c(i)=y0-m*x0;
    y(i)=m*x(i)+c(i);
end

plot(y,x)
hold on

x0=-3;
x00=-2;
y0=0;
m=1;
N=120;
dx=(x00-x0)/N;

for i=1:N;
    x(i)=i*dx;
    c(i)=y0-m*x0;
    y(i)=m*x(i)+c(i);
end

plot(y,x)

---

Example

clc
clear
x0=-5;
y0=0;
x00=0;
dx0=-5;
dy0=0;
dx00=-5;
m=1;
N=120;
for j=1:12;
x0=x0+dx0;
y0=y0+dy0;
x00=x00+dx00;
dx=(x00-x0)/N;
    k=-60;
for i=1:N;
    k=k+1;
    x(i)=k*dx;
    c(i)=y0-m*x0;
    y(i)=m*x(i)+c(i);
end
plot(y,x)
xlabel('X')
ylabel('Y')
grid on
axis equal
hold on
end

---

Plotting Heavy Side Function

clc
clear
x0=0;
y0=0;
x00=1;
y00=0;
x=1;
y=1;
x1=2;
y1=1;
x2=2;
y2=0;
v1=[ x0 x00 ]
v2=[ y0 y00 ]
f=line(v1,v2)
v3=[ x x1 ]
v4=[ y y1 ]
f1=line(v3,v4)
v5=[ x00 x ]
v6=[ y00 y ]
f2=line(v5,v6)
v7=[ x1 x2 ]
v8=[ y1 y2 ]
f3=line(v7,v8)
grid on
figure(1)
title('Heavy side')
xlabel('x')
ylabel('y')

---

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