lab1_saad.rtfName: Saad Aldawsari Class: Mat275_lab
Time: Wednesday 6:00 pm
format compact
% MAT 275 MATLAB Assignment # 1
% Exercise 1
theta=0:pi/4:5*pi/4
theta =
0 0.7854 1.5708 2.3562 3.1416 3.9270
r=2
r =
2
x=r*cos(theta)
x=
2.0000 1.4142 0.0000 -1.4142 -2.0000 -1.4142
y=r*sin(theta)
y =
0 1.4142 2.0000 1.4142 0.0000 -1.4142
R=sqrt(x.^2+y.^2)
R =
2 2 2 2 2 2
% R is equal to the sqrt(x^2+y^2). All the values of R is equal to 2, so we can say that R=2=sqrt(x^2+y^2).
% Exercise 2 -a
t = 1:0.1:10;
y = (exp(t./10).*sin(t))./(t.^2+1);
plot(t,y,'k-');
title('y = (e^{t/10}*sin(t))/(t^2+1)');
file_0.wmf
% The above is the plot of y = e^(t/10)sin(t)/(t^2+1). The color code for black is k.
Name: Saad Aldawsari Class: Mat275_lab
Time: Wednesday 6:00 pm
% Exercise 2 - b
plot(t,y,'o')
file_1.emf
file_2.wmf
% After using ‘o’, my plot became a series of circles.
plot(t,y,'o-')
file_3.emf
file_4.wmf
% After using ‘o-’, my plot became a series of circles with a blue line coursing through.
Name: Saad Aldawsari Class: Mat275_lab
Time: Wednesday 6:00 pm
% Exercise 3
t = 0:0.05:20;
x = sin(t);
y = cos(t);
z = t;
plot3(x,y,z);
file_5.emf
file_6.wmf
% I used a lot of points for this one. The 3d plot showed me a spiral curve.
% Exercise 4
x = 0:0.02:pi;
y = cos(x);
z = 1-x.^2./2+x.^4./24;
plot(x,y,'r',x,z,'--'); grid on;
file_7.emf
file_8.wmf
% Using the code above, I was able to plot y and z in one graph.
Name: Saad Aldawsari Class: Mat275_lab
Time: Wednesday 6:00 pm
% Exercise 5
function ex5
% function ex5.m similar to myplot1.m
x = 0:0.2:4; % define the vector x in the interval [0,4]
y1 = f(x,-1); % compute the solution with C = -1
y2 = f(x,0); % compute the solution with C = 0
y3 = f(x,1); % compute the solution with C = 1
plot(x,y1,'r-',x,y2,'b-',x,y3,'k-'); % plot the three solutions with different line styles
title('Solutions to dy/dx = x+2'); % add a title
legend('C = -1','C = 0','C = 1','Location','northwest'); % add a legend
end
function y = f(x,C)
y = x.^2./2+2.*x+C % fill-in with the expression for the general solution
end
file_9.png
file_10.wmf
% Exercise 6-a
f = inline('x^3+y*exp(x)/(x+1)','x','y')
f =
Inline function:
f(x,y) = x^3+y*exp(x)/(x+1)
f(2,-1)
ans =
5.5370
% The value of the function when x = 2 and y = -1 is equal to 5.5370.
Name: Saad Aldawsari Class: Mat275_lab
Time: Wednesday 6:00 pm
% Exercise 6 - b
clear f
function z = f(x,y)
% function f.m
z = x^3+y*exp(x)/(x+1)
end
f(2,-1)
z =
5.5370
ans =
5.5370
diary off
% Just the same answer with 6-a, but different method.
