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School
Arizona State University *
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Course
275
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
7
Uploaded by ProfessorWater27041
LAB 1 - Your Name - MAT 275
Exercise 1
Define input variable theta as discretized row vector (i.e. array)
theta = [0,pi/8,pi/6,pi/5,(6*pi)/5,(7*pi)/6,(8*pi)/7]
theta = 1×7
0 0.3927 0.5236 0.6283 3.7699 3.6652 3.5904
Define radius
r=6
r = 6
Define x and y in terms of theta and r
x= r*cos(theta)
x = 1×7
6.0000 5.5433 5.1962 4.8541 -4.8541 -5.1962 -5.4058
y= r*sin(theta)
y = 1×7
0 2.2961 3.0000 3.5267 -3.5267 -3.0000 -2.6033
r = sqrt(x.^2+y.^2)
r = 1×7
6.0000 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000
Check that x and y satisfy the equation of a circle
Explain results here.
Do x and y satisfy the equation of a circle? Why or why not?
How does the vector output at the end confirm your answer? x and y satisfy the equation of the circle because for all x and y r=sqrt(x^2+y^2)
Exercise 2
Define t-vector
t=2:0.1:10
t = 1×81
2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000
Define y-vector
1
y= exp(t/15).*cos(2*t)./(0.2*t.^2+4);
Part (a)
Plot results (should have 3 plots total)
figure;
plot(t,y,
'o'
);
title(
'y= exp(t/15).*cos(2*t)./(0.2*t.^2)+4;'
)
%couldn't figure out how to stop the +4 from appearing like an exponent
%It appears my default graph color is blue
Part (b)
Plot results as data points only and as data points with line.
figure %creates another figure window
plot(t,y,
'o-'
);
title(
'y= exp(t/15).*cos(2*t)./(0.2*t.^2+4)'
)
2
Exercise 3
Create t-vector (choose enough elements so that plot is smooth!)
t = 0:0.1:20;
Define x, y, x components in terms of t
x = 8*cos(2*t); y = 8*sin(2*t); z = 4*t;
Plot results
figure;
plot3(x,y,z)
3
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Exercise 4
Define input variable as vector
x= -pi/7:0.01:pi/7;
Define y and z
y = sin(7*x);
z =7*x-(343/6)*x.^3;
Plot results
figure;
plot(x,y,
'r'
,x,z,
'--'
)
axis tight
;
grid on
4
Exercise 5
type ex5.m
x=0:0.01:3;
y1=f(x,20);
y2=f(x,40);
y3=f(x,60);
plot(x,y1,'r-',x,y2,'b-',x,y3,'k-')
title('Solutions to dy/dx = 17*x+4*x.^2-2*cos(x)')
legend('C=20','C=40','C=60')
function y=f(x,C)
y=(17/2)*x.^2+(4/3)*x.^3-2*sin(x)+C;
end
Run your M-file--i.e. execute the M-file
run 'ex5.m'
5
Exercise 6
Part (a)
Define g as anonymous function
g=@(x,y)((x.^5/y.^3)+(cos(6*x*exp(9*y))))/((x.^6)+3);
Evaluate g at the given values of x and y
g(-9,3)
ans = -0.0041
Part (b)
Clear the function g out of the workspace
clear g
Print out g.m contents
type 'g.m'
6
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function z = g(x,y)
z=((x^5/y^3)+(cos(6*x*exp(9*y))/(x^6+3)));
end
Evaluate g at the given values of x and y
g(-9,3)
ans = -2.1870e+03
The End!!!
7