 # Numerical Methods

## Question

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## Transcribed Text

Problem 1 The solar radiation for Tucson, Arizona has been tabulated as, Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Radiation 144 188 245 311 351 359 308 287 260 211 159 131 assuming each month is 30 days long, fit a sinusoid to this data. Use the results to predict the radiation on the 15th of October. Problem 2 The periodic triangular wave function f(f) is defined as n for n 2 2 for " f(t) 2 2 n Find the Fourier coefficients 80.9 28 and b, bb and approximate the periodic triangular wave function by the Fourier series. Plot the first four approximations along with the triangular wave. f(t) " f(t)=-t * 2 n 7 " 2 " t 2 n 2 T T 2 2 Problem 3 Given the function of time, k astf(t) iza ac-a Find the amplitude spectrum of f(t), IP(w) and graph both functions. Problem 4 Compare the continuous Fourier Transform tothe discrete Fourier Transform for the function, Use 64 sampling points, ie N=64 and a scaling factor of T=0.25 so that NT=16. Graph the real and imaginary comparisons for separately. Consider the modified form of the discrete Fourier Transform with wo 2itw, N-1 Fk n-0

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function main()
clear all
close all %empty variables in memory then close all windows, pictures etc start fresh
options=odeset('RelTol',1e-12,'AbsTol', 1e-12);
time1=8147; %time it takes for earth to do one revolution in seconds
mu=3.986004415*10^5;
r0=[6678.1363, 0, 0];
v0=[0, 7.725760634075587,0];%
[propagatedtime,propagatedposvel] =ode45(@(t,x)twobody(t,x,mu),[0, time1],[r0, v0]',options);
N=length(propagatedtime); %length of the vector propagatedtime
size(propagatedposvel)
plot3(propagatedposvel(:,1),propagatedposvel(:,2),propagatedposvel(:,3))
% we plot the values x,y,z in 3d
hold on
xlabel('x')
ylabel('y')
zlabel('z')

disp('-------Part 3----------')
options=odeset('RelTol',1e-12,'AbsTol', 1e-12);
a=propagatedposvel(N,:) % propagatedposvel is of size N times 6...
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