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Compute the derivative of f(t) cos(37t) on the interval 1,1) using a centered differences approximation with discretization s

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Matlab function for finding derivative using central difference clear all close all Function for which derivative have to doExact and numerical derivative for various N 10 -For N. 10 -For N:40 -For N:70 Exact value -4 -6 10 1 08 6.4 -02 06 08 Publis

%%Matlab function for finding derivative using central difference
clear all
close all

%Function for which derivative have to do
f=@(t) cos(3*pi*t);

%exact derivative of the function
df=@(t) (3*pi)*(-sin(3*pi*t));

%numerical derivative of the function
num_df=@(t,h) (cos(3*pi*(t+h))-cos(3*pi*(t-h)))./(2*h);

%all time value for which derivative have to find

tt=linspace(-1,1,1000);

%all discretization size
N=[10 40 70];

%loop for findind derivative for all N
for i=1:length(N)
  
    h=2/N(i);
    for j=1:length(tt)
        val(i,j)=num_df(tt(j),h);
    end
  
    hold on
    plot(tt,val(i,:))
    %finding maximum error
    err=max(df(tt)-squeeze(val(i,:)));
    fprintf('\tMaximum error for N=%d is %f.\n',N(i),err)
end
%plot for exact derivative
plot(tt,df(tt),'linewidth',2)
title('Exact and numerical derivative for various N')
xlabel('t')
ylabel('derivative of f(t)')
legend('For N=10','For N=40','For N=70','Exact value')

%%%%%%%%%%%%%%%%%% End of Code %%%%%%%%%%%%%%%%%%

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