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Ingy döt Net 2023-07-01 11:58:00 -04:00
parent 7387c8f97b
commit cb5bb5e222
199093 changed files with 3378972 additions and 0 deletions
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8
Task/Numerical-integration/MATLAB/numerical-integration-1.m Normal file
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function integral = leftRectIntegration(f,a,b,n)
format long;
width = (b-a)/n; %calculate the width of each devision
x = linspace(a,b,n); %define x-axis
integral = width * sum( f(x(1:n-1)) );
end

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Task/Numerical-integration/MATLAB/numerical-integration-2.m Normal file
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function integral = rightRectIntegration(f,a,b,n)
format long;
width = (b-a)/n; %calculate the width of each devision
x = linspace(a,b,n); %define x-axis
integral = width * sum( f(x(2:n)) );
end

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Task/Numerical-integration/MATLAB/numerical-integration-3.m Normal file
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function integral = midPointRectIntegration(f,a,b,n)
format long;
width = (b-a)/n; %calculate the width of each devision
x = linspace(a,b,n); %define x-axis
integral = width * sum( f( (x(1:n-1)+x(2:n))/2 ) );
end

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Task/Numerical-integration/MATLAB/numerical-integration-4.m Normal file
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function integral = trapezoidalIntegration(f,a,b,n)
format long;
x = linspace(a,b,n); %define x-axis
integral = trapz( x,f(x) );
end

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Task/Numerical-integration/MATLAB/numerical-integration-5.m Normal file
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integral = quad(f,a,b,tol)

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Task/Numerical-integration/MATLAB/numerical-integration-6.m Normal file
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trapezoidalIntegration(@(x)( exp(-(x.^2)) ),0,10,100000)
ans =
0.886226925452753

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Task/Numerical-integration/MATLAB/numerical-integration-7.m Normal file
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quad(@sin,0,pi,1/1000000000000)
ans =
2.000000000000000

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Task/Numerical-integration/MATLAB/numerical-integration-8.m Normal file
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function answer = fermiDirac(x)
k = 8.617343e-5; %Boltazmann's Constant in eV/K
answer = 1./( 1+exp( (x)/(k*2000) ) ); %Fermi-Dirac distribution with mu = 0 and T = 2000K
end

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Task/Numerical-integration/MATLAB/numerical-integration-9.m Normal file
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rightRectIntegration(@fermiDirac,-1,1,1000000)
ans =
0.999998006023282