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Math Help - MatLab Approximations

  1. #1
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    MatLab Approximations

    I have this problem to do, involving estimating the error for the derivative as well as the Gaussian Approximation. I am having a lot of trouble figuring out if I can alter this code or if I have to write something new. This is the first time I've ever used MatLab, and I could use some help if anyone has any ideas. The assignment is attached. I used this, which was given in class, to do (ii)

    % f(x), the function to integrate
    % f= @(x) x^4-2*x ;
    % f= @(x) exp(x);
    f=@(x) sin(x);
    % a, the lower limit of integration
    a=0 ;
    % b, the upper limit of integration
    b=pi ;
    % b=1.0;
    % n, the number of segments. Note that this number must be even.
    % n=20 ;
    %************************************************* *********************
    format long g
    h=(b-a)/n ;
    % Sum the odd index function values, and multiply by 4
    sumOdd=0 ;
    for i=1:2:n-1
    sumOdd=sumOdd+f(a+i*h) ;
    end
    % Sum the even index function values, and multiply by 2
    sumEven=0 ;
    for i=2:2:n-2
    sumEven=sumEven+f(a+i*h) ;
    end
    sum=4*sumOdd+2*sumEven+f(a)+f(b) ;
    % Then multiply by h/3
    approx=h/3*sum ;
    %exact = quad(f,a,b) ;
    %exact=exp(b)-exp(a);
    exact=-cos(b)-(-cos(a));
    error=abs(approx-exact);
    disp(approx);
    disp(exact);
    disp(error);
    Attached Thumbnails Attached Thumbnails MatLab Approximations-scan0036.jpg  
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  2. #2
    Member
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    Mar 2012
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    USA
    Posts
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    Re: MatLab Approximations

    This is what I've been able to come up with. Does anyone see any issues with it that would be what is preventing it from running?

    % f(x), the function to integrate
    % f= @(x) x^4-2*x ;
    % f= @(x) exp(x);
    f=@(x) sin(x);
    % a, the lower limit of integration
    a=0 ;
    % b, the upper limit of integration
    b=pi ;
    % b=1.0;
    % n, the number of segments. Note that this number must be even.
    N=10 ;
    %************************************************* *********************
    format long g
    h=(b-a)/n ;
    s=0;
    for i=1:1:n
    if i<=1
    s=(-3*f(a+(i-1)*h)+4*f(a+i*h)-f(a+(i-1)*h))/2*h;
    elseif 1<i<n
    s=(f(a+(i+1)*h)-f(a+(i-1)*h))/2*h;
    elseif i>=n
    s=(f(a+(i-1)*h)-4*f(a+i*h)+3f(a+(i-1)*h))/2*h;
    end
    approx=s ;
    %exact = quad(f,a,b) ;
    %exact=exp(b)-exp(a);
    exact=-cos(b)-(-cos(a));
    error=abs(approx-exact);
    disp(error);



    % f(x), the function to integrate
    % f= @(x) x^4-2*x ;
    % f= @(x) exp(x);
    f=@(x) sin(x);
    % a, the lower limit of integration
    a=-1.0 ;
    % b, the upper limit of integration
    b=1.0 ;
    % b=1.0;
    % n, the number of segments. Note that this number must be even.
    n=10 ;
    %************************************************* *********************
    format long g
    h=(b-a)/n ;
    sum=h/3*(f((a+(i-1)*h)+f(a+i*h))/2)+h/2*(-1*sqrt(1/3))+ (f((a+(i-1)*h)+f(a+i*h))/2)+h/2*sqrt(1/3) ;
    for i=1:1:n
    approx=sum
    %exact = quad(f,a,b) ;
    %exact=exp(b)-exp(a);
    exact=-cos(b)-(-cos(a));
    error=abs(approx-exact);
    disp(approx);
    disp(exact);
    disp(error);
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