HW3_Work

%Question 1

    v = 15;
    g = -9.81;
    height = @(theta) 2.37*tan(theta) + .5*g.*((2.37./(v*cos(theta))).^2); %eq in terms of theta
    dh_dtheta = @(theta) 2.37.*(sec(theta).^2) + (g*2.37^2.*(sec(theta).^2).*tan(theta))./(v^2); %derivative of equation

    %begin eval four methods 

    [root1,fx1,ea1,iter1] = bisect(height,0,.1,0.00001,100);
    [root2,fx2,ea2,iter2] = falsepos(height,0,.1,0.00001,100);
    [root3,ea3,iter3] = newtraph(height,dh_dtheta,.1,0.00001,100);
    [root4,ea4,iter4] = mod_secant(height,.0001,.1,0.00001,100);
    
    %Table of answers
    t_iter = [ iter1 iter2 iter3 iter4];
    ig = { .1 .1 'Na' 'Na' };
    ea = [ ea1 ea2 ea3 ea4 ];
    
    %Make Table
    T = table;
    T.Solver = {'bisect', 'falsepos','newtraph', 'mod_secant'}';
    T.Initial_Guess = ig';
    T.ea = ea';
    T.Iterations = t_iter';
    T
    
    %function for plotting
    e_b = zeros(length(iter1));
    e_f = zeros(length(iter2));
    e_n = zeros(length(iter3));
    e_m = zeros(length(iter4));
    
    %Creating vectors for error approximation vs iteration
    
    for c = 1:iter1
        [r, y, e_b(c), k] = bisect(height,0,.1,0.00001,c);
    end
    
    for c = 1:iter2
        [r, y, e_f(c), k] = falsepos(height,0,.1,0.00001,c);
    end
    
    for c = 1:iter3
        [r, e_n(c), k] = newtraph(height,dh_dtheta,.1,0.00001,c);
    end
    
    for c = 1:iter4
        [r, e_m(c), k] = mod_secant(height,.0001,.1,0.00001,c);
    end
    
    %Ploting 
    
    setdefaults
    plot(1:iter1, e_b, 'g', 1:iter2, e_f, '--', 1:iter3, e_n, 'c:', 1:iter4, e_m, 'o')
    title('Approximate Error of Convergent Functions versus Number of Iterations');
    xlabel('Iteration');
    ylabel('Approx Error');
    legend('bisect','falsepos', 'newtraph', 'mod secant');