Here's a piece of what I did today: Hooray Matlab!

function [p,ite] = bisect(fstring,a,b,tol)

%[p,ite] = bisect(fstring,a,b,tol)

%   Bisect uses bisection method to solve a nonlinear equation f(x) = 0 on

%   interval a,b. fstring is nonlinear function as a string, and tol is the

%   tolerance to stop the iteration.

%   Returns, p the approximate zero, and ite the number of iterations used

%   Stopping Criterion: |f(p)| <= tol

%   NOTE: fstring must be continuous between a and b!

%   Author: Ryan Boyer

f = inline(fstring);

y_a = feval(f,a);

y_b = feval(f,b);

if y_a == 0

    p = a;

    ite = 0;

    return

elseif y_b == 0

    p = b;

    ite = 0;

    return

end

%check to make sure bisection applies, that is y_a and y_b have different

%signs

if y_a * y_b > 0

    fprintf('Error: y_a and y_a do not have opposite signs\n');

    fprintf('Bisection method does not apply\n');

    return

end

%set up loop

p = (a + b)/2;

ite = 0;

y_p = feval(f,p);

%loop

while abs(y_p) > tol

    if y_a * y_p < 0 %y_a and y_p have opposite signs

        b = p;

        p = (a + b)/2;

    else

        a = p;

        p = (a + b)/2;

    end

    

ite = ite + 1;

y_p = feval(f,p);

y_b = feval(f,b);

y_a = feval(f,a);

end

end

Any questions? Glad your calculator does this for you? Well, it doesn't, it uses faster methods than this.

This wasn't a particularly hard problem, but it had lots of strings and loops and notes so it turned out colorful and I thought I would share another glimpse into what I get to do as a math major.