This is NOT a project (programming assignment) to be turned in for grading. You should have this completed BEFORE I post the first Program (Coding) Assignment.
This Maple script uses the bisection method to approximate the zero of a function on an interval from x = a to x = b.

Do NOT copy and paste these commands into a Maple session. Doing so WILL introduce errors. Instead, manually type them into a Maple session. Learn from your mistakes.

The user must enter the following quantities in the script:

function f
a — the left interval endpoint
b — the right interval endpoint
TOL — the stopping tolerance
Maxits — the maximum number of iterations to allow

> restart ;    (Start EVERY code with restart. You should put that in the first line in every code.)

> Digits := 16 ;    (enter this as an integer... no decimal point)

Enter f as a function (not as an expression).

> f := x -> evalf( exp(-x) – cos(x) ) ;
   The evalf command automatically converts the results to floating point (decimal) form whenever function f is evaluated.

Plot function f on appropriate intervals to determine where the zero might be.
size specifies the desired width and height of the plot in pixels.

> plot( f(x), x = 0.0 .. 6.0, thickness = 4, size = [450, 345] ) ;

Based on the plot, we observe that the first positive zero is between x = 1 and x = 2. So we set the left and right endpoints accordingly:

> a := 1.0 ;    (enter this with a decimal point)

a := 1.0

> b := 2.0 ;    (enter this with a decimal point)

b := 2.0;

> xL := a ;    (This stores the current value of a in xL.)

> xR := b ;    (This stores the current value of b in xR.)

Calculate the y values at the interval endpoints.

> yL := f(xL) ;

> yR := f(xR) ;

Set the maximum iterations (as a safeguard to prevent infinite looping in case of human error) and the stopping tolerance. In fact, while debugging your code you should set Maxits to something smaller, like 4 for example. Make Maxits larger (like 50) once you are sure your code is bug-free.

> Maxits := 50 ;    (enter this as an integer... no decimal point)

> TOL := 0.5 * 10^(–6) ;

The following line initially sets ym to a value greater than the tolerance. This is done once only and before the loop below is entered.

> ym := TOL + 1.0 ;

ym := 1.000000500000000

Let's now uses Maple's fsolve command to numerically obtain the zero of function f, having it look on the interval from x = 1 to x = 2.

Comments:

To re-run the script, you must go up to the line where xL and xR are set, and either hit return or change their values and hit return. Then hit return on each subsequent command line to re-run the entire script. Alternatively, after making any changes to the code, click on the !!! button at the top to run the entire worksheet.

Maple Notes:

     a) Maple is case sensitive.
         For example, xr, xR, Xr, and XR are treated as different quantities in Maple.

     b) Indentation and spacing are not necessary but greatly enhance readability.

     c) do must end with od: or end do:

     d) if must end with fi: or end if:

     e) If the sign test passes, then all commands between if and else are executed.
         If the sign test fails, then all commands between else and fi are executed.