Commands: Remarks and keying instructionsm=ipart((n+1)/2) The Sharp automatically prompts for the undefined variable n (the number of subdivisions). The function ipart means "integer part", for example ipart(3.2)=3. To enter it, use the MATH menu, then A for math, followed by 3 for ipart. The reason for this line is that Simpson's rule requires n to be even. We want m=n/2, but if the value of n entered is not an even integer, m would have a fractional part. The more complicated formula used here ensures that eg n=3 and n=4 both give m=2. n=2*m By setting n=2*m, we have made sure that n will be even in what follows. h=(-a+b)/n Use the minus sign below 3 to enter "minus a" The Sharp automatically prompts for undefined variables. Here a is the lower limit and b is the upper limit. For /, press the division key, under the the ) key. i=0 This initializes the counter i. x=a This initializes x to equal the first point x0 in the subdivision. Gosub 2 Call the subroutine (GOto SUBroutine) that evaluates the function f(x) for this x value. The answer is returned in the variable f. The subroutine is labelled 2 and can be found at the end of the program. After running the subroutine the program RETURNs here, to the calling point with the value of f set. To enter Gosub, press 2ndF followed by MATH ("COMMAND"), then B for BRNCH, followed by 4 for Gosub. s=f Initialize the sum s to equal f(x) = f(x0). Label 1 This spot in the program is labelled 1. x=x+h Move to the next point of the subdivision. Gosub 2 Evaluate the function at the point x. s=s+4*f Add 4*f(x) to the sum s. x=x+h Move to the next point of the subdivision. Gosub 2 Evaluate the function at the point x. s=s+2*f Add 2*f(x) to the sum s. i=i+1 Add 1 to the counter. If i< m Goto 1 For If and Goto get to BRNCH menu as before, then press 3 key for If and 2 key for Goto. For < press 2ndF key followed by COMMAND key, then C key for INEQ menu, then 2 key. If i is equal to m, (the sum is complete and) the program goes on to the next command. s=s-f The program gets here with x = b, f = f(b) and s=f(x0)+4f(x1)+2f(x2)+...+4f(x(n-1))+2f(xn), but in Simpson's rule the last term in s should be f(xn), so we need to subtract off one lot of f(xn)=f(b), which is what we do in this line. r=s*h/3 The result (r) of Simpson's rule is s*h/3. Print r The calculator will display r=(value). End For End, goto the PROG menu as before, then press 6 key. The program stops running here. Label 2 This spot in the program is labelled 2. It is the start of the subroutine that evaluates f(x). f=sin x This line defines the function to be summed.To change functions, edit this line.Return End the subroutine, return to the calling point.

*Running the program:*
Remeber to re-edit when you switch functions.
In the program menu (upper middle key) choose A (for RUN menu),
then right arrow then down arrow to LSUM, then ENTER.
Enter numbers at the question mark (a=? etc.) prompts.

*Check:* for f = sin x, lower limit 0, upper limit 2, and 20
subdivisions, the Simpson's rule approximation should be 1.416147624.

Math Dept SUNY Stony Brook

duncan@math.sunysb.edu

November 10 1997