SIMPSON'S RULE PROGRAM

TI-82 and TI-83

Commands:			Remarks and keying instructions

Prompt A,B,N			Receive the interval endpoints and
                                number of subdivision points from user.
				Prompt is 2 on the I/O menu, reached
                                via the PRGM button.

iPart ((N+1)/2)->M              The function iPart means "integer
                                part", for example iPart(3.2)=3.  To
                                enter it, use the MATH menu, then
                                press right-arrow for "NUM", followed
                                by 2 for iPart.  For /, press the
                                division key, under the the ^ key.

				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.

2*M->N				By setting n=2*m, we have made sure that n
				will be even in what follows.
				
(B-A)/N->H			H is what we usually call "delta-x",
				the subinterval size.

A->X				This initializes x to equal the first
				point x0 in the subdivision.

Y1->S				Initialize the sum s to equal f(x) = f(x0).
                                "Y1" is obtained by pressing "2nd"
                                then "VARS" for the Y-Vars menu, then
                                1 for Functions and 1 again for Y1.
				Y1 must be defined to give the
                                function f which we are integrating
                                (see below)


FOR(I,0,M-1,1)			Begin a loop with counter I, beginning
                                at 0 and continuing through M-1,
                                incrementing by 1 each time. Thus, I is set
                                to 0 (zero) here, and the instructions
                                below are executed until the command
                                END is reached. Then I is incremented
                                by 1 and we go through the same list
                                of instructions again. This repeats
                                for each value of I including M-1. Finally
                                after running through the instructions
                                the last time with I=M-1, we 
                                proceed with the first command
                                following the END.
                                
X+H->X				Move to the next point of the subdivision.

S+4*Y1->S			Add 4*f(x) to the sum s.

X+H->X				Move to the next point of the subdivision.

S+2*Y1->S			Add 2*f(x) to the sum s.

End                             Increment I by 1, then go back to beginning
                                of FOR loop unless I has reached M.


S-Y1->S				The program gets here with x = b, Y1 = 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.

S*H/3->R			The result (r) of Simpson's rule is s*h/3.

Disp "RESULT ",R		The calculator will display RESULT value