Calculator User Manual

250
Chapter 19: Applications
19APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 250 of 1819APPS.DOC TI-86, Chap 19, US English Bob Fedorisko Revised: 02/13/01 2:41 PM Printed: 02/13/01 3:05 PM Page 250 of 18
Program: Taylor Series
When you run this program, you can enter a function and specify the order and center
point. Then the program calculates the Taylor Series approximation for the function and
plots the function you entered. This example shows how to call a program from another
program as a subroutine.

Before you enter the program
TAYLOR
, select
EDIT
from the
PRGM
menu, enter
MOBIUS
at the
Name=
prompt, and then enter this brief program to store the Mobius Series. The program
TAYLOR
calls this program and runs it as a subroutine.
PROGRAM:MOBIUS
:{1,
L
1,
L
1,0,
L
1,1,
L
1,0,0,1,
L
1,0,
L
1,1,1,0,
L
1,0,
L
1,0}
¶
MSERIES
:Return

Select
EDIT
from the
PRGM
menu, enter
TAYLOR
at the
Name=
prompt, and then enter this
program to calculate the Taylor Series.
PROGRAM:TAYLOR
:Func:FnOff
:y14=pEval(TPOLY,x
N
center)
:GrStl(14,2)
H
is on the
CHAR GREEK
menu
:1
E
L
9
¶
H
:.1
¶
rr
:ClLCD
User enters equation function
:InpSt "FUNCTION: ",EQ
:St
8
Eq(EQ,y13)
User enters order
:Input "ORDER: ",order
:order+1
¶
dimL TPOLY
:Fill(0,TPOLY)
User enters center
:Input "CENTER: ",center
:evalF(y13,x,center)
¶
f0
:f0
¶
TPOLY(order+1)
The higher-order derivative
values necessary for this
program are calculated
numerically based on the
methods in “Numerical
Differentiation of Analytic
Functions,” J. N. Lyness and
C. B. Moler, SIAM Journal of
Numerical Analysis 4 (1967):
202-210.