Program: taylor series – Texas Instruments TI-86 User Manual

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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 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.

ᕡ 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,

L1,L1,0,L1,1,L1,0,0,1,L1,0,L1,1,1,0,L1,0,L1,0}¶MSERIES

:Return

ᕢ 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

Ncenter)

:GrStl(14,2)

is on the CHAR GREEK menu

L9¶H:.1¶rr

:ClLCD

User enters equation function

:InpSt "FUNCTION: ",EQ
:St

8Eq(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.