TI-58/TI-59 Week: Numerical Derivative
Introduction
The program estimates the numeric derivative:
d/dx f(x) = (f(x + h) - f(x)) / h
Registers used:
R01: x
R02: h
R03: d/dx
Labels:
[ A ]: store x
[ B ]: store h
[ C ]: calculate derivative
LBL E: store f(x), assume x is in the display. You can use registers R00 and R06 and above for registers. Use Rad ( [ 2nd ] [ - ] ) if f(x) contains trigonometric functions. End each function with the steps =, INV SBR (RTN)
Function Listings
(step number, key code, key)
000 76 LBL
001 11 A
002 42 STO
003 01 01
004 92 INV SBR (RTN)
005 76 LBL
006 12 B
007 42 STO
008 02 02
009 92 INV SBR (RTN)
010 76 LBL
011 13 C
012 43 RCL
013 01 01
014 85 +
016 43 RCL
017 02 02
018 71 SBR
019 15 E
020 42 STO
021 03 03
022 43 RCL
023 01 01
024 71 SBR
025 15 E
026 94 +/-
027 85 +
028 43 RCL
029 03 03
030 95 =
031 55 ÷
032 43 RCL
033 02 02
034 95 =
035 42 STO
036 03 03
037 92 INV SBR (RTN)
038 76 LBL
039 15 E
... .... ....
n-1 95 =
nnn 92 INV SBR (RTN)
Examples
f(x) = sin x; Rad, sin
x = 0.5, h = 0.1, [ C ] returns 0.8521693479
x = 0.5, h = 1E-8, [ C ] returns 0.87755
f(x) = (1 + cos x)^1.5; Rad, cos, +, 1, =, y^x, 1.5
x = 2, h = 0.01, [ C ] returns -1.035743295
x = 2, h = 1E-8, [ C ] returns -1.04206
f(x) = x * e^(x); STO, 00, e^x * RCL, 00
x = 3, h = 0.01, [ C ] returns 80.84630054
x = 3, h = 1E-5, [ C ] returns 80.342648
Eddie
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