TI-95 ProCalc: Approximate Derivative and Bisection Method
Introduction: The Label FX and Flags to set Radians Mode
The two programs presented today will use a subroutine with the label FX. FX is going to be where you store your function. I have designated the variables such that X can be used as storing and recall in the subroutine. To edit FX:
In run mode (out of LEARN): [ 2nd ] [ 2 ] (GTL) FX, [ LEARN ] [ F2 ] (PC)
The subroutine FX must end with = RTN.
Radians mode can be set during programming with the following flag commands: RF 34 SF 33.
FYI, Degrees Mode: RF 34 RF 33
And Gradians Mode: RF 33 SF 34
Approximate Derivative
This program calculates f'(x), rounds, and displays the answer to five decimal places.
f'(x) ≈ ( f(x + h) - f(x - h) ) / ( 2 * h ), h is set to 10^-5
FIX 9 resets the TI-95 ProCalc to floating (all/standard) mode.
TI-95 ProCalc File DRV
Size: varies
RF 34 SF 33 1 EE 5 +/- STO H
CLR 'X?' BRK STO A
+ RCL H = SBL FX STO D
RCL A - RCL H = SBL FX ST- D
RCL D / ( 2 * RCL H ) =
FIX 5 RND FIX 9 STO D HLT
LBL FX [insert f(x) here, do not store values to A or H] = RTN
Examples
f(x) = x * sin x
FX: STO X * SIN = RTN
f'( π/5 ) returns 1.09611
f'( 1.6*π ) returns 0.60223
f(x) = 3 * e^x
FX: INV LN * 3 = RTN
f'( 1 ) returns 8.15485
f'( -1.215 ) returns 0.89013
Bisection Method
The bisection method finds a root for the equation f(x) = 0. An advantage to the bisection method is that there is no requirement to calculate the derivative. However, two initial guesses a and b are required such that f(a) * f(b) < 0, and the calculation process can be lengthy.
I set the tolerance to 10^-10.
Note: I will need a variable to store the 0 value. IF tests on the TI-95 ProCalc can not compare to numeric values directly. I use the variable Z to store 0.
TI-95 ProCalc File BIS
Size: varies
'BISECTION F(X)=0' PAU
CLR 'A?' BRK STO A
CLR 'B?' BRK STO B
10 +/- INV LOG STO T
0 STO Z
LBL A0 ( RCL A + RCL B ) / 2 = STO C
SBL FX STO F ABS IF <T GTL BO
RCL B SBL FX * RCL F = IF >Z GTL A1
RCL C STO A GTL A0
LBL A1 RCL C STO B GTL A0
LBL B0 CLR 'SOL=' COL 16 MRG C HLT
LBL FX [insert f(x) here, do not store values to A, B, C, T, or Z] = RTN
Examples
3*x - e^x = 0
FX: STO X * 3 - RCL X INV LN = RTN
Interval: [1, 2] (A = 1, B = 2)
Result: 1.512134552
x - 2^(-x) = 0
FX: STO X - 2 y^x RCL X +/- = RTN
Interval: [0, 1] (A = 0, B = 1)
Result: 0.6411857446
Source:
Byju's Classes "Bisection Method - Definition, Procedure, and Example" https://byjus.com/maths/bisection-method/ Retrieved June 5, 2021
Commas added to the results for readability.
Eddie
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