(71B) Fun with the 71B '20

[Eddie W. Shore]

Link: http://edspi31415.blogspot.com/2020/07/f...1b-20.html

Differential Equations: Runge Kutta Method 4th Order

Find a numerical solution to the differential equation:

dy/dx = f(x, y)

x is the independent variable, y is the dependent variable. You define f(x,y) on line 10. For example, dy/dx = sin(x * y) should have this as line 10:

10 DEF FNF(X,Y) = SIN(X*Y)

Line 5 is a remark line. Remarks are followed by exclamation points on the HP 71B.

HP 71B Program: RK4

Size: About 300 - 330 bytes

Code:

5 ! FNF(X,Y) = dY/dX
10 DEF FNF(X,Y) = [ insert f(x,y) here ]
15 DESTROY X,Y,H,K1,K2,K3,K4
20 INPUT "X0? "; X
25 INPUT "Y0? "; Y
30 INPUT "STEP? "; H
40 K1 = FNF(X,Y)
45 K2 = FNF(X+H/2,Y+H*K1/2)
50 K3 = FNF(X+H/2,Y+H*K2/2)
55 K4 = FNF(X+H,Y+H*K3)
60 X=X+H
65 Y=Y+H*(K1+2*K2+2*K3+K4)/6
80 DISP "(";X;",";Y;")" @ PAUSE
85 DISP "NEXT? Y/N"
90 A$=KEY$
95 IF A$="Y" THEN 40
99 IF A$="N" THEN DISP "DONE" @ END ELSE 85

Example:
dy/dx = sin(x * y) with inital condition y(0) = 0.5, h = 0.2 * π

First three results:
( .628318530718 , .607747199386 ) ( [ f ] [ +] (CONT), [ Y ] )
( 1.25663706144, 1.02432288082 )
( 1.88495559216, 1.51038862362 )

Hyperbolic Functions

[ S ] = sinh(x)
[ C ] = cosh(x)
[ A ] = asinh(x)
[ H ] = acosh(x)
[ X ] to exit

HP 71B Program: HYP

Size: 401 bytes
acosh(x) requires that | x | ≥ 1

Code:

100 DESTROY A,X
115 DISP "sinh S/A, cosh C/H, X"
120 A$=KEY$
125 IF A$="S" THEN INPUT "X? ";X @ CALL SINH(X)
130 IF A$="C" THEN INPUT "X? ";X @ CALL COSH(X)
135 IF A$="A" THEN INPUT "X? ";X @ CALL ASINH(X)
140 IF A$="H" THEN INPUT "X? ";X @ CALL ACOSH(X)
145 IF A$="X" THEN 150 ELSE 115
150 DISP "DONE" @ END
200 SUB SINH(X)
205 DISP (EXP(X)-EXP(-X))/2 @ PAUSE
210 END SUB
300 SUB COSH(X)
305 DISP (EXP(X)+EXP(-X))/2 @ PAUSE
310 END SUB
400 SUB ASINH(X)
405 DISP LOG(X+SQR(X^2+1)) @ PAUSE
410 END SUB
500 SUB ACOSH(X)
510 DISP LOG(X+SQR(X^2-1)) @ PAUSE
515 END SUB

Example:
X = 2.86

sinh(2.86) returns 8.70212908815
cosh (2.86) returns 8.75939784845
asinh(2.86) returns 1.77321957441
acosh(2.86) returns 1.71190019325

Arithmetic-Geometric Mean

The arithmetic-geometric mean (AGM) is found by the iterative process:

a = 0.5 * (x + y)
g = √(x * y)

The values of a and g are stored into x and y, respectively. The process repeats until the values of a and g converge. A tolerance of 10^(-9) is used to display an 8-digit approximation.

HP 71B Program: AGM

Size: 148 Bytes

Code:

10 DESTROY X,Y,A,B
15 DISP "AGM(X,Y)" @ WAIT .5
20 INPUT "X? ";X
25 INPUT "Y? ";Y
30 A=.5*(X+Y)
35 G=SQR(X*Y)
40 X=A
45 Y=G
50 IF ABS(X-Y)>1E-9 THEN 30
55 DISP USING 60;X
60 IMAGE 10D.8D    // (10 digit integer parts with rounding to 8 decimal places)
65 END

Example:
AGM(178, 136)

Result: 156.29380544

Pythagorean Triple Generator

Given two positive integers m, n; where m > n, a pythagorean triple is generated with the following calculations:

a = 2*m*n
b = m^2 - n^2
c = m^2 + n^2

Properties:

a^2 + b^2 = c^2
Perimeter: p = a + b + c
Area: r = a * b / 2

HP 71B Program: PYTHTRI

Size: 217 bytes

Code:

10 DESTROY M,N,A,B,C,R,P
20 DISP "M>N, INTEGERS" @ WAIT .5
25 INPUT "M? "; M
30 INPUT "N? "; N
35 A=2*M*N
40 B=M^2-N^2
45 C=M^2+N^2
50 P=A+B+C
55 R=A*B/2
60 DISP 'A = ';A @ PAUSE
65 DISP 'B = ';B @ PAUSE
70 DISP 'C = ';C @ PAUSE
75 DISP 'PERIM.=';P @ PAUSE
80 DISP 'AREA =';R
85 END

Example:
M = 16, N = 11

Results:
A = 352, B = 153, C = 377, P = 864, R = 23760


Impedance of An Alternating Current

The program ALTCURR calculates the impedance (magnitude and phase angle) of a sinusoidal alternating current consisting of one resistor, one capacitor, and one inductor in a series.

HP 71B Program: ALTCURR

Size: 210 bytes

Code:

10 DESTROY F,L,C, R,W,Z,T
15 DEGREES
20 INPUT "FREQUENCY? ";F
25 INPUT "INDUCTANCE? ";L
30 INPUT "CAPACITANCE? ";C
35 INPUT "RESISTANCE? ";R
40 W=2*PI*F
45 Z=SQR(R^2+(W*L-1/(W*C))^2)
50 T=ATAN((W*L-1/(W*C))/R)
55 DISP "MAGNITUDE= "; Z @ PAUSE
60 DISP "PHASE ANGLE = "; T

Example:
F = 152 Hz
L = 4.75E-3 H (4.75 mH)
C = 8E-6 F (8 μF)
R = 6400 Ω

Results:
Magnitude: 6401.24704262
Phase Angle: -1.1309750812°

Source:
Rosenstein, Morton. Computing With the Scientific Calculator Casio. Japan. 1986. ISBN 1124161430