HP 75C Program Collection
Merry Christmas everyone! I hope everyone is safe, happy, and blessed.
LAWCOS: Law of Cosines
335 bytes
100 DISP "Law of Cosines" @ WAIT .25
105 OPTION ANGLE DEGREES
180 DISP "Θ is opp. side a" @ WAIT .25
110 INPUT "1) Side, 2) Angle? "; H
115 ON H GOTO 1000, 2000
1000 INPUT "b?, c?, Θ? "; B,C,T
1010 A=SQR(B^2+C^2-2*B*C*COS(T))
1020 DISP "a: "; STR$(A) @ END
2000 INPUT "a?, b?, c? "; A,B,C
2010 T=ACOS((B^2+C^2-A^2)/(2*B*C))
2020 DISP "Θ:"; STR$(T); "°" @ END
Example:
1) Side: 1
B = 11.78, C = 32.12, T = 60
Result: a = 28.1440793063
2) Angle: 2
A = 14.55, B = 12.65, C = 17.00
Result: Θ = 56.5108780171°
SPECPOLY: Special Polynomials
526 bytes (10/27/2022)
1.Cheb: Chebyshev Polynomial of the 1st order
2.Herm: Hermite Polynomial
3.Lagur: Laguerre Polynomial (with α=0)
4.Legen: Legendre Polynomial of the 1st Order
100 DISP "Polynomials: Type?" @ WAIT .5
105 INPUT "1.Cheb 2.Herm 3.Lagur 4.Legen:"; H
110 INPUT "x? "; X
115 INPUT "order? ";N
120 A=1 @ B=X*(H=1 OR H=4)+2*X*(H=2)+(1-X)*(H=3)
300 IF N=0 THEN DISP A @ END
302 IF N=1 THEN DISP B @ END
305 FOR I=2 TO N
310 ON H GOSUB 500,505,510,515
315 A=B
320 B=C
325 NEXT I
330 DISP C
335 END
500 C=2*X*B-A @ RETURN
505 C=2*X*B-2*(I-1)*A @ RETURN
510 C=((2*(I-1)+1-X)*B-(I-1)*A)/I @ RETURN
515 C=((2*I-1)*X*B-(I-1)*A)/I @ RETURN
Source:
Davidson, James J. "Chebyshev Polynomials, First & Second Kind, Tn(x) & Un(x)", "Hermite Polynomials, H(n); n≥n", "Laguerre Polynomials, Generalized, Ln^(α)(x)", "Legendre Functions, First & Second Kinds, Pn(x) & Qn(x)" ENTER 65 NOTES Vol. 3 No. 8 September 1976 pp. 11-12
Examples:
x = 11, order = 6
1. Cheb: 55989361
2. Herm: 106439224
3. Lagur: -35.5902777778
4. Legen: 25289461
ENGINE: Automotive Engine Mathematics
630 bytes (10/27/2022)
100 DISP "Engine Math" @ WAIT .5
110 INPUT "# cylinders? "; N
120 DISP "Solve for?" @ WAIT .25
125 INPUT "1)DSP, 2)STROKE, 3)BORE "; H
130 IF H#1 THEN INPUT "DSP? "; D
135 IF H#2 THEN INPUT "STROKE? "; S
140 IF H#3 THEN INPUT "BORE? "; B
145 IF H=1 THEN LET D=PI/4*B^2*S*N
150 IF H=2 THEN LET S=D/(PI/4*B^2*N)
155 IF H=3 THEN LET B=SQR(D/(PI/4*S*N))
160 DISP "DPS= "; D @ STOP
165 DISP "STORKE= "; S @ STOP
170 DISP "BORE= "; B @ STOP
205 INPUT "RPM? (y/n) "; I$
210 IF UPRC(I$)="N" THEN 400
300 INPUT "RPM? "; R
310 P=S*R/6
320 E=R*D*.85/3456
350 DISP "Piston Speed="; P @ STOP
360 DISP "St. Carb CFM= "; E @ STOP
370 INPUT "Again? (y/n) "; I$
375 IF UPRC(I$)="Y" THEN 300
400 DISP "Done."
Source:
Lawlor, John. Auto Math Handbook. Calculations, Formulas, Equations, and Theory for Automotive Enthusiasts. HP Books: Berkeley Publishing Group: New York, NY. 1991. ISBN 1-55788-020-4
LINREG: Linear Regression
568 bytes (10/31/2022)
100 DISP "y=mx+b" @ WAIT .5
110 S0=0 @ S1=0 @ S2=0 @ S3=0 @ S4=0 @ S5=0
120 DISP 'Σ+ Σ- Calc'
130 K$=KEY$ @ IF K$='' THEN 130
140 IF K$="+" THEN H=1 @ GOTO 200
150 IF K$="-" THEN H=-1 @ GOTO 200
160 IF UPRC$(K$)='C' THEN 400
170 GOTO 130
200 INPUT 'x,y? '; X,Y
210 S0=S0+H @ S1=S1+H*X @ S2=S2+H*Y
220 S3=S3+H*X^2 @ S4=S4+H*Y^2 @ S5=S5+H*X*Y
230 DISP S0 @ WAIT .5 @ GOTO 120
400 B=(S5-S1*S2/S0)/(S3-S1^2/S0)
440 A=(S2-B*S1)/S0
450 R=B*SQR((S0*S3-S1^2)/(S0*S4-S2^2))
470 DISP 'type cont...' @ WAIT .5
500 DISP 'SLP=';B @ STOP
510 DISP 'ITC=';A @ STOP
520 DISP 'CORR=';R
Instructions:
Press + to add data. Separate x and y with a comma.
Press - to delete data. Separate x and y with a comma.
Press C to determine the slope, intercept, and correlation.
Example:
Data:
5, 4.066
8, 4.125
11, 4.202
18, 4.293
21, 4.349
ITC ≈ 3.99046
SLP ≈ 0.01719
CORR ≈ 0.99376
Source:
Hewlett Packard. HP 12C User Guide Edition 4. San Diego, CA 2004.
SIMPSON: Integral Using Simpson’s Rule Approximation
size varies - around 300 bytes
∫ FNF(X) dX from X = a to X = b
Line 100 is where you have to define your function (of X).
100 DEF FNF(X) = [define f(x) here]
115 OPTION ANGLE RADIANS
120 INPUT "a? ";A
125 INPUT "b? ";B
130 INPUT "# parts (even)? ";N
135 T=FNF(A)+FNF(B)
140 H=(B-A)/N
145 FOR I TO N-1
150 IF FP(I/2)=0 THEN 155 ELSE 160
155 T=T+2*FNF(A+I*H) @ GOTO 165
160 T=T+4*FNF(A+I*H)
165 NEXT I
170 T=T*H/3
175 DISP "Integral = ";T
Examples:
For both examples, n = 24
FNF(X)= 2*X^2+3, a = 1, b = 6, result: 158.333333333
FNF(X)=2*COS(X), a = 0, b = .785398163398, result: 1.41421357139 (exact √2)
Happy Holidays everyone!
Next post will be on New Years' Eve: December 31, 2022.
Eddie
All original content copyright, © 2011-2022. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
