PCalc 42 User Functions ( iOS )

PCalc 42 User Functions ( iOS )

Programs for the iOS App PCalc 42 from Previous Posts (during May 2014):

http://edspi31415.blogspot.com/2014/05/pcalc-programming-introduction.html

Mohr’s Circle:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-mohr-circle.html

Period of Orbit Around the Sun:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-period-of-orbit-around.html

Horizontal Pipe Discharge:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-horizontal-pipe.html

Newton’s law of Gravity Solver:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-newton-law-of-gravity.html

Distance of a Star by Parallax:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp50g-distance-of-star-by.html

Escape Velocity:  http://edspi31415.blogspot.com/2014/05/pcalc-and-hp-50g-escape-velocity.html

Time to revisit this app:

PCalc42 Decimal to Degrees-Minutes-Seconds (d.mmssss form): 

D > DMS

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Subtract X from R1

Multiply R1 by 60

Set R2 to R1

Truncate R1

Multiply R1 by 0.01

Add R1 to X

Set R3 to R2

Truncate R3

Subtract R3 from R2

Multiply R2 by 0.006

Add R2 to X

Example:   1.85 in DMS form is 1.51 (1° 51’)

PCalc42 Degrees-Minutes-Seconds (d.mmssss form) to Decimal

DMS > D

Switch to Decimal

Set R0 to X

Truncate X

Set R1 to R0

Subtract X from R1

Multiply R1 by 100

Set R2 to R1

Truncate R1

Subtract R1 from R2

Divide R2 by 60

Multiply R2 by 100

Add R1 to R2

Divide R2 by 60

Add R2 to X

Example:  1.3052 (1° 30’ 52”) in decimal form is 1.514444444

PCalc42 Snell’s Law of Refraction

Input: Y: n1, X: n,  n1 ≤ n2

Switch to Degrees

Invert X

Multiply Y by X

Inverse Sine X

Example:  n1 = 1.33, n2 = 1.50.   Output:  62.4573248455

PCalc42 Doppler Effect (RPN)  (SI Units)

Input:  Z:  emitted frequency (Hz), Y:  receiver velocity (m/s), X: source velocity (m/s)

Output:  observed frequency (Hz) on stack X

Negate X

Add Y to X

RPN Swap

RPN Roll Down

Divide X by 299752458

Add 1 to X

Multiply Y by X

RPN Roll Down

Example: 

Z:  Emitted Frequency:  525 Hz

Y:  Receiver Velocity:  214,000,000 ft/s

X:  Source Velocity:  208,000,000 ft/s

Output:  Observed Frequency:  535.5086711249 Hz

PCalc42 Sums (RPN) Σ m, Σ m^2, Σ m^3

The sum of Σ m^X from m = 1 to m = Y, where X is the power, Y is the power (up to 3).  If Y > 3, an error condition occurs. 

Formulas:

Σ m = (X^2 + X) / 2

Σ m^2 = (2*X^3 + 3*X^2 + X) / 6

Σ m^3 = (X * (X+1))^2 / 4

Set R0 to Y

Truncate X

Skip 3 if X = 1

Skip 7 if X = 2

Skip 16 if X = 3

Error

RPN Roll Down

X To Power of 2

Add R0 to X

Divide X by 2

Stop

RPN Roll Down

X To Power of 3

Multiply X by 2

Set R1 to R0

R1 To Power of 2

Multiply R1 by 3

Add R1 to X

Add R0 to X

Divide X by 6

Stop

RPN Roll Down

Add 1 to X

Multiply X by R0

X To Power of 2

Divide X by 4

Example:

Y = 6, X = 1:  Sum is 21

Y = 6, X = 2:  Sum is 91

Y = 6, X = 3:  Sum is 441

PCalc42 Present Value Factor of a Single Sum

PV:  (1 + Y/100)^-X

Y:  interest rate

X:  periods

Negate X

Divide Y by 100

Add 1 to Y

Y To Power of X

RPN Roll Down

Example:  Y = 7 (7%), X =  5 (n = 5)

Output:  0.7129861795

Happy New Year’s Everyone! See you in 2017!    

Eddie

This blog is property of Edward Shore, 2016.

Fun with HP 71B IV

Fun with HP 71B IV

For the previous entries:

Links to other HP 71B Programs:
Fun with the 71B:
http://edspi31415.blogspot.com/2012/06/fun-with-hp-71b.html

Fun with the 71B II:
http://edspi31415.blogspot.com/2016/06/fun-with-hp-71b-ii.html

Fun with the 71B III:

http://edspi31415.blogspot.com/2016/06/fun-with-hp-71b-iii.html

71B: Cubic Polynomials:
http://edspi31415.blogspot.com/2012/06/cubic-formula-basic-program-hp-71b.html

Rake Wall

The program RAKEWALL calculates:

*  The positions and lengths of studs on a rake wall

*  Angle of the incline

Program RAKEWALL

192 Bytes, 12/22/2016

10 DESTROY B,R,L,N,A

15 DESTROY I,T,O

50 INPUT “BASE:”; B

52 INPUT “RISE:”; R

54 INPUT “RUN:”; L

56 INPUT “O.C. :”; S

74 N = INT(L/S)

76 DEGREES

78 T = ATAN(R/L)

80 DISP “ANGLE =”; T; “°”  @ PAUSE

90 FOR I=L TO 0 STEP –S

92 A = I*TAN(T)+B

94 DISP I; “, “; A  @ PAUSE

96 NEXT I

98 DISP 0; “, “; B

Notes:

Degree symbol (°):  [ g ], [RUN] (CTRL), [ A ]

Example: (amounts are in feet)

BASE:  4

RISE:  3

RUN:  6

O.C.:  16/12  (1 foot, 4 inches)

Output: 

ANGLE = 26.5650511771 °

(Position from where the incline meets the base, length of studs)

6, 7

4.66666666667, 6.33333333334

3.33333333334, 5.66666666667

2.00000000001, 5

0.66666666668, 4.33333333334

0,  4

Automotive Cylinders:  Calculating Displacement and Piston Speed

The program supplies default values which can be accepted or changed.

Program AUTOCYN

217 Bytes, 12/22/2016

10 DESTROY N,B,S,R,E,P

15 INPUT “# CYLINDERS:”,  “6”; N

20 INPUT “BORE (IN):”, “4”; B

25 INPUT “STROKE (IN):”, “4”; S

30 E = PI/4 * B^2 * S * N

35 INPUT “RPM:”; R

40 P = S * R / 6

45 DISP “ENGINE DISPLACEMENT =” @ WAIT 1

50 DISP E; “ IN^3” @ PAUSE

55 DISP “PISTON SPEED =” @ WAIT 1

60 DIPS P; “FPM”

Example 1:

N = 6 cylinders, B = 4 in, S = 4 in, RPM = 3500

Output:  E ≈ 301.59290 in^3, P ≈ 2333.33333 FPM

Example 2:

N = 6 cylinders, B = 4 in, S = 3 in, RPM = 4500

Output:  E ≈ 226.19467 in^3, P = 2250 FPM

Right Triangle Solver

The program RIGHTTRI is a solver for the sides A, B, and C.  To solve for the third side, the desired side needs to have a 0 value, while the other two sides have non-zero values.  Each time a solution is found, the values of A, B, and C are reset (set to 0).

Program RIGHTTRI

502 Bytes, 12/22/2016

10 DESTROY A,B,C,Z$

11 ! LOOP

12 DISP “A, B, C, Solve, Exit”

14 DELAY 0, 0

16 Z$ = KEY$

18 IF Z$ = “A” THEN 30

20 IF Z$ = “B” THEN 40

22 IF Z$ = “C” THEN 50

24 IF Z$ = “S” THEN 60

26 IF Z$ = “E” THEN 96

28 GOTO 12

30 INPUT “A = “; A

32 GOTO 12

40 INPUT “B = “; B

42 GOTO 12

50 INPUT “C = “; C

52 GOTO 12

60 IF A=0 AND B AND C THEN 62 ELSE 70

62 S=SQR(C^2-B^2) @ Z$ = “A”

64 GOTO 90

70 IF A AND B=0 AND C THEN 72 ELSE 80

72 S=SQR(C^2-A^2) @ Z$ = “B”

74 GOTO 90

80 IF A AND B AND C=0 THEN 82 ELSE 86

82 S=SQR(A^2+B^2) @ Z$ = “C”

84 GOTO 90

86 DISP “MUST HAVE ONE 0” @ BEEP @ WAIT .5

88 GOTO 10

90 DISP Z$; “ = “; S @ PAUSE

92 GOTO 10

94 DISP “DONE”

Notes:

The line of IF A=0 AND B AND C… tests whether A is zero, B and C are non-zero.  You can test whether a variable is non-zero by just typing the variable in an IF condition.

The function SQR is the square root function of the HP 71B.

Anything following an exclamation point (!) is a comment.

Basic Bridged-T Notch Filter

The program NOTCH calculates the required capacitor and resistor to null out an undesired frequency.

Inputs:  inductance (H), frequency to nullified (Hz), resistance of the required coil (Ω)

Source:  Rosenstein, Morton.  Computing With the Scientific Calculator Casio: Tokyo, Japan.  1986.  ISBN-10: 1124161430

Program NOTCH

244 Bytes, 12/22/2016

10 DESTROY L,F,I,C,R

20 DISP “INDUCTANCE” @ WAIT 1

22 INPUT “in H: “; L

24 DISP “FREQUENCY” @ WAIT 1

26 INPUT “in Hz: “; F

28 DISP “COIL’S RESISTENCE” @ WAIT 1

30 INPUT “in Ω: “; I

40 C = 1/(2 * PI^2 * F^2 * L)

42 R = (PI * F * L)^2 / I

44 DISP “NOTCH CAPACITOR” @ WAIT 1

46 DISP C; “ F” @ PAUSE

48 DISP “NOTCH RESISTENCE” @ WAIT 1

50 DISP R; “ Ω”

Notes:

Capital Omega Character (Ω):  [ g ], [RUN] (CTRL), [ Q ]

Example:   L = 0.12 H, F = 1170 Hz, Coil Resistance = 30 Ω

Output: 

NOTCH CAPACITOR ≈ 3.08402 * 10^-7 F

NOTCH RESISTENCE ≈ 6485.04070 Ω

Differential Equations and Half-Increment Solution, Numerical Methods

The program HALFDIFF solves the numerical differential equation

d^2y/dt^2 = f(dy/dt, y, t)  given the initial conditions y(t0) = y0 and dy/dt (t0) = dy0

In this notation, y is the independent variable and t is the dependent variable.

The Method

Let C = f(dy/dt, y, t).  Give the change of t as Δt.

First Step:

With t = t0:

h_1/2 = dy0 + C * Δt/2

y1 = y0 + dy0 * Δt

Loop:

t = t0 + Δt

h_I+1/2 = h_I-1/2 + C * Δt

y_I+1 = y_I +h_I+1/2 * Δt

Repeat as many steps as desired.

For more details, click here:  http://edspi31415.blogspot.com/2016/11/ti-84-plus-and-hp-prime-differential.html

Source:  Eiseberg, Robert M.  Applied Mathematical Physics with Programmable Pocket Calculators  McGraw-Hill, Inc:  New York.  1976.  ISBN 0-07-019109-3

Program HALFDIFF

250+ bytes, 12/22/2016

Edit f(A,Y,T) at line 5 where

A = y’(t), Y = y(t),  T = t

5 DEF FNF(A,Y,T) = insert function y’(t), y(t), and t here

10 DESTROY A,Y,D,N,H,T

12 RADIANS

20 INPUT “dY/dX (0) = “, “0”; A

22 INPUT “Y(0) = “, “0”; Y

24 INPUT “DELTA T = “,”1”; D

26 INPUT “TMAX = “,”5”; N

28 T = D

44 H = A + FNF(A,Y,T) * D/2

48 Y = Y + H * D

50 DISP D; “, “;  Y @ PAUSE

70 FOR I = 2 * D TO N STEP D

72 T = I @ A = H

76 H = H + FNF(A,Y,T) * D

78 Y = Y + H * D

80 DISP I; “, “; Y @ PAUSE

82 NEXT I

Example:  y’’(t) = y’(t) + 2 *  t with y’(0) = 0, y(0) = 1, Delta t = 1, Max t = 6

FNF(A,Y,T) = A + 2 * T

Results:

T	Y
1	2
2	8
3	26
4	70
5	168
6	376

  

This blog is property of Edward Shore, 2016.

Happy Holidays

To everyone, Happy Holidays and Merry Christmas! Thank you everyone for all the support and comments on this blog.  

Coming up is another series on the HP 71B.  I have some things planned for 2017; let's see where it goes.  

See you after the 25th! - Eddie

TI-84 Plus CE: Updated TI-84 RPN Program

TI-84 Plus CE:  Updated TI-84 RPN Program

For the original TI84RPN program, click here:

http://edspi31415.blogspot.com/2016/09/ti-84-plus-ce-basic-rpn.html

Introduction to TI84RPNS

The program TI84RPNS puts the TI-84 Plus CE into RPN (reverse polish notation) mode with arithmetic functions, power, square root, reciprocal, and π.  The program contains room for one independent memory and a four level stack that works like the classic Hewlett Packard RPN calculators. 

The program uses list 6 (L₆) as the stack, with six elements:

L₆(1): X stack (displayed – bottom number)

L₆(2): Y stack (displayed – top number)

L₆(3): Z stack

L₆(4): T stack

L₆(5): Independent memory stack

L₆(6): (temporary memory)

What’s New:  TI84PRNS adds trigonometric, logarithmic, and additional numeric functions have been added.  Also, the [ XTθN ]/(link) key is used to switch angle modes between Degrees and Radians.  

If you need an idea how RPN works, please check this out:  http://edspi31415.blogspot.com/2011/09/rpn-basics.html

You can download TI84PRNS here:  https://drive.google.com/open?id=0B7R8x9Yi26yGNHRSblRhNU5PQzQ

To enter numbers, this program requires you to press the [enter] key prior to entering a number on the stack.  

The following keys with the associated functions are available:

Primary Keys

[ enter ]  Enter number

[ + ] Add: Y + X

[ - ] Subtract: Y - X

[ × ] Multiplication: Y * X 

[ ÷ ] Divide: Y/X

[ ^ ]  Exponent: Y^X

[ x² ] Square:  x^2

[ x^-1 ]  Reciprocal:  1/x

[ (-) ] Switch the sign of X (multiply X by -1)

[ sto> ] Store X in independent memory

[ alpha ] Recall memory 

[ clear ] Clear X stack to 0

[ sin ]  Sine of X

[ cos ] Cosine of X

[ tan ] Tangent of X

[ log ]  Common Logarithm (base 10) of X

[ ln ] Natural Logarithm (base e) of X

Function Keys:

[ Y= ] (F1):  CIRC:  Area of the Circle, radius is on stack X

[ window ] (F2):  DIAG:  Diagonal/Polar Radius, √(X^2 + Y^2)

[ zoom ] (F3): PRCH:  Percent Change from Y to X

[ trace ] (F4): ANGL:  Angle Function, angle(Yi+X)

[ graph ] (F5): REAL:  Real portion of the complex number in X

Stack operations:

[ ( ] Swap with X and Y

[ ) ] Roll stack down, result { Y, T, Z, X }

Mode operations:

[ XTθN ] Switch to Degrees Mode

Exit TI84PRNS:

Press [ mode ]

Secondary Keys: Keys pressed after [ 2^nd ] is pressed

[ 2^nd ]  Cancels 2^nd

[ ^ ] ( π )   Enters π to the Stack

[ x² ] ( √ ) Square Root of X

[ sin ] (sin^-1)   Arcsine of X

[ cos ] (cos^-1)  Arccosine of X

[ tan ]  (tan^-1)  Arctangent of X

[ log ] (10^x)  Common antilog (base 10) of X

[ ln ] (e^x) Exponential function (base e) of X

Function Keys:

[ Y= ] (F1):  ABS:  Absolute Value of X

[ window ] (F2):  INT:  Integer Part of X

[ zoom ] (F3): FRC:  Fractional Part of X

[ trace ] (F4): SIGN:  Sign of X

[ graph ] (F5): IMAG:  Imaginary portion of the complex number in X

Mode operations:

[ 2^nd ], [ XTθN ] Switch to Radians Mode

Example:   2 + 3 + 9 = 14

Keys:

[ enter ], 2, [ enter ]

[ enter ], 3, [ enter ], [ + ], 

[ enter ], 9,  [ enter ], [ + ]

See more examples below. 

TI-84 Plus Program TI84RPNS:

Disp "TI-84+ BASIC RPNS"

Disp "DEC. 2016"

Full

a+bi

{0,0,0,0,0,0}→L6

ClrHome

Lbl 1

While 1

getKey→K

While K=0

getKey→K

Output(2,1,L6(2))

Output(3,1,L6(1))

Output(4,1,"(: SWAP, ): ROLL")

Output(5,1,"MODE: EXIT, ALPHA: RCL")

Output(6,1,"XTθN: DEG/RAD")

Output(7,1,"ENTER: ENTER NUMBER")

Output(8,1,"CIRC/DIAG/PCHG/ANGL/REAL")

End

If K=22:Then:ClrHome:Stop:End

If K=21:Then:Goto 20:End

If K=45:Then:0→L6(1):ClrHome:End

If K=55:Then:L6(2)^L6(1)→L6(6)

Goto 2:End

If K=65:Then:L6(2)/L6(1)→L6(6)

Goto 2:End

If K=75:Then:L6(2)*L6(1)→L6(6)

Goto 2:End

If K=85:Then:L6(2)-L6(1)→L6(6)

Goto 2:End

If K=95:Then:L6(2)+L6(1)→L6(6)

Goto 2:End

If K=105:Then:Goto 4:End

If K=51:Then:1/L6(1)→L6(1):ClrHome:Goto 1:End

If K=61:Then:L6(1)²→L6(1):ClrHome:Goto 1:End

If K=52:Then:sin(L6(1))→L6(1):ClrHome:Goto 1:End

If K=53:Then:cos(L6(1))→L6(1):ClrHome:Goto 1:End

If K=54:Then:tan(L6(1))→L6(1):ClrHome:Goto 1:End

If K=71:Then:log(L6(1))→L6(1):ClrHome:Goto 1:End

If K=81:Then:ln(L6(1))→L6(1):ClrHome:Goto 1:End

If K=104:Then:­L6(1)→L6(1):ClrHome:Goto 1:End

"CIRC"

If K=11:Then:L6(1)²*π→L6(1):ClrHome:Goto 1:End

"DIAG"

If K=12:Then:√(L6(1)²+L6(2)²)→L6(6)

L6(6)→L6(1):L6(3)→L6(2):L6(4)→L6(3)

ClrHome

Goto 1:End

"PCHG"

If K=13:Then:100*(L6(1)-L6(2))/L6(2)→L6(6)

L6(6)→L6(1):L6(3)→L6(2):L6(4)→L6(3)

ClrHome

Goto 1:End

"ANGL"

If K=14

Then:angle(L6(1)+L6(2)*i)→L6(6)

L6(6)→L6(1):L6(3)→L6(2):L6(4)→L6(3)

ClrHome

Goto 1:End

"REAL"

If K=15:Then:real(L6(1))→L6(1):ClrHome:Goto 1:End

If K=63:Then:Goto 5:End

If K=64:Then:Goto 6:End

If K=91:Then:L6(1)→L6(5):Goto 1:End

If K=31:Then:L6(5)→L6(6):Goto 3:End

If K=32:Then:Degree:Goto 1:End

If K=22:Then:ClrHome:Stop:End

Goto 1

Lbl 2

"TWO OPERATION"

L6(6)→L6(1):L6(3)→L6(2):L6(4)→L6(3)

ClrHome

Goto 1

Lbl 3

"RCL/INPUT"

L6(3)→L6(4):L6(2)→L6(3):L6(1)→L6(2)

L6(6)→L6(1):ClrHome

Goto 1

Lbl 4

"INPUT NUMBER"

ClrHome

Input "NUMBER:",N

N→L6(6)

Goto 3

Lbl 5

"SWAP"

L6(1)→L6(6):L6(2)→L6(1):L6(6)→L6(2)

ClrHome

Goto 1

Lbl 6

"ROLL"

L6(1)→L6(6)

L6(2)→L6(1):L6(3)→L6(2):L6(4)→L6(3)

L6(6)→L6(4)

ClrHome

Goto 1

End

Lbl 20

ClrHome

While 1

getKey→K

While K=0

getKey→K

Output(2,1,L6(2))

Output(3,1,L6(1))

Output(4,1,"2ND")

Output(8,1,"ABS /INT /FRC /SIGN/IMAG")

End

If K=21:Goto 1

"PI"

If K=55:Then:

π→L6(6)

L6(3)→L6(4):L6(2)→L6(3):L6(1)→L6(2)

L6(6)→L6(1):ClrHome

Goto 1

End

"OTHERS"

If K=32:Then:Radian:Goto 1:End

If K=61:Then:√(L6(1))→L6(1):ClrHome:Goto 1:End

If K=52:Then:sin^-1(L6(1))→L6(1):ClrHome:Goto 1:End

If K=53:Then:cos^-1(L6(1))→L6(1):ClrHome:Goto 1:End

If K=54:Then:tan^-1(L6(1))→L6(1):ClrHome:Goto 1:End

If K=71:Then:10^(L6(1))→L6(1):ClrHome:Goto 1:End

If K=81:Then:e^(L6(1))→L6(1):ClrHome:Goto 1:End

"ABS "

If K=11:Then:abs(L6(1))→L6(1):ClrHome:Goto 1:End

"INT "

If K=12:Then:iPart(L6(1))→L6(1):ClrHome:Goto 1:End

"FRC "

If K=13:Then:fPart(L6(1))→L6(1):ClrHome:Goto 1:End

"SIGN"

If K=14:Then:abs(L6(1))/L6(1)→L6(1):ClrHome:Goto 1:End

"IMAG"

If K=15:Then:imag(L6(1))→L6(1):ClrHome:Goto 1:End

End

Remember to keep the Order of Operations in mind when running this program.

Example 1:   1/(10 – 1.5^2.5) = 0.1380391041

[ enter ], 10, [ enter ]

[ enter ], 1.5, [ enter ]

[ enter ], 2.5, [ enter ]

[ ^ ], [ - ], [ x^-1 ]

Example 2:   √(6^2 + 7^2) = 9.219544457

[ enter ], 6, [ enter ], [ x² ]

[ enter ], 7, [ enter ], [ x² ]

[ + ], [ , ]

Example 3:  Store 1.758 in memory. (Let M = 1.758)

Calculate 10 – 1.1^M + 2M = 12.33358933

[ enter ], 1.758, [ enter ], [ sto> ]

[ enter ], 10, [ enter ]

[ enter ], 1.1, [ enter ]

[ alpha ], [ ^ ], [ - ]

[ enter ], 2, [ enter ]

[ alpha ], [ × ], [ + ]

Example 4:  (10 + (8 – 5%)) + 9% = (10 + (8 * .95)) * 1.09 = 19.184

[ enter ], 8, [ enter ]

[ enter ], .95, [ enter ], [ × ]

[ enter ], 10, [ enter ], [ + ]

[ enter ], 1.09, [ enter ], [ × ]

Example 5:  e^(1.5) = 4.48168907

[ enter ], 1.5, [ enter ]

[ 2^nd ], [ ln ] (e^x)

Example 6:  sin((10/√(2^2 + 2.5^2))°) = 0.0544879291

Use the DIAG function for √(2^2 + 2.5^2)

[ XTθN ] (set Degrees mode)

[ enter ], 2, [ enter ]

[ enter ], 2.5, [ enter ]

[ window ] (F2)

[ x^-1 ], [ enter ], 10, [ enter ]

[ * ], [ sin ]

Example 7:  What is the percent change from 10.99 to 20.99?  90.99181074 (%)

[ enter ], 10.99, [ enter ]

[ enter ], 20.99, [ enter ]

[ zoom ] (F3)

This blog is property of Edward Shore, 2016