HP 33S Integral Demonstration and Programs

HP 33S Integral Demonstration and Programs

Integration

I'm going to start with a demonstration on how to calculate integrals with the HP 33S through the equation list.  The steps will be similar for the HP 32SII and the later HP 35S.  

1.  Enter the lower limit, press [ ENTER ], the higher limit.

2.  Press [ |→ ] [ STO ] (EQN), enter or select an equation.  

3.  Press [ |→ ] [ e^x ] ( ∫ ), to calculate the integration.  You will be prompted for the variable to integrate.  

Example:  Fresnel Integral 

Select Radians angle mode.  

Fresnel Sine:  

Equation:  SIN(SQ(T)), variable to integrate:  T   

Note:  [ x^2 ] -> SQ (square)

Use lower limit as 0.

S(2.4):   lower = 0, upper = 2.4,  S(2.4) ≈ 0.457864

S(5.8):   lower = 0, upper = 5.8,  S(5.8) ≈ 0.678004

Fresnel Cosine:

Equation:  COS(SQ(T)), variable to integrate:  T   

Use lower limit as 0.

C(2.4):   lower = 0, upper = 2.4,  C(2.4) ≈ 0.510157

C(5.8):   lower = 0, upper = 5.8,  C(5.8) ≈ 0.695845

Source:

"Fresnel Integral"  Wikipedia  https://en.wikipedia.org/wiki/Fresnel_integral  Retrieved May 2, 2022

Atmospheric Parameters

Given the height (H) in meters, the following can be estimated:

Temperature in Celsius  (°C):

T ≈ 15.04 - 0.00649 * H

Pressure in kilopascals (kPa):

P ≈ 101.29 * ((T + 273.15) / 288.08)^5.256

(note, the source had 273.1 but I had 27.3.15 for better accuracy)

Atmospheric Density (km/m^3):

D ≈ P/(0.2869 * (T + 273.15))

Program:

HP 33S:  Size: LN = 174, CK = 7625

A0001  LBL A

A0002  15.04

A0003  0.00649

A0004  INPUT H

A0005  ×

A0006  -

A0007  STO T

A0008  VIEW T

A0009  273.15

A0010  +

A0011  288.08

A0012  ÷

A0013  52.56

A0014  y^x

A0015 101.29

A0016  ×

A0017  STO P

A0018  VIEW P

A0019  0.2869

A0020  273.15

A0021  RCL+ T

A0022  ×

A0023  ÷

A0024  STO D

A0025  VIEW D

A0026  RTN

Example:

H = 50 m

Results:

T ≈ 14.715580 °C  (about 58.4879 °F)

P ≈ 100.894225 kPa

D ≈ 1.221648 kg/m^3

Source:

"Engineering Formula Sheet"  Project Lead The Way. https://www.madison-lake.k12.oh.us/userfiles/680/Classes/16192/IED-Review%20Engineering%20Formula%20Sheet.pdf   Last Retrieved April 29, 2022 

Legendre Polynomials

The value of Legendre Polynomials can be calculated using a closed formula from Rodrigues' formula:

P_n(x) = Σ( comb(n, k) * comb(n+k, k) * ((x - 1)/2)^k,  k= 0, n)

Program:  

HP 33S:  

LBL L:  Size:  LN = 30, CK = 14EC

LBL M: Size:  LN = 105, CK = AA05

Run XEQ L.  

L0001  LBL L

L0002  0

L0003  STO P

L0004  INPUT X

L0005  INPUT N

L0006  STO K

M0001  LBL M

M0002  RCL N

M0003  RCL K

M0004  nCr

M0005  RCL N

M0006  RCL+ K

M0007  LASTx

M0008  nCr

M0009  ×

M0010  -1

M0011  RCL+ X

M0012  2

M0013  ÷

M0014  RCL K

M0015  y^x

M0016  ×

M0017  STO+ P

M0018  DSE K

M0019  GTO M

M0020  1

M0021  STO+ P

M0022  RCL P

M0023  RTN

Examples:

N = 2, X = 0.25;  Result:  -0.406250

N = 3, X = -0.46;  Result:  0.446660

N = 4, X = 0.73;  Result:  -0.380952

Source:

"Legendre polynomials"  Wikipedia.  https://en.wikipedia.org/wiki/Legendre_polynomials  Updated April 6, 2022.  Last Accessed April 29, 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. 

Retro Review: Hewlett Packard HP 33S

Retro Review:   Hewlett Packard HP 33S

The calculator with the Chevron Keyboard!

Quick Facts

Model:  HP 33S

Company:  Hewlett Packard

Years:  2003-2007

Type:  Scientific

Batteries: 2 x CR-2032

Operating Modes:  RPN, ALG

Memory:  31,277 bytes

Number of Registers: 27, A-Z, i

Display:  2 stack levels

Features

*  standard scientific calculator functions: trig, logs, power, absolute value, integer and fractional part, combinations, permutations, random numbers, hyperbolic functions, and more

*  factorial function that allows real numbers;  Γ(x) = (x - 1)!

*  polar and rectangular conversion functions,  very popular (for good reason) 

*  40 scientific constants

*  8 sets of SI-US conversions

*  base conversions 

*  algebraic mode (which I don't know anyone who would use this calculator in algebraic mode, but it's there)

*  linear regression  (y = mx + b)

*  fraction display mode ( [ ←| ] [ . ] (FDISP))

*  storage and recall arithmetic

We can store equations for evaluation, solving, and integration.  

Full list of conversions:

Polar (→θ,r) - Rectangular (→y,x)

Hours (→HR) - Hours-Minutes-Seconds (→HMS)

Degrees - Radians

Kilograms - Pounds

Degrees Celsius - Degrees Fahrenheit

Centimeters - Inches

Liters - Gallons

Programming

The HP 33S has keystroke programming and the set of commands similar from the HP 32SII:  

*  INPUT var

*  VIEW var  (views the variable without putting the variable's value on the stack)

*  Subroutines and Return

*  Comparison tests between x and 0, x and y.  If the test is true, execute the next step, otherwise skip the next step

*  ISG:  Increment and skip if greater

*  DSE:  Decrement and skip if equal or less than

The HP 33S designates one register, lower case i, for indirect addressing.  The absolute integer value of i determines where storage, recall, label, subroutine, integration variable, exchange, and function designation.  Use (i) to use indirect addressing.  Indirect registers can also access statistical sums:

(i) = 27,  i 

(i) = 28,  n

(i) = 29,  Σx

(i) = 30,  Σy

(i) = 31,  Σx^2

(i) = 32,  Σy^2

(i) = 33,  Σxy

The HP 33S has 26 labels, which restrict programs to 26.  Hence, LBL A instead of LBL A0001.   At first, I didn't like the restriction, but I learned to live with it and don't mind it as much.  

Let's Talk About the Chevron Keyboard

The HP 33S is a unique calculator it's keyboard style:  the keys take a slanted quadrilateral shape, with the center column of keys taking a chevron style shape.   At the top there is a directional pad.  Hewlett Packard took a chance with the design from the standard calculator shape, and it was not a homerun.   

The beginning production of the HP 33S was not successful. Keys had bad responses, the display was not up to par, and some keys are hard to press.   It took Hewlett Packard several production runs to get the keyboard working right, which unfortunately killed the reputation of the HP 33S.  Towards the end of its run, the keyboards were fixed.

I don't mind the unique keyboard, my biggest issue was the spacing the keys where sometimes the shifted functions and alpha characters did not have much space.  This made the keyboard busy.  I also do not like the black arrows on the green and purple backgrounds on the shift keys, I use HP used a lighter font for those arrows.  

A Phoenix of Calculators  

When the HP 33S first hit the market, the calculator was disliked.  Now, it is a sought after calculator.   The original price for the 33S was about $50 US dollars, now if you want one, be prepared to pay at least $75 US dollars, sometimes triple digits.  Make sure you are buying the HP 33S from later in the run (towards 2007).  

Another factor of why the HP 33S is becoming a collector's calculator, the successor, the HP 35S, had several shortcomings such as the number of mathematical bugs and the lack of the rectangular and polar conversion functions.   The HP 33S is closer to the classic style, like the HP 32S and HP 32SII.  

I don't expect to ever be an anniversary edition of the HP 33S but it was an underrated calculator and has its place in calculator history.

Tomorrow I have a list of programs and an integer demonstration.  

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. 

TI 84 Plus CE and HP 33S: Scaled Data for Statistics

TI 84 Plus CE and HP 33S:  Scaled Data for Statistics

Introduction and the Mathematics

The goal of the programs posted today is to take a data set of real numbers and scale it down to the range [1,10].  Why?  Sometimes scaling data by applying a linear transformation, it could make curve fitting and data analysis more accessible and open up regression analysis previously not available, such as logarithmic or power regression.   

Let:

max = maximum value of the data set

min = minimum  value of the data set

And:

min * a + b = 1

max * a + b = 10

Solving for a and b:

a = 9/(max - min)

b = 1 - a * min = 10 - a * max

Apply this transformation to the data set to get:

x' = a*x + b

And to convert back:

x = (b - x')/a

TI-84 Plus CE Program:  DSCALE   (TI-Basic)

Disp "DATA SCALE TO [1,10]","BY EDWARD SHORE"

Input "XLIST: ",L5

9/(max(L5)-min(L5))→A

1-A*min(L5)→B

Disp "FORMULA:","X'="+toString(A)+"X+"+toString(B)

Pause

A*L5+B→L6

Disp "SCALED DATA:"

Pause L6

Note:

L5:  List 5, used for input, [ 2nd ] [ 5 ]

L6:  List 6, used for output, [ 2nd ] [ 6 ]

HP 33S Programs

LBL Y:  determine A and B.  Stack:  Y:  max, X:  min

HP 33S Size:  LN = 72, CK = B830

Y0001  LBL Y

Y0002  -

Y0003  LASTx

Y0004  x<>y

Y0005  1/x

Y0006  9

Y0007  ×

Y0008  STO A

Y0009  VIEW A

Y0010  ×

Y0011  1

Y0012  x<>y

Y0013  -

Y0014  STO B

Y0015  VIEW B

Y0016  RTN

LBL X:  Calculate x'

HP 33S Size:  LN = 15, CK = 08B6

X0001  LBL X

X0002  RCL- B

X0003  RCL÷ A

X0004  STOP

X0005  GTO X    // this allows for repeated calculations by pressing R/S

LBL Z:  Calculate x

HP 33S Size: LN = 15, CK = 4552

Z0001  LBL Z

Z0002  RCL× A

Z0003  RCL+ B

Z0004  STOP

Z0005  GTO Z   // this allows for repeated calculations by pressing R/S

Instructions:

1.  Do this first:  max [ ENTER ] min [ XEQ ] Y  

2.  XEQ Z  to calculate X'.  XEQ X to calculate X'. 

X' = A * X + B

Example

Data Set:  [-5, -3, 2, 3, 6]

max = 6

min = -5

(results are rounded to six decimal places)

a = 0.818182

b = 5.090909

Translated Data: 

x to x':

x = -5,  x' = 1.000000

x = -3,  x' = 2.636364

x = 2, x' = 6.727273

x = 3, x' = 7.545455

x = 6, x' = 10.000000

x' to x:

x' = 2.5, x = -3.16667

x' = 5,  x = -0.111111

x' = 7.5, x = 2.944444

Hope you find this helpful.  Next week is a retro review of the HP 33S Calculator, once abhorred now held as valuable.  

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.