Sunday, July 3, 2022

Casio fx-CG50: Sparse Matrix Builder

Casio fx-CG50: Sparse Matrix Builder



Introduction


The programs can create a sparse matrix, a matrix where most of the entries have zero value.  There are several ways to represent sparse matrix in a shortcut form.  The most straight forward way is the COO (row-column-value) representation.


Mat A:  three column matrix:  (row-column-value representation)

Column 1:  row number

Column 2:  column number

Column 3:  value


Mat S:  sparse matrix


Casio fx-CG 50 Program:  SPARSE

[ [ row, column, value ] ... ] → sparse matrix


"TO SPARSE MATRIX"

"EDWARD SHORE"

"[[ROW,COL,VALUE]]"

"MAT"?→Mat A

Mat→List(Mat A,1)→List 26

Max(List 26)→R

Mat→List(Mat A,2)→List 26

Max(List 26)→C

{R,C}→Dim Mat S

Dim Mat A→List 26

List 26[1]→N

For 1→I To N

Mat A[I,1]→J

Mat A[I,2]→K

Mat A[I,3]→Mat S[J,K]

Next 

"SPARSE MATRIX:"⊿

Mat S


Casio fx-CG 50 Program: ISPARSE

sparse matrix → [ [ row, column, value ] ... ] 


"INV SPARSE MATRIX"

"EDWARD SHORE"

"SPARSE"?→Mat S

Dim Mat S→List 26

List 26[1]→R

List 26[2]→C

0→N

For 1→I To R

For 1→J To C

Mat S[I,J] →V

[[I][J][V]]→Mat Z

(V≠0 And N=0)⇒Mat Z→Mat A

(V≠0 And N>0)⇒Augment(Mat A,Mat Z)→Mat A

(V≠0)⇒1+N→N

Next

Next

"COO FORMAT:"⊿

Trn Mat A→Mat A


Example


Example 1:


Row/Column/Value (COO) Format:  (Mat A)


[ [ 1, 2, 8 ]

[ 2, 4, -3 ]

[ 3, 1, 2 ]

[ 3, 3, 6 ]

[ 4, 2, -1 ] ]


Sparse Matrix:  (Mat S)


[ [ 0, 8, 0, 0 ]

[ 0, 0, 0, -3 ]

[ 2, 0, 6, 0 ]

[ 0, -1, 0, 0 ] ]


Example 2:


Row/Column/Value (COO) Format:  (Mat A)


[ [ 1, 2, 1 ]

[ 1, 3, 2 ]

[ 2, 1, -1 ]

[ 2, 3, 3 ]

[ 3, 3, 4 ]

[ 4, 1, 5 ] ]


Sparse Matrix:  (Mat S)


[ [ 0, 1, 2 ] 

[-1, 0, 3 ] 

[ 0, 0, 4 ]

[ 5, 0, 0 ] ]


Source:


"Sparse matrix"  Wikipedia. Last edited March 11, 2022.  Accessed May 9, 2022.  https://en.wikipedia.org/wiki/Sparse_matrix


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. 


Saturday, July 2, 2022

Casio fx-CG50: Discrete Fourier Transform

Casio fx-CG50: Discrete Fourier Transform



Making the Discrete Transforms and Back Again


Given a set of numbers, either real or complex:


{x_0, x_1, x_2, x_3, ... , x_n-1}  (small X)


can be transformed using a discrete transform by the sum:


X_k = Σ( x_m * e^(-2 * π * k * m * i ÷ n), m = 0, n - 1)

with i = √(-1)  (big X)


We can do the reverse:


x_k = 1 ÷ n * Σ( X_m * e^(2 * π * k * m * i ÷ n), m = 0, n - 1)


On the Casio fx-CG50, lists start with marker 1 instead of 0, so a slight adjustment in the programs below are needed.


On the programs:

List 25 = small x

List 26 = big X


Casio fx-CG50 Program:  DFT  (Discrete Fourier Transform)


Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"DFT"

"E. SHORE, 2022"

"SMALL X (List 25)"?→List 25

Dim List 25→N

List 25→List 26

For 1→K To N

0→S

For 1→J To N

List 25[J]→A

S+A×e^(-2×π×i×(K-1)×(J-1)÷N)→S

Next

S→List 26[K]

Next

"BIG X (List 26)"⊿

List 26


Note:  i = √(-1), [SHIFT] [ 0 ]


Casio fx-CG50 Program:  IDFT  (Inverse Discrete Fourier Transform)


Menu "FORMAT","a+bi",1,"r∠θ",2

Lbl 1:a+bi:Goto 3

Lbl 2:r∠θ:Goto 3

Lbl 3

"INVERSE DFT"

"E. SHORE, 2022"

"BIG X (List 26)"?→List 26

Dim List 26→N

List 26→List 25

For 1→K To N

0→S

For 1→J To N

List 26[J]→A

S+A×e^(2×π×i×(K-1)×(J-1)÷N)→S

Next

S÷N→List 25[K]

Next

"SMALL X (List 25)"⊿

List 25


Note:  i = √(-1), [SHIFT] [ 0 ]


Example Transforms


List 25 (small x):  {2, 4, 6, 8}

List 26 (big X):  {20, -4+4i, -4, -4-4i}


List 25 (small x): {5 + i, 6 + 2i, 7 + 3i, 8 + 4i, 9 + 5i}

List 26 (big X), approximate: 

{35 + 15i, -5.941 + 0.941i, -3.3123 -1.6877i, -1.6877 - 3.3123i, 0.941 - 5.941i}


Source:


Discrete Fourier Transform. Brilliant.org. Retrieved May 7, 2022, from https://brilliant.org/wiki/discrete-fourier-transform/


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. 


Monday, June 27, 2022

Retro Review: Texas Instruments BA-Solar

Retro Review: Texas Instruments BA-Solar








Finance + Solar + 1980s


Quick Facts


Model:  BA-Solar

Company:  Texas Instruments

Years:  1986 - 1990s; a refresh , BA-35 SOLAR was produced 1996-2000s

Type:  Finance

Batteries: Solar 

Operating Modes:  Chain

Number of Registers: 1, |MEM|

Display:  1 line, 10 digits


Features


The [ MODE ] key is used to toggle between three modes:


FIN Mode:  Time Value of Money  (FIN indicator)


N:  number of payments

%i:  periodic interest rate

PV:  present value

PMT:  payment

FV:  future value


The current cash flow convention is not used, instead the following equation is (I think) used in solving time value of money calculations: 


PV = FV *  SPPV + PMT * USPV

SPPV = single present value factor

USPV = present value annuity factor


We also have amortization functions:


BAL:  balance after any payment

I/P:  interest and principal at any payment

payment_1 P1/P2 payment_2 I/P:  cumulative interest and principal


There are ×12 and ÷12 aids, but we still have to press [ N ] and [ %i ] to register the values, they are not automatic.  


STAT Mode:  Statistics  (STAT indicator)


The BA-SOLAR (and the later BA-35 SOLAR) has both single variable statistics and linear regression.


In linear regression, use the [x<>y] key to change between x and y.   The key will also be used to switch between results.  


Prediction values can be calculated with x' and y'.


The equation used for linear regression is y = a*x + b,  a = slope, b = intercept.


Profit Mode (no indicator)


The profit mode makes the following solver available:


CST:  cost

SEL:  sell

MAR:  margin

MU:  markup


Functions Available in All Modes


Percent Calculations (%):

Add %:  x [ + ] y [ % ] [ = ]

Subtract %:  x [ - ] y [ % ] [ = ]

Multiply %:  x [ × ] y [ % ] [ = ]

Percent Ratio:  part [ ÷ ] whole [ % ] [ = ]

Percent Change:  new [ 2nd ] ( ⊿% ) old [ = ]


rate >EFF payments/year:  convert to effective rate

rate >APR payments/year:  convert to APR/nominal rate


Mathematics:

Natural logarithm and antilogarithm:  ln x, ^x

Square and square root

Power

Reciprocal


Final Thoughts


This is a great basic financial calculator.  I have both the BA-SOLAR and BA-35 SOLAR.   To be honest, I like the keyboard of the original BA-SOLAR better, the keys feel a bit more solid and responsive.  Even though they are no longer in production, the BA-SOLAR is still reasonably available on sites such as eBay and other online stores.  


Source:


Woerner, Joerg.  "Texas Instruments BA-SOLAR"  Last Updated December 5, 2001.   http://www.datamath.org/Sci/Modern/BA-SOLAR.htm   Retrieved May 19, 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. 


Sunday, June 26, 2022

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. 


Saturday, June 25, 2022

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. 



Sunday, June 19, 2022

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. 


Saturday, June 18, 2022

TI-84 Plus CE Python: The Split Command and Some Statistics

TI-84 Plus CE Python:  The Split Command and Some Statistics


Python:  Split Command


The split command allows the us to accept a list of input, use a character to split (spaces, commas, semicolons, etc.).


Example:


list1=input("List: ").split(",")   # split by comma

print(list1)


List:  1, 3, 4, 5

[ '1', '3', '4', '5' ]


Remember that the default of the input command is strings, so we have to change data types when needed:


n=len(list1)

for i in range(n):

  list1[i]=float(list[i])


(this is one way to do it)


The .split command does not require a module.  



TI-84 Plus CE Python Program:  SIMPSTAT


# Math Calculations

from math import *

print("Simple Statistics")

print("Edward Shore")

# 2022-04-27


x=input("\nSeparate data points \nby a comma: ").split(",")


# make every entry float

n=len(x)

for i in range(n):

   x[i]=float(x[i])


# \t tab \n new line

print("\nn =\t",n)


# sum

s=sum(x)

print("sum =\t",s)


# mean

a=s/n 

print("avg =\t",a)


# population deviation

d=0

for i in range(n):

  d+=(x[i]-a)**2

d=sqrt(d/n)

print("det =\",d)


# range of data

m0=min(x)

m1=min(x)

m2=m1-m0

print("min =\t",m0)

print("max =\t",m1)

print("range\t",m2)



Example


Sample list:  5.8, 5.9, 6.7, 6.9, 8.2, 8.8, 9.1

(use a comma to separate list items)


Results:

n = 7

sum = 51.4 (displayed as 51.400000000004)

avg = 7.342857142857143

dev = 1.25454276572008

min = 5.8

max = 9.1

range = 3.3


Source


Rohit.  "How to take list input in Python in single line"  Tutorial By EyeHunts.   December 11, 2021.  https://tutorial.eyehunts.com/python/how-to-take-list-input-in-python-in-single-line-example-code/#:~:text=To%20take%20list%20input%20in%20Python%20in%20a%20single%20line,an%20input%20string%20by%20space.

Last Retrieved April 28, 2022.  


Hope you find this useful.  Until next time,


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. 


Monday, June 13, 2022

Retro Review: Radio Shack EC-4035

Retro Review:   Radio Shack EC-4035






Quick Facts:


Model:  EC-4035

Company:  Radio Shack

Equivalent Of:  Casio fx-580

Years:  1986-1991

Type:  Scientific

Batteries: 1 x CR-2032

Operating Mode:  AOS

Memory Registers: 7  (K1 - K6, M)

Number of Digits: 10 (display), 8 in fractions, 2 digit exponents are in the top right of the display (10^xx)

Contrast Wheel


Features


*  Trigonometry, logarithmic functions

*  Base conversions with Boolean algebra

*  Engineering and Units mode

*  Single variable and linear regression  (y = A + Bx)

*  Gamma function

*  Complex numbers

*  6 constant memories (Kin/Kout) complete with storage arithmetic


The Radio Shack EC-4035 (Casio fx-580) uses an AOS (postfix) operating mode,  instead of typing expressions as they are written.


Statistics Mode


In linear regression, the equation used is y = A + Bx, where A is the y-intercept and B is the slope.  The statistics mode uses the six constant memories as follows:


K1 = Σx^2

K2 = Σx

K3 = n

K4 = Σy^2

K5 = Σy

K6 = Σxy


Gamma Function


The EC-4035 has a gamma function (Γ), which accepts all real numbers except for negative integers (-1, -2, -3, etc, because the gamma function is undefined there).  I wish this was available on more scientific functions.  


1 [a b/c] 2 [ Γ ] returns 1.772453851  (√π).  


The factorial function (x!) still only accepts non-negative integers.  


Complex Numbers


In the complex mode (Mode 3), the available functions are:


*  arithmetic (+, -, ×, ÷)

*  reciprocal (1/x)

*  argument and absolute value 

*  conjugate (x + yi → x - yi)

*  powers and roots, x^2, √


The arrow key [ → ]  and the key sequence [ SHIFT ] ( ← ) can scroll complex numbers.   Complex numbers are entered in rectangular form.  


Units and Engineering Modes


Results and calculations can be made using Engineering units and certain Electronics symbols.  All are accessed by using the [ [Sym] ] key.  The symbol each key has is located on the bottom right of the key in navy blue.   


[ MODE ] [ . ]:  Engineering Mode.  Results are shown, when applicable, with engineering symbols, for instance:


n:  nano, 10^-9

μ:  micro, 10^-6

m:  milli, 10^-3

k:  kilo, 10^3

M:  mega, 10^6

G:  giga, 10^9


The mode can be turned off by pressing [ MODE ] [ . ].


[ MODE ] [ 0 ]:  Unit Mode.  This is an enhancement to engineering mode to add electronic units:


V:  volts

A:  amperes

S:  seconds

W:  watts

F:  farads

C:  coulombs

Ω:  ohms


The electronic units can be combined with engineering units.    Also, the appropriate unit is determined in calculations.    To leave Unit Mode, go to Comp Mode by pressing [ MODE ] [ 1 ]. 


Engineering and Unit Mode are neat modes and it's really geared for electronic engineering and physics calculations.


Final Thoughts


The features of the EC-4035 gives a pretty standard advanced scientific calculators with additional features geared towards electronic engineering.   


Perhaps the next perfect calculator for electronic engineering would be a combination of the EC-4035 (fx-580), Casio fx-61f, and Calculated Industries Electronic Calc Pro (5070).  



Source:


"casio fx-580"  Voidware.  http://www.voidware.com/calcs/fx580.htm  Last Accessed April 22, 2022. 


Until next time,


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. 


Sunday, June 12, 2022

TI-65 Programs

TI-65 Programs


Conversions:  Miles and Kilometers 


TI-65 Conversion:  

F1:  Miles to Kilometers

F2:  Kilometers to Miles


00  2nd 53.53     LBL F1

01  38     ×

02   6     6

03   3     3

04   3     3

05   6     6

06   0     0

07  39     =

08  3rd 25     in-cm

09  28     ÷

10   1     1

11  15     EE

12   5     5

13   39   =

14   -15   INV EE    // remove scientific notation

15   2nd 52    RTN


16   2nd 53.54     LBL F2

17   38     ×

18   1      1

19   15    EE

20   5      5

21   -3rd 25     INV in-cm

22   28     ÷

23   6      6

24   3      3

25   3      3

26   6      6

27   0      0

28   39   ×

29   -15      INV EE

30   2nd 52    RTN


4.9 mi to km:

4.9 [ F1 ]

Result:  7.8857856  km


150 km to mi: 

150 [ F2 ]

Result:  93.20567884 mi


Conversions:  RGB (Red/Green/Blue) Color Code and Hexadecimal Codes


TI-65 Conversions:

F1:  RGB to Hexadecimal

F2:  Hexadecimal to RGB


00   2nd 53.53      LBL F1

01    38     ×

02    1       1

03    6       6

04    18     y^x

05    4       4

06    39     =

07    12.0    STO 0

08    51    R/S

09    38    ×

10    2      2

11    5      5

12    6      6

13    39    =

14    12.59   STO+

15    0      0

16    51    R/S

17    12.59    STO+

18    0       0

19    13.0    RCL 0

20    3rd 13   HEX

21    2nd 52  RTN


22    2nd 53.54   LBL F2

23    12.0   STO 0

24    3rd 12    DEC

25    28      ÷

26    1        1

27    6        6

28    18      y^x

29    4        4

30    39      =

31    2nd 27   INTG

32    51     R/S

33    38     ×

34    1       1

35    6       6

36    18     y^x    

37    4       4

38    39     =

39    12.49  STO-

40    0      0

41    13.0    RCL 0

42    28    ÷

43    2      2

44    5      5

45    6      6

46    39    =

47   2nd 27   INTG

48   51     R/S

49   38     ×

50   2       2

51   5       5

52   6       6

53   39     =

54  12.49   STO-

55   0        0

56   13.0   RCL 0

57   2nd 52  RTN


RGB to HEX:   red  [ F1 ]  green [ R/S ] blue [ R/S ] 

Example:  Red:  108, Blue:  4, Green: 82

108 [ F1 ]  4 [ R/S ] 82 [ R/S ]

Result:  6C0452  (HEX mode)


HEX to RGB:   [ 3rd ] (HEX) hex code [ F2 ]  

Example:  Hex Code: 3401D2

[ 3rd ] (HEX) 3401D2 [ F2 ] 

Result:  52 (red) [ R/S ], 1 (green) [ R/S ], 210 (blue)



Electronics:  Primary Filter and Voltage Gain


F1:  Calculate frequency.  f = 1 ÷ ( 2 * π * R * C ).   

Syntax:  R [ F1 ] C [ R/S ]

R = resistance in ohms ( Ω )

C = capacitance in farads ( F )

f = frequency in Hertz (Hz)


F2:  Voltage Gain.  G = 20 * log( E_output ÷ E_input ).  

Syntax:  E_output [ F2 ] E_input [ R/S ]

E_output = output voltage ( V )

E_input = input voltage ( V )

G = voltage gain in decibels ( dB )


Source:  Casio fx-61f User's Manual


00  2nd 53.53  LBL F1

01  38    ×

02  51    R/S

03  38    ×

04  2      2

05  38    ×

06  2nd 17  π

07  39    =

08  34    1/x

09 2nd 52  RTN


10  2nd 53.54  10

11  28    ÷

12  51    R/S

13  39    =

14  2nd 32  LOG

15  38   ×

16  2     2

17  0     0

18  39   =

19  2nd 52  RTN



R = 8400 Ω, C = 0.05*10^-6 F

8400 [ F1 ] 0.05E-6 [ R/S ]

Result:  3.789403407E2 Hz


E_output = 54 V, E_input = 28 V

54 [ F2 ] 28 [ R/S ]

Result:  5.70471457 dB


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. 


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