Retro Review: HP 40gs

Retro Review:  HP 40gs

Quick Facts

Model:  HP 40gs

Company:  Hewlett Packard

Years:  2006-2010s

Type:  Graphing

Batteries: 4 x AAA plus backup batter CR2032

Operating Mode:  Algebraic

Memory Registers: 27 real variables (A - Z, Θ); and 10 of Lists (L#), Statistics (C#), Complex Numbers (Z#), Matrices (M#), Graphic Objects (G#)

Original Price:  about $100.00 

Memory:  256 KB RAM and 2 MB Flash

Other Features

*  Numerical calculus:  integral and derivative

*  Floor, ceiling, fraction, integer, mantissa, exponent parts

*  Complex numbers

*  Polynomial calculations and roots 

*  Matrices and lists

*  Conversions and library of scientific constants

A great feature is the HELPWITH command, as called with the keystrokes [ SHIFT ] [ 2 ] (SYNTAX).  

Keyboard

The keys are pretty responsive.  The keyboard is a beautiful dark gray with light gray and black keys.  The knocks:  first, the alpha characters are in gold, which the font does not contrast well the background.   Another thing I do not like is the alpha characters are placed below keys.  For example:  [ VARS ] has the character A, [ SIN ] has the character E.  

Another challenge is that the double quotes and single quotes are not available directly from the keyboard, and must be accessed through the CHARS menu.   In regular calculation, this may not make much of a difference, but in programming, it makes a big difference when it comes to messages and prompts.   The alpha-lock is regulated to a soft key.  

Equation Writer and CAS 

The HP 40gs has two ways to operate computer algebra system commands:

*  From Home, use of the symbolic variables which takes the form of S# (S1, S2, S3, etc).

*  Equation writer, which is selected by the (CAS) soft key.   In the equation writer, you can build and simplify equations.   The equation writer can use any variable, and is similar to the HP 48S and 48G family (including the HP 50g).   

Aplets 

Aplets are the HP 40gs' applications which includes:

*  Finance:  Time Value of Money and Amortization Table

*  Function:  Plot up to ten functions, F#(X)  where # 0-9

*  Inference:  Hypothesis tests

*  Linear Solver:  Solve 2 x 2 or 3 x 3 linear systems

*  Parametric:  Plot up to ten parametric pairs, X#(T), Y#(T)

*  Polar:  Plot up to ten polar equations, R#(Θ)

*  Quad Explorer: Dynamic graphing, y = a*(x+h)^2 + v

*  Sequences: Plot up to ten sequences, U#(N), with one or two initial conditions

*  Solve:  Store up to ten equations, solve for any one at a time

*  Statistics:  Statistics for 1 or 2 variables.  In 2 variable statistics, 8 regressions plus a user-defined 

*  StreamSmart:  Data streamer device which collects data, stream it, and analyze data 

*  Triangle Solve:  Solves for right triangles and regular triangles

*  Trig Explorer: Dynamic graphing:  f = sin(x ± n*π) and f = cos(x ± n*π)

Aplets can be modified and copied.  

Programming

The program language of the HP 40gs is the same as the HP 38G/39G series.  Each line, except for the last line, must end with a colon (:).   Arguments are separated with a semicolon (;).  

The learning curve of the programming language is little complex, especially when it comes to setting views and customizing aplets.   Thankfully the user guide is thorough, so make sure you have the book or the pdf download, which you can access here:

http://h10032.www1.hp.com/ctg/Manual/c00748685.pdf

  

Two Sample Programs

HP 40gs Program RANDLIST

Generate a list of random numbers of length N.

INPUT N; "LIST LENGTH"; "N:"; ""; 5:

MAKELIST(RANDOM,X,1,N,1)▶L0:

ΣLIST(L0)▶S:

S/N▶A:

-10 ▶Xmin:

10 ▶Xmax:

-10 ▶Ymin:

10 ▶Ymax:

ERASE:

DISPXY -6; 4; 2; "Σ:":

DISPXY 0; 4; 2; S:

DISPXY -6; 1; 2; "μ:":

DISPXY 0; 1; 2; A:

DISPXY -6; -2; 2; "n:":

DISPXY 0; -2; 2; N:

FREEZE:

HP 40gs Program PLOTPX

Asks for A, B, and C in a quadratic equation and stores it to the Function F0(X)

DISP 1; "2022-08-15 EWS":

DISP 2; "y=Ax^2+Bx+C":

FREEZE:

SELECT Function:

INPUT A; ""; "A"; ""; 1:

INPUT B; ""; "B"; ""; 1:

INPUT C; ""; "C"; ""; 1:

'A*X^2+B*X+C' ▶ F1(X)

CHECK 1:

MSGBOX "PRESS PLOT"

Note:  This language is similar to the later HP Prime, which most line ending with a semicolon.  

A Predecessor to the HP Prime?  Final Thoughts 

A lot of the features and structure of the HP 40gs would be present in the HP Prime:  among other things, a solver, program that can select aplets (apps) and set custom views but most of all, a separate CAS mode.  

The HP 40gs is a nice calculator with a ton of features.  I think the HP 40gs was rarely available in the United States because of the CAS mode, because like the HP 39gs, the 40gs is aimed towards the education market.  The key contrast could be better and adding the quotes to the keyboard would be nice.

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. 

HP and Swiss Micros 41C and 42S Series: Stack Storage Operations

HP and Swiss Micros 41C and 42S Series: Stack Storage Operations

Introduction  

The HP 41C and HP 42S families, including the Swiss Micros DM41, DM42, Free42, and Plus42, includes the ability to execute storage arithmetic on any of the four* stack levels X, Y, Z, and T.  

The storage arithmetic operator takes whatever value is in the X stack and applies it to any stack level.  If we enter a number before the stack arithmetic operation, the stack lifts first, then executes the stack arithmetic operation.   See the examples section for illustrations.  

*Some calculators allow for a bigger number of stack levels, like 8.  

Examples

Example 1:  

Keystrokes:  3 [ ENTER ] [ ENTER ] 1 [ ENTER ]

Stack:

T:  3

Z:  3

Y:  1

X:  1

Keystrokes:  41:  [ STO ] [ + ] [ . ] (Y)    42:  [ STO ] [ + ] [ . ]  (ST Y)

Stack:

T:  3

Z:  3

Y:  2

X:  1

Keystrokes:  3 

Stack:

T:  3

Z:  2

Y:  1

X:  3_

Keystrokes:   41:  [ STO ] [ + ] [ . ] (Y)    42:  [ STO ] [ + ] [ . ]  (ST Y)

Stack:

T:  3

Z:  2

Y:  4

X:  3

Example 2:  

Keystrokes:  3 [ ENTER ] [ ENTER ] 1 [ ENTER ]

Stack:

T:  3

Z:  3

Y:  1

X:  1

Keystrokes:  41:  [ STO ] [ + ] [ . ] (Z)    42:  [ STO ] [ + ] [ . ]  (ST Z)

Stack:

T:  3

Z:  4

Y:  1

X:  1

Keystrokes:  3 

Stack:

T:  4

Z:  1

Y:  1

X:  3_

Keystrokes:   41:  [ STO ] [ + ] [ . ] (Z)    42:  [ STO ] [ + ] [ . ]  (ST Z)

Stack:

T:  4

Z:  4

Y:  1

X:  3

Note:  Casio fx-991EX Week - September 5, 2022 to September 9, 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. 

Lists in Numworks - Version 19.2

Lists in Numworks - Version 19.2

Introduction

In Version 19,  lists were added as an object in the Numworks calculator.  We can define and name lists with any values that we want. Lists are designated by the brackets { }. 

*   The values can be real number, complex numbers, numbers with units, scientific constants, and combinations of those types.   What is not allowed in lists are strings and matrices.

*  The indexing of lists starts with 1.   We can call a list's elements by the parenthesis after the list name.  For example,  xlist(10) recalls the 10th element of the list xlist.

*  { f(k) }_k≤value generates a list of f(k) from k=1 to value, step 1.   The variable can be almost any variable you want, except e and i.  e is designated as the exponential constant (about 2.71828...) and i is designated as the imaginary number √-1.   The limits are strictly from 1 to value.

*  Once a user defined list is created, the individual values cannot be changed.   Furthermore, there are no augment or delete commands.  In this sense, user defined lists acts like tuples in Python.

*  Lists can be recalled in the Statistics and Regression apps.   The system named lists V#, X#, and Y# are updated accordingly.

* Defining a list of random values will always change the randomized values every time a user defined list is recalled.  

Please note that this is for Version 19.2.  

Screenshots are captured using the Numworks Emulator on July 10, 2022:  www.numworks.com/emulator

Note:  Casio fx-991EX Week - September 5, 2022 to September 9, 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. 

Rationalizing a Quadratic Polynomial

Rationalizing a Quadratic Polynomial

Problem

Rewrite the Quadratic Polynomial 1 + A*x + B*x^2 as a rational function of polynomials.  A and B are real numbers (however, this should work if A and B were complex numbers).  

1 + A*x + B*x^2 → p(x) / q(x)

Attempt 1:  1 + A*x + B*x^2 → (1 + C*x) / (1 + D*x)

1 + A*x + B*x^2 = (1 + C*x) / (1 + D*x)

(1 + A*x + B*x^2) * (1 + D*x) = (1 + C*x) / (1 + D*x) * (1 + D*x)

A*x + B*x^2 + D*x + A*D*x^2 + D*B*x^3 = C*x

Comparing the powers of x:

constant:  0 = 0

x:  A + D = C

x^2:  B + A*D = 0

x^3:  B*D = 0

This leads to either B=0 or D=0

Assume B=0. 

Then B + A*D = 0

A*D = 0

If A=0, then D = C, which leads to:

1 + A*x + B*x^2 = (1 + C*x) / (1 + D*x)

1 = (1 + C*x) / (1 + C*x)

1 = 1

If D=0, then A = C

1 + A*x + B*x^2 = (1 + C*x) / (1 + D*x)

1 + C*x = (1 + C*x) 

If D=0, then B=0, and we get the same results as above.   

Ultimately this transformation to (1 + C*x) / (1 + D*x) leads to nothing useful.

Attempt 2:  1 + A*x + B*x^2 → (1 + C*x^2) / (1 + D*x)

 

1 + A*x + B*x^2 = (1 + C*x^2) / (1 + D*x)

(1 + A*x + B*x^2) * (1 + D*x) = 1 + C*x^2 

(A + D)*x + (B + A*D)*x^2 + B*D*x^3 = C*x^2

Comparing the powers of x:

constant:  0 = 0

x:  A + D = 0

x^2:  B + A*D = C

x^3:  B*D = 0

A + D = 0 implies that A = -D or D = -A

Also either B = 0 or D = 0.

Assume B = 0. Then with A = -D:

A*D = C

-D*D = C

C = -D^2

1 + A*x + B*x^2 = (1 + C*x^2) / (1 + D*x)

1 -  D*x = (1 - D*x^2) / (1 + D*x)

1 -  D*x = ((1 - D*x) * (1 + D*x))/ (1 + D*x)

1 - D*x = 1 - D*x

If we assume that D = -A, then:

C = -A^2 and

1 + A*x = (1 - A*x^2) / (1 - A*x)

1 + A*x = ((1 - A*x)  * (1 + A*x)) / (1 - A*x)

1 + A*x = 1 + A*x

Assume D = 0.

Then A = 0 and B = C:

1 + B*x^2 = 1 + B*x^2

1 + C*x^2 = 1 + C*x^2

Again, we have transformations that are trivial.

Attempt 3:  1 + A*x + B*x^2 → (1 + C*x^3) / (1 + D*x)

1 + A*x + B*x^2 = (1 + C*x^3) / (1 + D*x)

(1 + A*x + B*x^2) * (1 + D*x) = 1 + C*x^3

(A + D)*x + (B + A*D)*x^2 + B*D*x^3 = 1 + C*x^3

Comparing the powers of x:

constant:  0 = 0

x:  A + D = 0

x^2:  B + A*D = 0

x^3:  B*D = C

This implies that:

A + D = 0

D = -A

B + A*D = 0

B+ A*-A = 0

B = A^2   (this restricts A and B)

B * D = C

(A^2)*(-A) = C

C = -A^3

We can conclude that B = A^2, C = -A^3, D = -A

The relationship between A, B, C, and D are all connected in this case.

Examples:

A = 2 ⇒ B = 4, C = -8, D = -2 and

1 + 2*x + 4*x^2 = (1 - 8*x^3) / (1 - 2*x)

A = -2 ⇒ B = 4, C = 8, D = 2 and

1 - 2*x + 4*x^2 = (1 + 8*x^3) / (1 + 2*x)

Note:  Casio fx-991EX Week - September 5, 2022 to September 9, 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. 

Plus42: The Solver SEQ Command

Plus42: The Solver SEQ Command

Solver SEQ Function

In the calculator app Plus42, we can evaluate a sequence of calculations to return a result.  The SEQ is also good for the FOR loop because it allows us to initialize several variables.

Syntax:

SEQ( expr1 : expr2 : expr3: ... : expr_n )

I think this is best illustrated by example.

Example 1

Calculate   f(x) = x * p ÷ t^2

where:

p = 0.01 * a^2

a = 36 *t^2 - 280

Equation:

SEQ1:F=SEQ(L(A:36×T^2-280):L(P:.01×G(A)^2))×X÷EXP(T)

The commands listed in the SEQ are:

1.  L(A:36×T^2-280):  Let A = 36 * T^2 - 280.  T is the input variable.  

2.  L(P:.01×G(A)^2)):  Let P = 0.01 * A^2;  the Get command (G) is used to keep A from the variable menu

The answer is stored in P.

Variables in calculation:  F, T, X

X = 2, T = 0.8, solve for F = 593.3698253

X = 0.3, T = 9, solve for F = 2.57253759

T = 11.1, F = 58.68, solve for X = 22.4853545434

Example 2

Calculate p = Π( n / 4, n = 1 to m)

Equation:

SEQ2: P=FOR(SEQ(L(A:1):L(N:1)):G(N)<=IP(M):L(N:G(N)+1):L(A:G(A)×(G(N)÷4)))

The commands listed in the SEQ are:

1.  L(A:1):   Let A = 1

2.  L(N:1):  Let N = 1

In this example, SEQ is in a FOR command and is used to initialize variables.   

Variables in calculation: M, P

M = 3, solve for P = 0.09375

M = 6, solve for P = 0.17578125

M = 18, solve for P = 93166.79943

If you have not checked out the Plus42 app, please check it out.  The Plus42 is an HP-42S Simulator which builds up on the Free42.   However, the Plus42 adds the solver in a style of the HP 17B and 27S, graphing commands, and units.

Thomas Okken's Plus42 page:  https://www.thomasokken.com/plus42/

Note:  Casio fx-991EX Week - September 5, 2022 to September 9, 2022 

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. 

Review: Casio Nursing Calculator SP-100UNSU

Review:  Casio Nursing Calculator SP-100UNSU

It's rare, but there are nursing-based calculators that are available in the market from time to time.  Here is a review of one.

Quick Facts

Model:  SP-100USNU

Company:  Casio

Years:  2022-current

Type:  Nursing 

Batteries: CR2016

Operating Modes:  Chain

Number of Registers: 1

Display:  10 digits, with prompts

Cost:  $39.99 USD

The calculator that I ordered came in an ecology-friendly package, with the calculator wrapped in a bubble wrap pocket.  Unfortunately, it does not have a hard sliding case or the calculator being in a wallet.

The calculator casing has a nice silver finish with white keys.

A Calculator for the Nursing and Pharmacy Industries

The SP-100USNU is built for the nursing and pharmacy industries.  Five of the keys deal with six calculations, which each of the top keys serving as a toggle.  What is great about the SP-100USNU is that the calculator gives prompts and menus as necessary.  The display is crisp and clean.  

[ BMI ]:   Body Mass Index.   Two input modes:  lbs/ft/in,  kg/cm

[ Dose ]:  Does Calculation.   Solve for Ordered Dose given Desired Dose, or solve for Desired Dose given Ordered Dose.  Doses are in mL, with amount of the medicine (per pill, capsule, gummy, etc.) in mg.

[ BSA ]:  Body Surface Area approximation in square meters.  Two input modes:  lbs/ft/in, kg/cm

[ eGFR ]:  Calculate the estimated glomerular filtration rate which assist in diagnosis of chronic kidney disease.   The CKD-EPI equation, which factors a person's skin color (black vs. non-black), sex (male vs. female), weight (for body surface area), creatinine secretion (mg/dL), and the person's age.  What is calculated?   CCr, Creatinine Clearance, in mL/min and eGFR, estimated glomerular filtration rate, in mL/min/1.73m^2.   The average body surface area is estimated to be 1.73 m^2.  

[ IV rate ] (date):  This key toggles between two types of calculations: IV Drip Rate and Date calculation.

IV Drip Rate:  three inputs are needed.   Volume of medicine in mL, time that the IV lasts in minutes, and drop factor in gtts/mL (typically 15 - 20 gtts/mL).  gtts stands for number of drops.  The drip rate is given in gtts/min.  

Date:  Calculate the date functions for all dates in the 21st century (January 1, 2000 to December 31, 2099).  

1.  Before:  calculate the date before the base date.  

2.  After:  calculate the date after the base date.  

3.  Period: calculate the days between dates.

The formulas are given at the back of box (expect for CCr and the date calculations) and listed in the manual (expect for date calculations).   Hence the box and the manual is a neat reference.   

Link to the manual, which has to be downloaded:  https://support.casio.com/storage/en/manual/pdf/EN/004/SP-100USNU_EN.pdf

Regular Calculator  

The SP-100USNU is also a regular four function calculator.  Unfortunately neither the percent function (%) nor the square root function (√) are present.  I would think that the nursing profession would work with percentages. We do have memory calculations (M+, M-, MRC).

Also you may need access to a conversion table (via calculator, book, internet, all of the above) to do common conversions.   I would have loved to see that present here too.

Conversion Factors

1 kg = 2.20462 lb

1 in = 2.54 cm

1 L = 1000 mL

1 hr = 60 min

During the prompts, we can execute side calculations before entering the required entry in the prompt.

Final Thoughts

I did not like the fact that that calculator does not have the % and the √ functions.  It would be nice if conversion factors were included (especially with the money).  However, the formulas included make a great specialized calculator.   

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 TI-Basic and TI Nspire CX II Python: Gamma by Multiplication Recursion Property

TI 84 Plus CE TI-Basic and TI Nspire CX II Python:   Gamma by Multiplication Recursion Property

Introduction

The program calculates the gamma function for any real positive number in tenths by the multiplication recursion:

Γ(x + 1) = x * Γ(x)

For example:  

Γ(2.5)

= 1.5 * Γ(1.5)

= 1.5 * 0.5 * Γ(0.5)

≈ 1.5 * 0.5 * 1.772453851

≈ 1.329340388

Reduce x by 1 until 1 is in between 0.1 and 1. 

Gamma Values:

Γ(0.1) = 9.513507699

Γ(0.2) = 4.590843712

Γ(0.3) = 2.991568988

Γ(0.4) = 2.218159544

Γ(0.5) = 1.772453851

Γ(0.6) = 1.489192249

Γ(0.7) = 1.298055333

Γ(0.8) = 1.164229714

Γ(0.9) = 1.068628702

Γ(1) = 1

TI-84 Plus CE Program: GAMMATEN

TI-Basic

Notes:

*  To get the small L to create lists with custom names, get the character with the key strokes:  [ 2nd ] ( list ), OPS, B.  L.   In this listing, I will write L^ to symbolize the lower case L.

* L^TEN is a custom list.

Program listing:

{9.513507699, 4.590843712, 2.991568988, 

2.218159544, 1.772453851, 1.489192249,

1.298055333, 1.164229714, 1.068628702

1}→L^TEN

ClrHome

Disp "GAMMA X (NEAREST 0.1)"

Input "X≥0.1, X?",X

round(X,1)→X

fPart(X)*10→F

If F=0:10→F

1→G

While X>1

G*(X-1)→G

X-1→X

End

G*L^TEN(F)→G

Disp "EST. GAMMA: ", G

TI-NSpire Python Script:  gammaten.py

The code is defined as a function.   

def gammaten(x):

  lten=[9.513507699]

  lten.append(4.590843712)

  lten.append(2.991568988)

  lten.append(2.218159544)

  lten.append(1.772453851)

  lten.append(1.489192249)

  lten.append(1.298055333)

  lten.append(1.164229714)

  lten.append(1.068628702)

  lten.append(1)

  #print("gamma(x) to the nearest 0.1")

  x=round(x,1)

  f=round(10*(x-int(x))-1)

  g=1

  while x>1:

    x-=1

    g*=x

  g*=lten[f]

  return [g,f]

# list[-1] gets last item too

# round integers for accurate results!

# 2022-06-13 EWS

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. 

Plus42 and Casio fx-9750GIII: Magnetic Flux Density of a Solenoid

Plus42 and Casio fx-9750GIII:  Magnetic Flux Density of a Solenoid

Introduction:  Ampère's Circuital Law

A solenoid is an electromagnetic coil or wire that controls a magnetic field.  The solenoid is a key part of the automobile starter.  

Constant Radius:  If the solenoid has a constant radius, the simplest case, the magnetic flux density is calculated as:

B = μ0 * N * I / L

where

μ0  = permeability in a vacuum.   More about this later.

N = number of turns

I = current in Amps

B = magnetic flux density in Telsa (T, or Wb/m^2, or kg/(A*s^2)

Various Radii:  If the radii vary in the solenoid, we can calculate the sum of the magnetic flux density per each point z_i and radius R_i.  

B_i = μ0 * I * N * R_i^2 / (2 * (R_i^2 + z_i^2)^1.5)

The μ0 Constant:  Or Is It?

The μ0 represents the permeability in a vacuum, and traditionally, it is a constant defined as:

μ0 = 4 * π * 10^-7  T * m/A  ≈ 1.25663706144 * 10^-6 T * m/A  

However, CODATA has a slightly different value assigned, here is the May 2019 value:

μ0 ≈ 1.25663706212 * 10^-6  T * m/A  

Since the traditional value is reasonably close, I am going to use it the programs presented here.

Casio fx-9750GIII Program:  SOLENOID

Option 1:  Constant Radius

Option 2:  Various Radii, the total flux is calculated

Program:

4×π×10^(-7)→U

Menu "SOLENOID","CONSTANT RADIUS",1,"DIFFERENT RADII",2

Lbl 1

"TURNS"?→N

"CURRENT (A)"?→I

"LENGTH (M)"?→L

Goto 3

Lbl 2

"TURNS"?→N

"CURRENT (A)"?→I

0→B

"NO. OF RADII"?→J

For 1→K To J

"DATA"

K⊿

"RADIUS"?→R

"LENGTH"?→Z

B+(U×I×N×R)÷(2×(R^2+Z^2)^1.5)→B

Next

Goto 3

Lbl 3

"FLUX DENSITY:"⊿

B

Plus42 (HP 27S/19B/17B) Equations:  SOLENOID

Constant Radius:

SOLE1:B=4×π×ALOG(-7)×N×I÷L

Various radii (single calculation):

SOLE2:B=(4×π×ALOG(-7)×I×N×R)÷(2×(R^2+Z^2)^1.5)

Use a register to store and sum B_i.

Examples 

Constant Radius:

N = 8000 turns

L = 0.06 m

I = 30 A

B ≈ 5.026548246 Telsa

Various radii (total):

N = 2500 turns

I = 15A

(point z, radii r)

z_1 = 0 m, r_1 = 0.6 m

z_2 = 0.5 m, r_2 = 1 m

z_3 = 0.8 m, r_3 = 0.7 m

B ≈ 0.09604006539 Telsa

Sources

"CODATA Recommended Values of the Fundamental Physical Constants:  2018"  National Institute of Standards and Technology.  United States Department of Commerce.  May 2019  https://physics.nist.gov/cuu/pdf/wall_2018.pdf   Retrieved June 7, 2022. 

"Solenoid"  Wikipedia.   Last edited April 30, 2022. https://en.wikipedia.org/wiki/Solenoid    Accessed June 1, 2022. 

Nave, Carl Rod.   "Solenoid as Magnetic Field Sources"  HyperPhysics  Georgia State University.  2016  http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/solenoid.html  Accessed June 3, 2022. 

This blog entry is dedicated to Chris B. 

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. 

Texas Instruments: TI-36X Pro and TI-30X Pro Mathprint

 Essentially, the Texas Instruments TI-36X Pro and the TI-30X MathPrint are functionally equivalent.  What makes the two calculators different?

*  The TI-36X Pro is sold in the United States and in lot of the world, with the TI-30X MathPrint is sold primarily from Europe.  I ordered my TI-30X Pro MathPrint from the United Kingdom.  

Product pages from Texas Instruments:

TI-36X Pro (United States and Canada)

https://education.ti.com/en/products/calculators/scientific-calculators/ti-36x-pro

TI-30X MathPrint (Denmark, in Danish):

https://education.ti.com/da/products/calculators/scientific-calculators/ti-30x-pro-mp#specifications

Australia has a TI-30XPlus MathPrint, which is styled like the TI-30X Pro MathPrint, but without calculus functions.

https://education.ti.com/en-au/products/calculators/scientific-calculators/ti-30x-plus-mp?category=overview

*  Thanks to the body of the calculator being curved, the TI-36X Pro is slightly bigger than the TI-30X Pro MathPrint. 

*  The screen on the TI-36X Pro is a curved trapezoid, while the screen of the TI-30X Pro MathPrint has is rectangular.  

*  The TI-36X Pro has a circular arrow keypad while the TI-30X Pro MathPrint has a rectangular arrow keypad.  

* The TI-30X Pro Math print has black characters, while the TI-36X Pro has blue characters.

* The font on the keys of the TI-30X Pro Math are larger than than the font on the TI-36X Pro's keys.

Here are some pictures.

Either calculator is worth buying.  You  can see my review of the TI-36X Pro from 2011 here:

http://edspi31415.blogspot.com/2011/04/ti-36-pro-review.html

P.S. I still wish the TI-36X Pro/TI-30X Pro MathPrint had an alpha key instead of one key to press multiple times to get different variables.  That is my biggest gripe. 

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.