Wednesday, January 31, 2018

HP Prime Collection of Functions

HP Prime Collection of Functions

Introduction

The program COLLECTION has 13 historical, archaic, and unusual functions.  They are:

Name
Function and Syntax
Formula Used
Versine
VERS(X)
1 – cos x
Coversine
COVERS(X)
1 – sin x
Haversine
HAV(X)
sin(x/2)^2
Normalized Sampling
NSINC(X)
sin(π * x)/(π * x)
Exsecant
EXSEC(X)
sec x - 1
Gundermannian
GD(X)
atan(sinh x)
Inverse Gundermannian
INVGD(X)
asinh(tan x)
Dilogarithm
DILN(X)
  (ln t / (t – 1) dt, 1, x)
Exponential Polynomial
EPOLY(N, X)
Σ(x^j / j!, j, 0, n)
Hypotenuse of a Right Triangle
HYPER(A,B)
(a^2 + b^2)
Langevin Function
LANGEVIN(X)
1/tanh x – 1/x
General Mean Function
GENMEAN(N,A,B)

N = 1, arithmetic mean
N = 2, root mean square
N = -1, harmonic mean
((a^n + b^n) / 2)^(1/n)
Logarithmic Integral
Li(X)
Ei(LN(x))

Radians mode is assumed. 

Note:  All the functions listed above can be called separately.  Note that there is no COLLECTION program per se, it is file that contains all the functions. 

HP Prime Program: COLLECTION

// 2018-01-28 EWS
// A collection of functions
// An Atlas of Functions-2nd Ed-2009

// Note the COLLECTION is a file
// EXPORT can't have a ; attached in this case

EXPORT VERS(X)
BEGIN
// versine
RETURN 1-COS(X);
END;

EXPORT COVERS(X)
BEGIN
// coversine
RETURN 1-SIN(X);
END;

EXPORT HAV(X)
BEGIN
// haversine
RETURN SIN(X/2)^2;
END;

EXPORT NSINC(X)
BEGIN
// normalized sampling
RETURN SIN(π*X)/(π*X);
END;

EXPORT EXSEC(X)
BEGIN
// exsecant
RETURN SEC(X)-1;
END;

EXPORT GD(X)
BEGIN
// Gundermannian
RETURN ATAN(SINH(X));
END;

EXPORT INVGD(X)
BEGIN
// Inverse Gundermannian
RETURN ASINH(TAN(X));
END;

EXPORT DILN(X)
BEGIN
// dilogarithm
RETURN ∫(LN(T)/(T-1),T,1,X);
END;

EXPORT EPOLY(N,X)
BEGIN
// exponential polynomial
// order, value
RETURN Σ(X^J/J!,J,0,N);
END;

EXPORT HYPER(A,B)
BEGIN
// hypotonuse of a right
// triangle
RETURN √(A^2+B^2);
END;

EXPORT LANGEVIN(X)
BEGIN
// Langevin function
RETURN 1/TANH(X)-1/X;
END;

EXPORT GENMEAN(N,A,B)
BEGIN
// General mean
// N = 1, arithmetic mean
// N = 2, root mean square
// N = −1, harmonic mean
RETURN ((A^N+B^N)/2)^(1/N);
END;

EXPORT Li(X)
BEGIN
// Logathmic Integral
RETURN CAS.Ei(LN(X));
END;


Source:

Keith Oldham, Jan Myland, and Jerome Spainer.  An Atlas of Functions  2nd Edition.  Springer:  New York.  2009  e-ISBN 978-0-387-48807-3

Eddie

This blog is property of Edward Shore, 2018.  

Monday, January 29, 2018

HP Prime and TI-84 Plus CE: Heat Properties of Water

HP Prime and TI-84 Plus CE:  Heat Properties of Water


Introduction

The program HEATH20 calculates three heat properties of liquid water based on its temperature.  The program accepts three measurements for liquid water, Fahrenheit (°F), Celsius (°C), or Kelvin (K).

Formulas Used:

Specific heat capacity of water (amount of heat added or removed from an object to cause a temperature change), measured in J/(g*°C):

C =

4.218 + 3.47*10^-4 *(T – 273)^2, for 233 K ≤ T < 274 K 

4.175 + 1.3*10^-5 * (T – 308)^2 + 1.6 * 10^-8 *(T-308)^4, for 274 K ≤ T ≤ 308 K

(slight adjustment on the limits to allow for 273 K to be calculated using the former formula)

Latent heat of evaporation, measured in kJ/kg: 

V = 1000 * (2.5 * (273.15/T)^(0.167 + 3.67 * 10^-4 *T))

Latent heat of fusion, measured in kJ/kg:

M = 333.5 + 2.05 * T – 0.0105 * T^2


HP Prime Program HEATH20

EXPORT HEATH2O()
BEGIN
// Water Properties
// EWS 2018-01-28
// Seinfeld, Pandis
// Atmospheric Chemistry - 2006

// input of temperature
LOCAL ch,T,C,V,H;
INPUT({T,{ch,{"°F","°C","K"}}},
"Temperature",
{"Temp: ","Unit: "});
IF ch==1 THEN
T:=5/9*(T-32)+273.15; END;
IF ch==2 THEN
T:=T+273.15; END;

// Specific heat (liquid)
CASE
IF T≥233 AND T<274 THEN
C:=4.218+3.47ᴇ−4*(T-273)^2; END;
IF T≥274 AND T≤308 THEN
C:=4.175+1.3ᴇ−5*(T-308)+
1.6ᴇ−8*(T-308)^4; END;
DEFAULT
C:=0; END;

// Latent Heat: Evaporation
V:=(2.5*(273.15/T)^
(0.167+3.67ᴇ−4*T))*1000;

// Latent Heat: Fusion
M:=333.5+2.05*(T-273.15)
-0.0105*(T-273.15)^2;

// Results
PRINT();

PRINT("Temp: "+STRING(T)+" K");

IF C≠0 THEN
PRINT("Spec. Heat-Liquid (kJ/g*K)");
PRINT(STRING(C)+" kJ/(g*K)");
END;

PRINT("Latent Heat - Evaporation:");
PRINT(STRING(V)+" kJ/kg");

PRINT("Latent Heat - Fusion");
PRINT(STRING(M)+" kJ/kg");

END;

TI-84 Plus CE Program HEATH20

"EWS 2018-01-28"
"SEINFELD, PANDIS"
"ATMOSPHERIC CHEMISTRY,2006"

Input "TEMPERATURE: ",T
Menu("TEMP. UNIT","°F",1,"°C",2,"K",3)
Lbl 1
5/9*(T-32)+273.15→T
Goto 3
Lbl 2
T+273.15→T
Goto 3
Lbl 3
0→C
If T≥233 and T<274
Then
4.218+3.74E­4*(T-273)^2→C
End
If T≥274 and T≤308
Then
4.175+1.3E­5*(T-308)^2+1.6E­8*(T-308)^4→C
End
(2.5*(273.15/T)^(.167+3.67E­4*T))*1000→V
333.5+2.05*(T-273.15)-.0105*(T-273.15)^2→M
ClrHome
Disp "TEMP (K):",T
If C≠0
Then
Disp "SPEC. HEAT (KJ/(G*K)",C
End
Disp "LATENT-EVAP. (KJ/KG)",V
Disp "LATENT-FUSION (KJ/KG)",M

Example

0°C (273.15 K):

Results:

Temp:  273.15  K
Specific Heat:  4.218008415 kJ/(g*K)
Latent Heat – Evaporation:  2500 kJ/kg
Latent Heat – Fusion:  333.5 kJ/kg

Source:

John H. Seinfeld, Spyros N. Pandis.  Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd Edition.  John Wiley & Sons, Inc:  Hoboken, New Jersey. 2006  ISBN-13: 978-0-471-72018-8

Eddie


This blog is property of Edward Shore, 2018.

Thursday, January 25, 2018

App Review: SciPro Math - Campusano (Apple iOS)

App Review:  SciPro Math - Campusano (Apple iOS)

Note:  This is a review of the first version of the app.  According to their Instagram page, Version 2 is going to be released in February 2018.  I look forward to what SciPro Math has in store.  


Title:  SciPro Math
Author:  Robert Antonio Campusano Acotsa of Unlimited Power
Platform:  iOS
Price: $4.99 (January 2018), $9.99 thereafter
Version:  unknown


Screen shots from SciPro Math
Introduction

The SciPro Math calculator app by Unlimited Power is a scientific calculator that features over 400 functions, including many applications such as conversions, linear, quadratic, cubic, and quartic equations, geometry formulas, linear systems, and finance. Depending on the orientation of your device (iPhone or iPod Touch), the app either is a basic calculator (portrait) or scientific calculator (landscape).  This review will focus on the scientific calculator.

Scientific Calculators: Four Modifier Keys!

The calculator has four modifier keys:  [ 2nd ], [ 3rd ], [ rad ] which acts like the 4th key and displays [ deg ] when its turned on, and [ 5th ].

The [ rad ] key is also the angle toggle.  When gray, the calculator is in degrees mode.  When the 4th key is turned on, the calculator is in radians mode.

Unlike most scientific calculators when modifiers are turned on for one keystroke, the modifiers on the SciPro Math, stay on until the user turns the modifier off.  You can have more than one modifier turned on (even all four) at once.  This is important because the keyboard changes depending on what modifier keys are turned on.  The SciPro Math website will give the keyboard layout, so I will just summarize the possible keyboards here:

Modifiers Turned On
Keyboard
None
Trig:  sin, cos, tan
Hyperbolic:  sinh, cosh, tanh
Other:  10^x, log, e^x, ln, x^3, x^2, square root, cube root, random numbers from 0 to 1, golden ratio constant (ϕ), reciprocal, π
Also sci, csi, and bta (bi-tangent).  I don’t know what these functions are.
Storage variables: A, B, C
2nd
Trig: csc, sec, cot
Hyperbolic: csch, sech, coth
Other: logarithms of base 2, e^(-x), ln(1+x), e^(x-1), gamma constant (γ), x^-2, power, root, absolute value, factorial (of positive integers only)
Also: log_u, but seems to only accept one argument, bsc, bcs, bct (again if you have information, I’d be greatful)
Storage variables: D, E, F
3rd
Trig:  sin^-1, cos^-1, tan^-1
Hyperbolic: sinh^-1, cosh^-1, tanh^-1
Other: degree and radian conversions, hypotenuse function, √2, fractions of π
Storage variables: G, H, I
Rad
Length Conversions:  in/mm, in/cm/ ft/m, gal/L, lb/kg, km/mi
Storage variables: M, N, O
5th
Linear Equations
2nd, 3rd
Combinations, permutations, factorials (of positive integers only), temperature conversions between Celsius, Fahrenheit, and Kelvin, random integers (dice, coin, deck of cards, from 1 to 10)
Also: [x-y], I don’t get this one either
Storage Variables: J, K, L
2nd, rad
Length Conversions: in/ft, ft/yd, yd/mi, mm/cm, cm/m, m/km
Storage Variables: P, Q, R
2nd, 5th
Systems of Linear Equations, 2 x 2 and 3 x 3
3rd, rad
Cooking Conversions: tablespoons/teaspoons, tablespoons/cups, cups/pints, pints/quarts, quarts/gallons/ teaspoons/milliliters
Storage Variables: S, T, U
3rd, 5th
Quadratic and Cubic Equations
Rad, 5th
Geometry:  spheres (.sp), circles (.c), trapezoids (/t), rectangles (.r), triangles (Heron’s formula, .t), boxes (.b)
2nd, 3rd, rad
Mass Conversions: oz/lb, lb/tons, tons/l.t., g/kg, t/kg, ton/t  (t is UK tons?, ton: US tons)
Storage Variables: V, W, X
2nd, 3rd, 5th
Quartic Equations
Storage Variables: C, D, E
3rd, rad, 5th
Geometry:  cylinders (.cy), Cones (.co)
Finance:  payment of a loan or mortgage (.b), present value of an annuity (.p), future value of an annuity (.f).
I have not figured out what the (.i) is for (yet).
2nd, 3rd, rad, 5th
Storage Variables A-Z

Chain Mode

The SciPro Math app does not follow the order of operations, as we would expect.  You would note that none of these keyboards has parenthesis.  This means the operation you press will have an effect on the number in the display.

For example, if you want to calculate (7 * 2) + (16 * 5), you would have use the temporary memory keys, like so:

[mc]  (to clear memory)
7 [ * ] 2  [ = ] [m+]
16 [ * ] 5 [ = ] [m+]
[mr]

Result: 94

Another example:  √((2^3 – 3)/(3^2 + 5)).  Let’s use memory variables A and B this time, with the no modifiers turn on.

2 [x^3] [ - ] 3 [ = ] [→Xv] [Av]
3 [x^2] [ + ] 5 [ = ] [→Xv] [Bv]
[Av] [ ÷ ] [Bv] [ = ]

Result:  0.5714285714286

Documentation

Despite having a website, on thing that this app lacks is documentation.  There is no on-help facility.  Their web page does not have any details on the keys. 

There are several keys on this app that I have questions about like [sci], [bct], and [x-y] that I mentioned that I do know what these functions are or how they work. If you do, please feel free to leave some comments, it is much appreciated. 

There are some tutorials on the SciPro Math’s YouTube page, which I will document next.

Tutorials

The SciPro Math app has a YouTube which has the following tutorials:


Quadratic Equations
Cubic Equations
Quartic Equations

I wish more videos were on this page (and hopefully they will put more tutorials on the page in the future).

I’m going to discuss some of the features for this App.

Hypotenuse Function
Modifiers: 3rd

The [hyp] function calculates the hypotenuse √(a^2 + b^2). Syntax:  a [hyp] b [ = ]

Example:  Calculate √(9^2 + 16^2)

Keystrokes:  9 [hyp] 16 [ = ]

Result:  18.3575597506858

CAUTION:  I think the keys for [ a ], [ A° ], [ b ], [ B° ], and [ c= ] are supposed to be used for Pythagorean Theorem.  With A° and B° are corresponding angles to the sides with length a and b.  However, when I tested these keys, c, which I think represents the hypotenuse, I get unexpected answers.

For example, if I entered a = 5 and b = 3, I expect answer of c = √(5^2 + 3^2) = 5.83095189485.  Instead, I get an answer of 8.  (5 + 3). 

Finance
Modifiers:  3rd, 4th (to rad), 5th

Notes:

* Interest is entered as a decimal.  For example, enter 5% as 0.05.

* Enter periodic interest rate, not annual interest.  For monthly mortgages or payments, divide the annual rate by 12.  This is similar to the HP 12C series or the classic BA 35.

*  End-of-period payments are assumed.

At the time of the review, there was not a lot documentation on the finance section, I compared results with financial calculators to figure some of the keys out.

Payment of a Loan/Mortgage (Installment Buying)

Input:
Amount of loan stored in A.b
Periodic interest stored in i.b
Number of periods stored in n.b

Output:
Press [R.b=] for the payment

Example:  Find the monthly payment of an auto loan with $22,000 to be financed at 4% annual rate.  The term is 6 years.

Keystrokes:
22000 [→(X)v] [ A.b ]
0.04 [ ÷ ] 12 [ = ] [→(X)v] [ i.b ]
6 [ * ] 12 [ = ] [→(X)v] [ n.b ]
[R.b=]

Result:  344.194027595888

The monthly payment is $344.19.

Present Value of an Annuity (Annuity PV)

Input:
Periodic payment stored in R.p
Periodic interest stored in i.p
Number of periods stored in n.p
Output:
Press [A.p=] for the present value of the annuity

Example:   What would an investor need to deposit if the investor expects to have a $1,500.00 monthly payment, every month for the next 30 years?  The bank is expecting to pay at a rate of 4.18% annual.

Keystrokes:
1500 [→(X)v] [R.p]
0.0418 [ ÷ ] 12 [ = ] [→(X)v] [i.p]
30 [ * ] 12 [ = ] [→(X)v] [n.p]
[A.p=]

Result:  307471.201192414

The investor should deposit $307,471.20. 

Future Value of an Annuity (Annuity Amount)

Input:
Periodic payment stored in R.f
Periodic interest stored in i.f
Number of periods stored in n.f

Output:
Press [A.f=] to calculate the future value of the annuity

Example:  An investor contributes $1,325.00 to a saving fund that compounds monthly at a 4.08% annual rate.  What will be the value of the annuity in 5 years?

Keystrokes:
1325 [→(X)v] [R.f]
0.0408 [ ÷ ] 12 [ = ] [→(X)v] [i.f]
5 [ * ] 12 [ = ] [→(X)v] [n.f]
[A.f=]

Result:  88024.3906860951

The annuity is expected to have a value of $88,024.39 in 5 years.

CAUTION:  I am not 100% sure of what the “.i” keys calculate. 

Systems of Linear Equations
Modifiers:  2nd, 5th

This keyboard is pretty much straight forward. 

2 x 2 Systems:

a1 * x + a2 * y = a3
b1 * x + b2 * y = b3

The [ D2*2 ] key calculates the determinant of the matrix [ [a1, a2], [b1, b2] ].  Store the values in to a1, a2, a3, b1, b2, and b3 by using the [ →Xv ] key.  Solutions can be found by pressing the [ x2*2 ] and [ y2*2 ] keys respectively.

Example:

Solve the system:

4x + 2y = 1
-3x + 6y = -8

Keystrokes:
[reset]
4 [→(X)v] [ a1 ], 2 [→(X)v] [ a2 ], 1 [→(X)v] [ a3 ]
3 [(-)] [→(X)v] [ b1 ], 6 [→(X)v] [ b2 ], 8 [(-)][→(X)v] [ b3 ]

[ x2*2 ] returns 0.733333333…
[ y2*2 ] returns -0.966666666…
[ D2*2 ] returns 30 (determinant)


3 x 3 System:

a1 * x + a2 * y + a3 * z = a4
b1 * x + b2 * y + b3 * z = b4
c1 * x + c2 * y + c3 *z = c4

Input:  [ a1 ] through [ c4 ] keys

Solutions:  [ x3*3 ], [ y3*3 ], [ z3*3 ]; with determinant [ D3*3 ]

Verdict

I really like what the SciPro Math app is going for:  app containing many solvers for common problems in mathematics, and life.  I also like the wide variety of mathematical constants, it’s not every day that a calculator has keys dedicated to ϕ, π/4, and √2. 

The keys are nice size and the screen is readable.  The user may like a chain operating system but it will take a little getting used to for a scientific calculator app.  The lack of parenthesis may be a turn off for some users.  Remember, this is not an RPN calculator.

I would to see the angle mode become a separate mode, not tied to a modifier.  Having it tied to a modifier key (4th) defeats the purpose of the angle mode.  There is also an absence of settings (fixed, engineering, scientific notation, not to mention, no scientific notation key).

If you are looking for statistical functions, including regression analysis, this is not the app to find it. 

The biggest problem I have is the lack of documentation.  This is a fairly young app (November 2017), so I hope to see more documentation and the bugs worked out in future revisions and updates.  I see the potential. 

If you are interested, I would suggest getting the app now (January 2018) for only $4.99 before it goes up to $9.99 in February. 

Eddie


This blog is property of Edward Shore, 2018.

Thursday, January 18, 2018

App Review: SciPro Calculator (Apple iOS)

App Review:  SciPro Calculator (Apple iOS)

Title:  SciPro Calc
Author:  Jerry Montgomery, Digital Ambience, Inc
Platform:  iOS
Price: Free (as of 1/18/2018)
Version:  1.2.5  (2017)



Portrait Orientation:  Basic Calculator

In the portrait orientation, SciPro Calculator is a basic function calculator.  The screen is impressive.  The black display clearly shows the large blue numbers and function indicators.  There is only 1 memory, but you get M+, M-, MC, and MR all on separate keys, which is nice.  You can turn the AC key into an AC/backspace key in Basic mode throughout the options.

Scroll down will give you access to the calculator’s history, allowing to view and copy results, even share them by email. 

Landscape Orientation:  Scientific and Programmer Calculator

Scientific Calculator



The calculator follows a post-fix algebraic system (think of a Texas Instruments TI-30 Xa or a Casio fx-260 II as examples).  The SciPro Calculator app can handle        numbers as high as 10^9864, which is very impressive.  

Functions include:

* trigonometry and their inverses (sine, cosine, tangent)
* hyperbolic functions
* factorial, which handles all real numbers not just integers (nice!)
* logarithms and exponentials, base e, 2, and 10
* square root, cube root, power, root
* modulus (see note below)
* Two angle modes: degrees, radians

Modulus Function

The modulus function works well on positive numbers.  Comparing results using negative numbers to an HP Prime:

78 mod -11:

HP Prime:  -10
SciPro Calculator:  1


-78 mod 11:

HP Prime: 10
SciPro Calculator: -1

The scientific app does lack fractions and statistics.  Other than that, it’s a good standard scientific calculator.

Programmer Calculator



The programmer calculator is a Boolean math calculator with four integer representations:  Binary (64 bits), Octal, Decimal, and Hexadecimal.  Depending on whatever mode you are in, the numeric keyboard highlights only the appropriate keys, so there is no accidently typing A in Decimal mode or 9 in Octal mode.



The ENC key turns on a unique feature, binary numbers which will give you the ASCII character, Unicode character, and the color determined by the RGB color.  This is most useful when the calculator is Hexadecimal representation.  You can use the arithmetic and the other functions to work with colors.  Sweet!

Functions featured in the Programmer Calculator:

*  Byte and Word Flip
*  Bit count and shift
*  Random integer
*  Boolean operators:  AND, OR, NOR, XOR
*  Modulus
*  1’s and 2’s compliments (Yes, there is a difference)

The programmer calculator can handle integers as high as:  18,446,744,073,709,551,615.

Caution:  No Sign Bit

Be aware that there are no sign bits with this calculator, everything is positive integer representation.  Hence this why 0 – 1 returns 18,446,744,073,709,551,615 (64 1s in Binary) instead of -1. 

Impressions

I like the unique feature of the programmer calculator having the ability to look up ASCII, Unicode, and RGB codes.  It’s a fun feature.

You probably won’t have to worry if you have to work with large numbers (at least numbers 10^100 and beyond), the SciPro Calculator app can handle it.

The blue numbers against the black screen is really nice, big, and readable, regardless of orientation of your iPhone or iPod Touch.

This is a nice calculator to have, especially for quick calculations.


Eddie

This blog is property of Edward Shore, 2018

Update to the Big Font Math Reference

Original post:   https://edspi31415.blogspot.com/2018/04/april-11-2018-seven-years.html I added several sections to the Big Math Referenc...