Casio fx-991CW: Second Derivative

Casio fx-991CW: Second Derivative

Calculating Higher Order Derivatives

A general formula to estimate derivatives of order n, where n is a positive integer (see Sources, Wikipedia):

d^n/dx^n = lim h→0 (1÷h^n * Σ((-1)^(k+n) * comb(n,k) * f(x+k*h), k=0, n)

The first, second, and third derivatives are derived from the above formula like so:

n = 1:

d/dx

= lim h→0 (1÷h * Σ((-1)^(k+1) * comb(1,k) * f(x+k*h), k=0 to 1)

= lim h→0 (1÷h * ((-1)^(0+1)*f(x) + (-1)^(1+1)*f(x+h))

= lim h→0 (1÷h * (-f(x) + f(x+h))

= lim h→0 (f(x+h) - f(x)) ÷ h

This is the famous forward difference formula.

n = 2:

d^2/dx^2

= lim h→0 (1÷h^2 * Σ((-1)^(k+2) * comb(2,k) * f(x+k*h), k=0 to 2)

= lim h→0 (1÷h^2 * ((-1)^2*comb(2,0)*f(x) + (-1)^3*comb(2,1)* f(x+h) + (-1)^4*comb(2,2)*f(x+2*h))

= lim h→0 (f(x) - 2*f(x+h) + f(x+2*h)) ÷ h^2

n = 3:

d^3/x^3

= lim h→0 (1÷h^3 * Σ((-1)^(k+3 * comb(3k) * f(x+k*h), k=0 to 3)

= lim h→0 (1÷h^3 * ((-1)^3*comb(3,0)*f(x) + (-1)^4*comb(3,1)*f(x+h) + (-1)^5*comb(3,2)*f(x+2*h)

+ (-1)^6*comb(3,3)*f(x+3*h))

= lim h→0 (-f(x) + 3*f(x+h) - 3*f(x+2*h) + f(x+3*h)) ÷ h^3

Using the fx-991CW

- - - - - - - - - -

Start with a note: Commentary and limitations: The functions f(x) and g(x), along with the calculus functions sum (Σ), integral (∫), and derivative (d/dx), has x as variable. It makes it a challenge that x is the only variable the functions f and g can take.

Example:

f(x)=x^2

g(x)=Σ(f(x),x=0 to 5)

Executing g(x) will take the values x=0 through x=5 no matter what value we put for g. The answer, in this example, will always return 0^2 + 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55.

- - - - - - - - - -

We can still use f and g to set up specific derivatives in order n. For the second dervative, set up f and g:

f(x) = <function in terms of x>

g(x) = (f(x+2×A)-2×f(x+A)+f(x))÷A²

Store h in A. We can also choose an h and write in the formula directly.

Remember, this will calculate an approximation. With the most appropriate settings for h, we can get the best approximation.

Examples

For all the examples, A is set as 10^-7. The calculator is set to Radians. g(x) is the second derivative approximation.

Example 1:

f(x) = sin(x), f''(x) = -sin(x)

g(x) = (f(x+2×A)-2×f(x+A)+f(x))÷A²

x = 0.6; g(x): -0.564642551 (actual: -0.5646424734)

x = 2.8; g(x): -0.334988057 (actual: -0.3349881502)

Example 2:

f(x) = 2×e^(0.3×x), f''(x) = 0.18×e^(0.3×x)

g(x) = (f(x+2×A)-2×f(x+A)+f(x))÷A²

x = 0; g(x): 9/50 = 0.18 (actual: 0.18)

x = 1.2; g(x): 0.25799928 (actual: 0.2579992946)

Example 3:

f(x) = 1.1×x^3, f''(x) = 6.6×x

g(x) = (f(x+2×A)-2×f(x+A)+f(x))÷A²

x = 0; g(x): 6.6×10^-7 (actual: 0)

x = 2.2; g(x): 14.52 (actual: 14.52)

Sources

McCarty, George. Calculator Calculus. EduCALC Publications. E. & F.N. Spon: London. 1975, ISBN 0- 419-12910-3

Wikipedia "Numeric differentiation" Wikimedia Foundation, Inc. Last Edited June 17, 2025. Last Accessed July 7, 2025. https://en.wikipedia.org/wiki/Numerical_differentiation

Eddie

All original content copyright, © 2011-2025. 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.

The author does not use AI engines and never will.

TI-84 Plus CE Python: Drawing Shapes with the ti_plotlib module

 TI-84 Plus CE Python: Drawing Shapes with the ti_plotlib module

Introduction

Here are four scripts to draw shapes:

RECT8: rectangles and squares centered at (0, 0)

ELLIPSE8: ellipses and circles centered at (0, 0)

POLYGON8: polygons given the vertex points and number of vertices

INVFUNC8: draws a function f(x) and it’s inverse f^-1(x). Define the function is defined in the f(x) subroutine in the program.

The plot window is sized in sync with the TI-84’s screen size (320 pixels x 220 pixels) so that squares look like squares and circles look like circles. The window parameters are set as such:

Xmin = -16, Xmax = 16

Ymin = -10.5, Ymax = 10.5

TI-84 PLUS CE Python Script: RECT8.py

import ti_plotlib as plt

from math import *

# draw an rectangle using ti_plqtlib

# get parameters

print("Press [clear] to \nexit the graph.")

print("x:[-16,16] \ny:[-10.5,10.5]")

a=eval(input("horiz. length? "))

b=eval(input("vert. length? "))

# plot routine

plt.cls()

plt.title("Rectangle")

plt.window(-16,16,-10.5,10.5)

plt.axes("on")

plt.grid(1,1,"dot")

# color: blue

plt.color(0,0,192)

# pen size

plt.pen("medium","solid")

plt.line(-a/2,b/2,a/2,b/2,"")

plt.line(-a/2,-b/2,a/2,-b/2,"")

plt.line(-a/2,-b/2,-a/2,b/2,"")

plt.line(a/2,-b/2,a/2,b/2,"")

plt.show_plot()

TI-84 PLUS CE Python Script: ELLIPSE8.py

import ti_plotlib as plt

from math import *

# draw an ellipse using ti_plqtlib

# get parameters

print("Press [clear] to \nexit the graph.")

print("x:[-16,16] \ny:[-10.5,10.5]")

a=eval(input("x axis? "))

b=eval(input("y axis? "))

# plot routine

plt.cls()

plt.title("Ellipse")

plt.window(-16,16,-10.5,10.5)

plt.axes("on")

plt.pen("medium","solid")

plt.grid(1,1,"dot")

# color: green

plt.color(0,192,0)

for i in range(128):

  x=a*cos(i*pi/64)

  y=b*sin(i*pi/64)

  plt.plot(x,y,"o")

plt.show_plot()

TI-84 PLUS CE Python Script: POLYGON8.py

import ti_plotlib as plt

from math import *

# draw an rectangle using ti_plqtlib

# get parameters

print("Press [clear] to \nexit the graph.")

print("x:[-16,16] \ny:[-10.5,10.5]")

n=int(input("# of vertices? "))

a=eval(input("x1? "))

b=eval(input("y1? "))

x=[a]

y=[b]

for i in range(n-1):

  print("vertex ",i+2)

  c=eval(input("x? "))

  d=eval(input("y? "))

  x.append(c)

  y.append(d)

x.append(a)

y.append(b)

# plot routine

plt.cls()

plt.title("Polygon")

plt.window(-16,16,-10.5,10.5)

plt.axes("on")

plt.grid(1,1,"dot")

plt.color(75,0,130)

plt.pen("medium","solid")

for i in range(n):

  x0=x[i]

  y0=y[i]

  x1=x[i+1]

  y1=y[i+1]

  plt.line(x0,y0,x1,y1,"")

plt.show_plot()

TI-84 PLUS CE Python Script: INVFUNC8.py

Define f(x) in the def f(x) function routine. The math module is imported.

import ti_plotlib as plt

from math import *

# f(x) and f**-1(x)

# define f(x)

def f(x):

  return x**2+6

# plot routine

plt.cls()

plt.title("f(x) and its inverse")

plt.window(-16,16,-10.5,10.5)

plt.axes("on")

plt.grid(1,1,"dot")

plt.pen("medium","solid")

for i in range(320):

  x=-16+i*32/320

  y=f(x)

  plt.color(0,0,192)

  plt.plot(x,y,"o")

  plt.color(255,165,0)

  plt.plot(y,x,"o")

plt.show_plot()

Download the four scripts here: https://drive.google.com/file/d/1ELL6mEzMXrIJlOSSFocOZGJTza-kBZoU/view?usp=sharing

Eddie

All original content copyright, © 2011-2024. 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 Prime and Casio fx-CG 50: Dedekind Sums

 HP Prime and Casio fx-CG 50: Dedekind Sums

Definition

The Dedekind Sum is defined as follows:

Let P and Q be relatively prime integers, that is GCD(P, Q) = 1.

Then S is the Dedekind sum as:

S = Σ( ((I ÷ Q)) × ((P × I ÷ Q)), for I=1 to Q)

The double parenthesis around the terms I ÷ Q and P × I ÷ Q signify a custom function:

(( X )) =

0, if X is an integer

X – FLOOR(X) – 1/2, if X is not an integer

If X is positive, X – INTG(X) – 1/2

HP Prime: DEDEKIND

EXPORT DEDEKIND(p,q)

BEGIN

// 2024-02-21 EWS

LOCAL s,i,a,b;

// Calculation

IF CAS.gcd(p,q)==1 THEN

s:=0;

FOR i FROM 1 TO q DO

a:=i/q;

IF FP(a)==0 THEN

a:=0;

ELSE

a:=a-FLOOR(a)-0.5;

END;

b:=p*i/q;

IF FP(b)==0 THEN

b:=0;

ELSE

b:=b-FLOOR(b)-0.5;

END;

s:=s+a*b;

END;

RETURN s;

ELSE

RETURN "p and q are not relatively prime.";

END;

END;

Casio fx-CG 50: DEDEKIND

244 bytes

Code:

 “DEDEKIND SUM: S(P,Q)”

“P”? → P

“Q”? → Q

If GCD(P,Q)≠1

Then

“P AND Q ARE NOT RELATIVELY PRIME”

Stop

For 1→ I To Q

I÷Q → A

Frac A=0 ⇒ 0 → A

Frac A≠0 ⇒ A – Intg A – 0.5 → A

P × I ÷ Q → B

Frac B=0 ⇒ 0 → B

Frac B≠0 ⇒ B – Intg B – 0.5 → B
S + A × B → S

Next

S

Note: The are 6 spaces between NOT and RELATIVELY to align the text.

Examples

P	Q	Results (fraction)	Results (decimal)
2	17	8/17	0.4705882353
1	21	95/63	1.50793650794
9	43	27/86	0.3139534884
8	67	53/134	0.3955223881
4	75	649/450	1.442222222
14	57	-140/171	-0.8187134503

Sources

Shipp, R. Dale. “Table of Dedekind Sums” Journal of Research of the National Bureau of Standards-B. Mathematics and Mathematical Physics Vol. 69B, No 4, October-December 1965 https://nvlpubs.nist.gov/nistpubs/jres/69B/jresv69Bn4p259_A1b.pdf

Retrieved February 21, 2024

Weisstein, Eric W. "Dedekind Sum." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DedekindSum.html

Retrieved February 18, 2024

Eddie

All original content copyright, © 2011-2024. 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.

Integrating Absolute Value Functions

Integrating Absolute Value Functions

Calculating ∫ abs(f(x)) dx

The function abs(f(x)) can be broken into two parts, depending on the sign of f(x):

abs(f(x)) = 

{   f(x)  when f(x) > 0

{  -f(x)  when f(x) < 0

General procedure:

1.  Find the roots of f(x).  

2.  Split the integral at the roots.

3.  For areas where f(x)>0, calculate the sub-area ∫ f(x) dx.

4.  For areas where f(x)<0, calculate the sub-area ∫ -f(x) dx.

5.  Total all the sub-areas.

Let's illustrate this with examples.  Screen shots are made with the HP Prime emulator.  The absolute value function |f(x)| is graphed in blue, while f(x) is graphed in red (for illustrative purposes).  

Example 1:  ∫ |4x- 2| dx from x = 0 to x = 5

∫ |4x- 2| dx from x = 0 to x =5

The root of (4x - 2) is x = 1/2.     

When x < 1/2, (4x - 2) < 0.   

When x > 1/2, (4x - 2) > 0.

Break down the integral into:

∫ (|4x- 2| dx from x = 0 to x =5)

= ∫ ( -(4x- 2) dx from x = 0 to x =1/2) + ∫ (4x- 2 dx from x = 1/2 to x =5)

=  1/2 + 81/2

=  82/2

=  41

We can type in the entire integral into a calculator or app.  Depending on the function and the advanced engine of the calculator, the accuracy may be affected.   Calculators and apps with advanced engines include the HP Prime, Wolfram Alpha, and Desmos.   (Your mileage may vary)

Example 2:  ∫ |x^3 - 28x + 48| dx from x = 0 to x = 3

∫ |x^3 - 28x + 48| dx from x = 0 to x = 3

The roots of x^3 - 28x + 48 are at x = -6, x = 2, and x = 4.   Since the root x = 2 is the only root in the interval [0, 3], this is the one root we are working with.  

With root x = 2, 

When x < 2, x^3 - 28x + 48 > 0

When x > 2, x^3 - 28x + 48 < 0

Then:

∫ ( |x^3 - 28x + 48| dx from x = 0 to x = 3 ) 

= ∫ ( (x^3 - 28x + 48) dx from x = 0 to x = 2 ) 

+ ∫ ( -(x^3 - 28x + 48) dx from x = 2 to x = 3 ) 

= 44 + 5.75

= 49.75

Example 3:  ∫ |e^(2x) - 2| dx from x = 0 to x = 2

The root of e^(2x) - 2 is x = ln 2 ÷ 2 ≈ 0.34657

Let A = ln 2 ÷ 2, and with root x = A,

When x < A, e^(2x) - 2 < 0

When x > A, e^(2x) - 2 > 0

∫ ( |e^(2x) - 2| dx from x = 0 to x = 2 )

=  ∫ ( -(e^(2x) - 2) dx from x = 0 to x = A ) + ∫( (e^(2x) - 2) dx from x = A to x = 2)

≈ 0.193147 + 22.99222

≈ 23.18537

Where is where this method returns approximates and using different calculators and apps may not produce the same results.  

HP Prime:  23.1853693777

Desmos:  23.1853693777

Wolfram Alpha:  23.1853693776920

TI-30X Pro MathPrint:  23.18537052

Hope this technique helps, 

Eddie

All original content copyright, © 2011-2023.  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 fx-991CW (and the lack of multi-statements)

Review:  Casio fx-991CW (and the lack of multi-statements)

Quick Facts

Model:  fx-991CW

Company:  Casio

Years:  Internationally: 2022 - present, United States: April 2023 - present

Type:  Scientific

Power:  Solar with 1 LR44 backup battery

Display:  Multiline, 4-color gray display

Original Price:  $21.00 - $22.99 U.S. Dollars, varies on the specific version

Number of Variables:  9

Operating System: Algebraic

Update on the Classwiz

The fx-991CW is an update in Casio's Classwiz series, specifically on the 2015 fx-991EX Classwiz.  

Check out my review on the fx-991EX Classwiz from November 2015 here:

http://edspi31415.blogspot.com/2015/11/casio-fx-991ex-classwiz-review.html

The modes on the Classwiz are:

Calculate:  the main app for mathematical calculations

Statistics:  1 to 2 variable statistics.  Regressions include:

Linear:  y=a+bx

Quadratic: y=a+bx+cx^2

Logarithmic:  y=a+b*ln(x)

Exponential:  y=a*e^(bx)

Power I:  y=a*b^x

Power II: y=a*x^b

Inverse:  y=a+b/x

Distribution:  Calculations involving the binomial, normal, and Poisson.  The Inverse Normal deal with the lower tail (left) probability only.  

Spreadsheet:  Like the fx-991EX and Casio's current graphing calculators, the fx-991CW has a spreadsheet which has a 5 x 45 cell capacity.  The total memory is increased to 2,380 bytes (from 1,700 bytes on the fx-991EX).  Basic spreadsheet features included are:  labeling cells, sum, mean, minimum, maximum, absolute cell references ($), copy, cut, and paste.  

Table:   Generate a table of one function or two functions.   The functions are defined as f(x) and g(x).  With a QR code, you can generate a graph of these functions.

Equation:   Solve linear systems, up to 4 x 4 equations.  Solve polynomials, up to 4th order.  Real coefficients only but complex roots are calculated.   The general equation solver is moved to this mode.   

Inequality:  Solve inequalities up for polynomials of orders 2, 3, and 4.

Complex Number:  Complex number arithmetic with polar/rectangular conversion, integer powers, real/imaginary parts, conjugate

Base N:  Integer arithmetic with Boolean logic.  Instead of keys, the [FORMAT] key cycles through the four modes: Decimal, Hexadecimal, Binary, Octal.   Binary integers are up to 31 bytes with 1 sign bit.  We can not store or recall varaible values in this mode.

Matrix:  Works with four matrices up to 4 rows and 4 columns.  Functions include transpose, inverse, and determinant.

Vector:  Works with 4 vectors with either 2 or 3 elements.  Functions include dot product, norm, and cross product.

Ratio:  Solves common ratio problems.

Math Box:  This is the a new feature to the Classwiz.   For the United States, the Math Box has two simulations:  Dice Rolls and Coin Toss.   Depending on the country, the CW may include additional features.  

Emulator and Classpad.net

Purchasing a fx-991CW came with a emulator license with ClassPad.net.   The license number can be obtained using the Get Started option from the Settings menu.   Use the QR code.  For my calculator, the license for using ClassPad.net is seven years at no cost.  However, using an emulator without first purchasing an eligible calculator will require an additional cost.  

You can find details about Classpad.net here:  https://classpad.net/intl/features/

Keyboard, What is Added, and What is Subtracted

The keyboard of the fx-991CW is quite different from the previous Casio calculators.   The keys are now round with a lot less labels.   Most of functions are now stored in the catalog and tools.  Let's go over some of these keys:

[ house icon ]: [HOME].   This is where we switch the modes of the fx-991CW.   There are no numerical shortcuts, so we have to arrow and scroll to select the mode we want.  

[ three lines ]: [SETTINGS].  The settings key replaces the SETUP key sequence.   

Also note that the sub menus are selected by either pressing [ → ] or [ EXE ].  If there are radio buttons, select the option desired.  

[ curved arrow ]: [EXIT/EDIT].  This key, on the 2nd row, 2nd key from the left, will be used to exit menus and re-edit expressions.   

[ double up arrow ]/[ double down arrow ]:  This key, top right of the calculator, is used to quickly scroll through menus or lists.  Think of this key as the Page Up/Page Down key.

[ < >x] ]/[VARIABLE]:  This is the variable key.

Here is where we will store and edit values that are stored in each of the nine variables.   This key replaces the STORE key.     If we are operate in a mode that does not allow for editing or store values, there will be a lock icon with the selected variable.  

To store a result:

1.  Execute operation or recalling a calculated stat variable.

2.  Press [VARIABLE].

3.  Select variable, press [ OK ].

4.  Select Store, press [ OK ].

To edit a variable's value:

1.  Press [VARIABLE].

2.  Select variable, press [ OK ].

3.  Select Edit, press [ OK ].

4.  Enter the new value, press [ OK ].

To recall a variable in a calculation:

1.  Press [ SHIFT ].

2.  Press any of the following keys to get the variable:

[ 4 ]:  A

[ 5 ]:  B

[ 6 ]:  C

[ 1 ]:  D

[ 2 ]:  E

[ 3 ]:  F

[ 0 ]:  x

[ . ]:  y

[ x10^ ]:  z

There is no ALPHA key as it was in past Casio calculators.  

[ f(x) ]/[FUNCTION]:  

Here is where we can store and use up to two functions: f(x) and g(x).  The great news is that f(x) and g(x) are no longer limited to the Table, they can be used in other modes such as Calculate.   The equations f(x) and g(x) are retained while switching modes but not retained when the calculator either is turned off or the Input/Output setting is changed.  A missed opportunity for the latter.

A plus is that either f(x) or g(x) can be a composite function.  That is f(x) can contain g(x) or g(x) can contain f(x).  

There are two ways to access the x variable:  its own key [ x ] or the key sequence [ SHIFT ] [ 0 ].  

[book]/[CATALOG]:  This is where all the functions and commands can be accessed.  The menu order of the catalog changes depending on the mode used.  Some submenus include:

Function Analysis:  The calculus functions, that used to be on the keyboard, are now stored in the Function Analysis menu:  derivative, integral, summation, logarithm*, log*, ln* (* also on the keyboard)

Probability:   % (divides the number by 100), factorial, permutation, combination, random number, random integer

Numeric:  Absolute Value, Round Off (round the number to the Fix settings internally)

Angle/Coord/Sexa...:  angle units (degrees, radians, grads, degrees minutes seconds*), polar/rectangular conversions (* also on the keyboard)

Sci Constants:  47 scientific Constants

Unit Conversions

[ three circles ]/[ TOOLS ]:  The TOOLS menu changes dynamically based on the mode.   For example, the Calculate mode will have an Undo function.

[ FORMAT ]:  Instead of the [S<=>D] key, we have the [FORMAT] key, which asks how to change the value:  Standard, Decimal, Improper Fraction, Mixed Fraction,  ENG (Engineering) Notation, Sexagesimal (degrees-minutes-seconds).

In Base mode, the [ FORMAT ] key toggles between the four bases (decimal, hexadecimal, binary, octal).

I did three comparison speed tests between the fx-991CW and fx-991EX  here:  https://www.youtube.com/watch?v=cj0Odnv0Mwk

As I understand, the fx-991CW has a faster processor than the previous fx-991EX.

Now let's talk about what is subtracted in this update.  You read this correctly, several features did not make it from the fx-991EX to the fx-991CW:

The  CALC feature where we could type in a formula, press [ CALC ] and have formula evaluation.  I was not able to find the CALC feature on the fx-991CW.

There is no longer the independent memory M, nor the storage arithmetic functions M+ and M-.  I miss this feature the most.  I really wish scientific and graphing calculators in general embrace store arithmetic like Hewlett Packard and Swiss Micros.

There is no longer the ability to use multi-statement expressions, with each expression separated with a colon.  Even when it was available, (1) storing results immediately terminated the expression (forcing the use of Ans and when available, PreAns to make using results in the next part possible), and (2) when replayed, the statement was broken up into separate parts.  

Addendum 

Note (4/12/2023):  I am wrong when I said that storing results in multi-statements on the fx-991EX (not the fx-991CW) is impossible.  We use the equals key ([ALPHA] ( = )), as in this example:

A = 9 : B = 8 * A

Csaba Tizedes uses the multi-statement and CALC feature on the fx-991EX to create an IF-THEN-ELSE structure.  In this video Tizedes uses this structure to solve equations using the Bisection method.  The IF-THEN-ELSE structure tests whether a number is positive or negative.  Please take a look his video:

https://www.youtube.com/watch?v=umxScZL1V6A

Gratitude to Csaba Tizedes, this video is shared with his permission.  

Final Thoughts

Overall, the fx-991CW is pretty solid calculator with a readable screen and a lot of features.  My favorite part of the updated is the ability to use the functions f(x) and g(x) outside of the table function.  I also like the catalog key and the page up/page down key.

I get that Casio is going for a simpler, non-busy keyboard.  However, I prefer a separate ALPHA key, along with a STORE key: it's the most efficient way to store variables.   A consequence of a non-busy keyboard is that a lot of the commands can only be accessed through menus.  The ALPHA key could have freed nine keys for more common shifted keys such as x!, polar/rectangular conversions, etc.   I would have liked to see a couple of customizable keys where we can store commands, which could be the shift of the multiplication and division keys.  The financial calculator FC-200V has two slots to store commands.

The faster processor and the better screen are pluses.  You will still get a lot for the money spent on the fx-991CW. 

Caveat:   However, if you want, need, or require subtracted features described above (CALC feature, independent memory, multi-statement expressions), you are better off buying the former fx-991EX or a fx-115ES Plus 2nd Edition.  

Unfortunately, removing the multi-statement, Casio sapped it's algorithmic power with the fx-991CW, and it needs to come back.  Furthermore, please put integer part, fraction part, and sign functions.   

Eddie

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