RealCalculator-Help Index
General usage
Supported PocketPCs
Changing the calculator
Clear, Backspace and scrolling
Using cut, copy and paste
Using undo
Using the history
The option dialog
Defining your own buttons and expressions
Defining your own constants
Changing calculation modes
Help
The scientific calculator
Using the function buttons
The input-field
Memory-Handling
Parameters
Calculation Sequence
The function-plotter
Specifying functions
Plotting functions
Plotting fractals
The plotting window
Zoom in and zoom out
Change the plotting region
Change the quality level
Save a bitmap of the plot
Cancel the calculation
The matrix-calculator
Input of matrices
Matrices with complex numbers
Matrices with real numbers
The complex-calculator
The function-calculator
Symbolic function derivation
Symbolic function simplifier
Symbolic function calculations
Calculating polynom parts
Polynomdivision
Numeric function solver
Numeric function derivation
Numeric extrema calculation
Numeric saddle point calculation
Numeric discontinues calculation
Calculation of f(0)
Calculation of f(x)
Calculation of an integral
The equation solver
General
Example
Loading and storing equations
Calculation of solutions
The computer-calculator
Changing the mode
Available Functions
Conversions
The statistic calculator
Changing the mode
Available Functions
Regression
Plotting
Loading and storing statistic data
The metrics converter
How it works
Adding and deleting metrics kind
Adding and deleting metrics
Reset the metrics
Copyright © 2003-2007 Vorwerk&Stengel GbR
In this chapter, the general usage of RealCalculator is explained.
Changing the view
You can switch between the different calculators by selecting a calculator from the menue "view"
In a registered shareware version, the following calculators are available :
- Scientific Calculator
- Function Plotter
- Function Calculator
- Matrix Calculator
- Complex Number Calculator
- Computer Calculator
- Statistic Calculator
- Metric Converter
Supported PocketPC
RealCalculator is available in 2 different versions. First, there exists a
setup for older PocketPC's with PocketPC 2002 or earlier. This version works
on PocketPC's with WindowsCE 3.0 or later which do have a mips-, sh3 or
arm-processor(StrongArm, too).
On the other hand, there is a version for PocketPC 2003 and PocketPC 2003
Second Edtion, which only works on ARM-Systems. Within this version, VGA-Display
(640x480) is supported, as well as the landscape display.
This software works normally on all standard PocketPCs.
Clear, backspace and scrolling
In every calculator, at the bottom of the display field there are 4 buttons:
- scroll to left (for both input and output)
- red arrow: backspace (or delete selection)
- clear: Clear whole input or matrix or the selected parts
- scroll to right (for both input and output)
Those buttons are working with the field that has the focus (is selected). For instance,
if a result is very big and you cannot see the whole result, select the result field and
press the "scroll to right"-button to see more of it.
Using cut, copy and paste
You can copy the content of an input field or output field to the clipboard by using the
"Edit->Copy" menu or by using the middle bitmap button of the menu.
You can cut the content of an input field and this content will be copied to the
clipboard by using the "Edit->Cut" menu or by pressin on the left bitmap button
of the menu
The content of the field which has the focus will be inserted in the clipboard. If you
have selected just a part of an expression, only this part will be copied to the clipboard.
By using the menu "Edit/Paste" (or the right bitmap button of the menu), the copied expression
will be pasted to another input field. As a result, you are able to enter an expression
in the scientific calculator and copy it to the function plotter's input field.
You can copy and paste a whole matrix in the matrix calculator. If you are editing a field
of the grid either the selected part or the whole field will be copied.
Please acknowledge, that the copied text is not available to other applications, yet.
Also, a copied text of another application cannot be pasted into RealCalculator.
Using undo
Whenever there is an input, the last expression is stored. By selecting the menu "Edit->Undo",
the last expression will be transferred to the input field again. This may be important, if you have
cleared the input field by accident.
Using the history
The last ten calculations you have made are stored in a history list. By selecting the item "Edit->History"
in the menu, you are able to select one of the last expressions and the selected item will be transferred
to the input field again.
The option dialog
Within the option dialog, it is possible to change the calculation mode, the
sign which is used for the imaginary part of a complex number, the
default language and the background color of the main window.
Changing the calculation mode
Within the option dialog you can change the mode of calculation between
floating mode, scientific mode and engineering mode.In the following table, the
result of the expression "sin(2)" is shown, with a selected precision of 4.
| floating |
scientific |
enginieering |
| 0.9093 |
9.093E-001 |
909.3E-003 |
The difference between scientific mode and engineering mode is, that the exponent
in engineering mode can always be divided by three. In floating mode, the precision
defines the decimal places. Please keep in mind, that the overall precision is limited
to 15 decimal places, so there may less decimal places than those you have specified.
This feature is only available either for the scientific or for the complex calculator.
Changing the background color
Furthermore, in the option dialog it is possible to change the background-color for all calculators.
By selecting the "Use standard"-checkbox, the background is lightgray and the
buttons are gray. If you deselect this checkbox, the color for the background is selectable
by clicking on the colors-button below of the checkbox.
Changing the language
By default, the language for RealCalculator is English. By selecting "Deutsch" from the
"Language"-combobox, all messages, menu-items and dialogs are in german.
Changing imaginary sign
The sign which is used for the imaginary part of a complex number can be selected
in the option dialog, too. In mathamatics, "i" is the standard, whereas in
electronics, very often "j" is used.
Show result in input field
With this option it is possible to show the result in the input field, and the
calculated expression is copied to the output field. Therefore, it is possible
to calculate something and use the result as an input for another calculation
immediatelly.
Defining your own buttons and expressions
With RealCalculator you are able to define your own buttons and expressions, for instance for
expressions you use very often. By selecting the "btns"-button, your user-defined
buttons are shown. The value of these buttons as well as the labelling can be changed
by selecting the "Edit->My Buttons / Functions" menu. A second way to edit and select
your user defined constants and expressions is the "const/expr"-button. After pressing it,
a dialog appears in which you can either select an constant or expression or start the edit-
dialog for them.
You do have the possibility to define new expressions with zero or up to four parameters.
For defining new expressions with zero parameters, you have to do the following:
1. Select the "Edit-->My Buttons" menu
2. Select the button from the combobox to which your expression will be assigned
3. If you have entered the expression in the input-field, press the button "Copy expression from input"
4. Enter or correct the expression in the big editfield.
5. Enter the text of the button
6. Press "OK".
For defining new expressions with one ore more parameters, you have to do the following:
1. Select the "Edit-->My Buttons" menu
2. Select the button from the combobox to which your expression will be assigned
3. If you have entered the expression in the input-field, press the button "Copy expression from input"
4. Select the number of paramters in the combobox right of the button mentioned above.
5. Replace "<name>" with the name of your function.
6. Enter or correct the expression after "=" in the big editfield.
7. Enter the text of the button
8. Press "OK".
Example:
You want to add a new function for calculation of percentage. Following steps have
to be done:
1. Select the "Edit-->My Buttons" menu
2. Select the button from the combobox to which your expression will be assigned
4. Select "2 Parameter" form the combobox. The text "<name>(x,y)=" will
be inserted into the big editfield.
5. Replace "<name>" with "perc".
6 Insert "x/y*100" after the "="-sign.
7. Enter "perc" as the text of the button. Of course, it must not be the same as the name
of the function previously entered.
8. Press "OK".
After that, you can press the "btns"-button and your user-defined button "perc"
will be shown with the text ("perc") you have entered. By pressing that button,
the expression "percentage(,)" will be inserted into the input field. After
defining the values for the 2 parameters (e.g. "percentage(12,100)") and pressing
the "="-button, the new function is calculated and the result (12) is shown in
the output-field.
Sometimes, the new function should be more readable. For this there exists the
possiblity to rename the parameters. For instance, if you want to add the
function u=r*i, you can define the function as "uri(r,i)=r*i". Furthermore, the
parameters name may contain more than one char, for instance you could define
a function hours like "hours(minutes,seconds)=minutes/60+seconds/3600".
Defining your own constants
There are a lot of constants in chemistry and physics. You can define new constants
by selecting the "Edit-->Constants" menu.
You can define up to 14 constants. They can be accessed by pressing the "btns"-button twice.
If you are pressing this button once more, the normal buttons will appear again. For defining
a constant, you have to do the following steps:
1. Select the "Edit-->Constants" menu
2. Select the number of the constant from the combobox.
3. Enter the constant name in the first editfield.
4. Enter the constant value in the second editfield.
5. Press OK.
You can define a constant with the name "a" and the value "9.81", for instance. Note,
that the value of the constant may be an expression, for example "sin(2)". By pressing
the "btns"-button twice, your user-defined constants will be displayed with the name you specified.
By pressing the mentioned "a"-Button, "{a}" will be inserted in the input field. At the time of
calculation, "{a}" will be replaced automatically by "9.81".
Changing calculation modes
For a lot of calculations, there are different modes which can be used. For
instance, for the scientific calculator, you can use deg, rad or grad for
changing the way how angles are calculated (degree, radiants, 100 radians).
You can set this mode easily by pressing on the corresponding button an the
top of the display, or - a little bit more complicated - by pressing the "mde"-button
one ore more times. The inv-button and the hyp-button is also selectable, directly.
For the computer calculator, the standard buttons inv, hyp, deg, rad and grad are not
selectable, but the buttons bin, hex, dec and oct.
Help
There are 4 menuitems in the help-menu:
- About RealCalculator: Shows informations about RealCalculator
- Shareware version: Shows, if the software has been registered
- Offline Help: This item is available for registered users only. Registered users
can download and install this helpfile which will be shown after selecting this item. Please
enter the registered users area at our website for more informations.
- Registering RealCalculator: Shows informations about how to register RealCalculator.
Back to top of page
|
The scientific calculator
|
The element on top of the scientific calculator is the input field of your expression.
Furthermore, the different options (like deg/rad/grad, hex/bin/dec/oct) will be displayed
in that field. By pressing the "="-button, the expression is evaluated and the result is
displayed in the read-only output field.
Some of the paragraphs in this chapter are also used by the other calculators, so please
read this chapter carefully.
Using the function buttons
The function buttons like sin, cos etc. will result in an expression like "sin()" to
be added in the input field. After that, you have to enter the parameter of the function.
So you can build such complex expressions like
ln(e/2)*8*(4+2)^6
By pressing the "inv"-button, the inverse-buttons will be shown. By pressing the "hyp"-button,
you can see the hyperbolicus of sin/cos/tan/cot. By selecting both hyp and inv, the
inverted hyperbolicus are shown, for example arcsinh.
The following table lists the buttons being available including their respective meanings.
| inv |
hyp |
btn |
meaning |
| off |
off |
sin |
sinus-function |
| off |
off |
cos |
cosinus-function |
| off |
off |
tan |
tangens-function |
| off |
off |
cot |
cotangens-function |
| off |
off |
abs |
absolute value of a number
abs(-2)=2
abs(2)=2 |
| off |
off |
ln |
natural logarithm |
| off |
off |
sqr |
square root |
| off |
off |
sum |
sum of n (n +(n-1)+...+2+1)
sum(4)=10
Sum is only defined for natural numbers! |
| off |
off |
n! |
factorial of n
(n*(n-1)*...*2*1)
3!=6 |
| off |
off |
mod |
modulu
mod(3,2)=1
mod(4,2)=0
mod(6,4)=2 |
| off |
off |
int |
integer-value of a number
int(2.1)=2
int(-2.1)=-2 |
| off |
off |
x^y |
power |
| on |
off |
asin |
arcsin |
| on |
off |
acos |
arccos |
| on |
off |
atan |
arctan |
| on |
off |
acot |
arccot |
| on |
off |
sig |
signum of a number
sign(-2.1)=-1
sign(2.1)=1 |
| on |
off |
e |
e |
| on |
off |
gcd |
Greatest common divisor |
| on |
off |
lg |
logarithm of base 10 |
| on |
off |
rand |
randomize numer (0-32768) |
| on |
off |
n over k |
(n!)/(k!(n-k)!)
n and k must be natural numbers
binom(6,2)=15 |
| on |
off |
# |
inverse modulu: 6#2=3, 6#4=1 |
| on |
off |
frac |
fraction of a number.
frac(6.12)=0.12)
frac(-6.12)=-0.12 |
| on |
off |
^(1/ |
x-root |
| on |
on |
asinh |
arcsin-hyperbolicus |
| on |
on |
acosh |
arccos-hyperbolicus |
| on |
on |
atanh |
arctan-hyperbolicus |
| on |
on |
acoth |
arccot-hyperbolicus |
| off |
on |
sinh |
sin-hyperbolicus |
| off |
on |
cosh |
cos-hyperbolicus |
| off |
on |
tanh |
tan-hyperbolicus |
| off |
on |
coth |
cot-hyperbolicus |
For functions with one parameter, the curson is automatically set between
the brackets after pressing the button. For functions with 2 parameters,
the cursor is set at the first input position (the first parameter of the
function). If you are pressing the arrow-button (right direction), the cursor is
set to the second input position (the secend parameter).
For entering e.g. sin(2), you can enter either "2", select it and press the
sin-key, or press the sin-key and then "2".
There are 2 predefined constants: e and pi. In future, more constants from the
areas of physical and chemical calculations will be available. e and pi are
defined as:
| constant |
value |
| e |
2.718281828459045 |
| pi |
3.1415926535897932384 |
Furthermore, there is a button "E". "E" means *10^, so you can write for instance
instead of "2.2*10^5" "2.2E5", which is much shorter and easier to enter.
With the "mde"-button, you can switch between deg, rad and grad mode.
The input-field
The value of the button you have pressed will be inserted at the position of the
caret in the input line. The two special buttons at the right side under the output
line are for deleting the character before the caret and for deleting the whole input
line ("Clear").
Memory-Handling
The buttons M+, M- and MS are used for memory-handling. By pressing the
"M+"-button, the value of the input field is copied to the combobox. The
selected combobox item can be deleted by pressing the "M-"-button. All entries
will be deleted by pressing the "MC"-button. By selecting a combobox entry,
the entry will be inserted in the input field at the caret position.
If you set the cursor into the output field and press M+, the content of the
output-field is copied into the memory combobox. By putting the cursor to the
input field, the whole input field (or the selected part of the expression of
the input field) is copied into the combobox as a new entry.
Parameters
The buttons "w", "x", "y" and "z" are buttons for building expressions with parameters.
By pressing f.e. button "w", "[w]" will be inserted in the input field. At the time you
are pressing the calculate button, you will be asked to enter the value of the w-parameter.
All in all you are able to build expressions with up to 4 different parameters.
For instance, you can enter an expression
[w]*sin([x])
and at the time you are pressing the calculate button, you are asked to enter the values
for w and x. Futhermore, you can assign this expression to a user-defined button.
Calculation Sequence
Some notations on the sequence of the calculation of expressions. The sequence is:
1. Parenthesis
2. Functions
3. Faculty
4. Exponential
5. Division
6. Multiplication
7. Plus
8. Minus
Because of this order, the expression "1/8*6^6" is calculated like this: (1/8)*(6^6).
You have to use parentheses, if you want that the expression is calculated exactly in
the order you want - otherwise you will get a different result.
Back to top of page
Most of the buttons of the function plotter inputview are also available in
scientific-calculator. To get more informations on their meanings, please look at the chapter
Usage of the scientific calculator.
Specifying functions
This dialog looks looks like the dialog of the scientific-calculator
But instead of memory-handling, there is a combobox for holding the functions that
should be plotted. The input is transfered to the combobox by pressing the "M+"-button.
By pressing the "M-"-button, the selected function in the combobox is deleted. All
functions in the listbox as well as the present functions in the input field will be plotted.
Note, that of course different kinds of functions cannot be plottet at one time. For
instance, it is not possible to plot a fractal and a 3D-function at one time.
You can define different types of functions. The following table shows the type, an
example and the number of functions which can be plotted at one time for each function.
| Type |
Example |
Cnt |
| f(x) |
f(x)=sin(x) |
n |
| f(t,x) |
f(t,x)=t*x^2 |
n |
| f(y) |
f(y)=y^2 |
n |
| f(x,y) |
f(x,y)=1=sin(x)+cos(y) |
n |
| 3D(x,y) |
z=f(x,y)=sin(x)+cos(y) |
1 |
| 3D(t) |
z=f(t)=
[x:=sin(t);y:=cos(t);
z:=t/4;t:=0..20] |
1 |
| f(t) |
f(t)=
[x:=8*sin(t)-2*sin(4t);
y:=8*cos(t)-2*sin(4t);
t:=0..2*pi] |
1 |
| f(t)=p |
f(t)=p=[4*sin(8t);
t:=0..2*pi] |
1 |
| f(n) |
f(n)=(1+1/n)^n |
n |
| f(n-1) |
f(n)=f(n-1)-n;f(0)=1 |
n |
| Julia |
z(n+1)=sin(z(n)^2)+
(-1+0*j) |
1 |
| Mandel |
z(n+1)=z(n)^3+(0+0j);
z(0)=0+0j |
1 |
For defining those functions, the buttons Fx, Ftx, Fy, Ft, p, Fxy,
3D, 3D(t), Fn, Fn-1, julia and mand(elbrot) are available. Futhermore, the buttons
x, x^2, x^3, y, y^2, y^3, t, n, n^2, n^3, n-1, j and z(n) are shown dynamically
depending on the function type.
If you enter for instance f(t,x)=t*x^2 and press the plot-button, a dialog is
shown which asks for the values for t. You have to enter the start value, the
end value and the step width for t. By this way, you can plot n functions at one
time by only entering one function.
Plotting functions
By pressing the "plot" button the functions will be plotted in a new window.
The plotting options
By pressing the parameter button, a dialog appears in which you can select the
plotting options.
Plotting options for 2D-graphs
For 2D-graphs, you can select the plotting regions (from x1 to x2, from y1
to y2) from comboboxes, or you are entering the values manually using the
keyboard. If you select pi from the combobox "multiplicate", he values of the are multimplicated with pi. For instance, if you do have function f(x)=sin(x) and do select this combobox, the x-axe has values of 3pi, -2pi, -pi, 0, pi, 2pi, 3pi, ... You can select in the multiplication combobox e, too.
Furthermore, you can set the quality-level (1 is the best), the line width and
if you want to plot the line (equals) or mark the area which is less or greater
than the function.
Last but not least, it is possible to change the background color of the dialog
in which the function(s) will be plotted. And it is possible to set the colors
of the first four functions which are plotted, too.
Plotting options for 3D-graphs
For 3D-graphs, you can select the plotting regions (from x1 to x2, from y1
to y2, from z1 to z2) from comboboxes. If you check the checkbox, the z-regions
is automatically choosen by calculating the lowest and highest z-value in the
given x- and y-range.
Furthermore, you can set the quality-level (1 is the best), the line width, the
view angle (for y and z) and the fore- and background color.
Plotting options for fractals
For fractals (juliaset, mandelbrot), the number of iterations and the limes of
the absolute value is important, and since version 1.3.4 you can specify the
colors which are used. By pressing the colors-button, a new dialog is shown where you
can select the back- and foreground colors. Furthermore, you can set the quality-level (1 is the best)
and of course the plotting area (imaginary and real part).
Plotting fractals
For plotting fractals, there is a lot of calculation needed. Therefore, it is not
very fast to plot fractals. The best way is to select quality level 4 in the options
dialog. The plot will be rather fast because only every 4th point is calculated, but
of course, the quality of the plot will not be good enough. Just zoom into your preferred
region and if you have found it, change the quality level to 1 by selecting this
value from the combobox (see
Change the quality level).
As in all other plot, e.g. the standard julia-function (z(n+1)=z(n)^2+(-1+0*j)) can
be changed, e.g. z(n+1)=sin(z(n)^2)+(-1+0*j) is possible, too. Just try other functions, too.
And don't forget to change the number of iterations and the border value in the
options dialog for fractals.
Back to top of page
The functions are plotted in a new dialog window. In this chapter, the available
buttons and functionalty of this window are explained. A sample plot is shown
in the following image.
Zoom in and zoom out
Use the first two buttons on the left side of the menu bar and you are able to zoom
in or zoom out. Furthermore, you can draw a rectangluar region in the view, and if
such a region is drawn, the zoom-in button results in a new plotting region exactly
as large and with the same boundaries as the rectangle you selected.
Change the plotting region
With the help of the next button, you can switch back to your last plotting region.
The red arrow-button resets the plotting region to the region which was displayed at
the time the dialog started.
With the four plotting region buttons you are able to move the x- and y-axis.
Change the quality level
In the plotter options dialog, you can set the quality-level between 1(the best)
and 4. With the combobox, you can change this level, too. The next time the function
is plotted, this will be done with the new selected quality level.
Save a bitmap of the plot
With the store-button, you can save the plotted function as a bitmap. When pressing
this button, you have to specify the output-bitmap-file in a standard file-save dialog.
Cancel the calculation
With the red button, you can cancel the calculation and the plotting of a function.
In case you press the OK-button while a function is plotted, this will also lead to
cancelling the calculation. Press the OK-button once again to close the dialog.
Back to top of page
Within the matrix calculator, you can define matrices with up to 10 x 10 elements
and make some calculations with matrices.
Input of matrices
The combo box in the middle defines the present matrix. You can define the first
and second matrix, but the result-matrix("=") cannot be changed. So if you want
to multiply two matrices, you have to select the first matrix ("1") first and
enter the data, after that you have to select the second matrix ("2") and enter
the data. Then, you can press the "="-button, and the combo box will automatically
be changed to the result-matrix ("=") and the result will be shown.
Please notice, that you have to specify both matices for some kind of calculations,
and for some other kinds only the first matrix must be filled.
Often, you want to have the result of a matrix operation as the input for another
operation. For doing this task easy, the left most button in the first button line
copies the result of an operation into the first input matrix.
Matrices with complex numbers
You can enter matrices with complex numbers by changing the left combo box to "complex".
The following table shows the type of calculations on complex matrices.
By pressing the "="-button, the calculation is executed.
| Calculation |
Meaning |
| addition |
2 matrices are added |
| subtraction |
2 matrices are subtracted |
| multiplication |
2 matrices are multiplied |
| transpose |
The transpose matrix of a matrix is calculated |
| determinant |
The determinant of a matrix is calculated |
| inverse |
The inverse matrix of a matrix is calculated |
| Complex conjugate |
The conjugate matrix is calculatedt |
| Adjoint |
The conjugate transpose matrix is calculated |
You can enter complex numbers in polar mode (pol(distance, angle)) as well as in
normal mode (j). The mode of the complex numbers in the result matrix can be
switched easily.
Matrices with real numbers
You can enter matrices with real numbers by changing the left combo box to "real".
The following list shows the type of calculations on real matrices.
By pressing the "="-button, the selected calculation will be executed.
| Calculation |
Meaning |
| addition |
2 matrices are added |
| subtraction |
2 matrices are subtracted |
| multiplication |
2 matrices are multiplied |
| transponent |
The transponent matrix of a matrix is calculated |
| determinant |
The determinant of a matrix is calculated |
| inverse |
The inverse matrix of a matrix is calculated |
| rank |
The rank of a matrix is calculated |
| gauss |
Different kinds of gauss-algorithm. |
For gauss-algorithm, there are 4 different kinds:
- gauss (applied on rows only)
The gauss-algorithm is executed, and one tries to get an upper triangular matrix of
the shape
1 x x
0 1 x
0 0 1
by exchanging rows only.
- gauss (applied on rows and columns)
The gauss-algorithm is executed, and one tries to get an upper triangular matrix of the shape
1 x x
0 1 x
0 0 1
by exchanging rows and columns. After that,the first column in the result-matrix
does not necessarily correspond with the first column of the original matrix.
- gauss (normal)
The gauss-algorithm is executed, and one tries to get an matrix of the shape
1 0 0
0 1 0
0 0 1
by exchanging rows and columns. After that,the first column in the result-matrix
does not necessarily correspond with the first column of the original matrix.
This kind of calculation is very important for calculating the rank of a matrix.
- linear equation
The gauss-algorithm is executed, and one tries to get an matrix of the shape
1 0 0 x
0 1 0 y
0 0 1 z
by exchanging rows and colums. But it is guaranteed, that the first column in the
result-matrix corresponds with the first column of the original matrix (and so on).
Apart from that, the last column will never be exchanged with another column. This
kind of calculation is very important for linear systems. Suppose you have following equation:
x+2y=2
4x+6y=3
You can define a matrix
1 2 2
4 6 3
and you will get the result-matrix
1 0 -3
0 1 2.5
So x is -3 and y is 2.5.
Back to top of page
With the complex calculator, calculations on complex numbers can be done.
The complex numbers can be entered either in polar form or in normal form.
This calculator is quite similar to the scientific calculator, but there are less
functions available and there are two additional buttons. The button "j" is used
for the imaginary part of a complex number. Be aware, that "j" is the same as "i".
"i" is normally used in mathematic calculations, whereas "j" is used in electronical
calculations. The button with the angle is used for the input of complex numbers
in polar form. With the help of the calculator for complex numbers, you can calculate
expressions like
2j*(2+2j) --> -4 + 4j
Furthermore, you can enter complex numbers in polar form (pol(distance,angle)) and
mix them with the normal form. So you can calculate expressions like
pol(3,30)*(j+1)
You can select from the combo box, whether you want the result to be calculated
in normal or in polar form.
The functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, asinh, acosh and
atanh are available for calculations with complex numbers.
Also, ln and lg are available for complex numbers.
Furthermore, the function "abs" calculates the absolute value of a complex number,
and "sign" calculates the signum of a complex number (z'=sign(z) --> abs(z')=1).
Last but not least, you can calculate the power of a complex number, e.g.
(3*j)^17, j^j, (2+3j)^(1-5j) etc and the square root (which is of yourse the
same as z^(1/2)).
Table of available functions
In the following table, the available functions for complex numbers are listed.
The parameters of trigonometrical functions are interpreted in rad-mode.
| inv |
hyp |
btn |
meaning |
| off |
off |
sin |
sine
sin(2-3j)=9.154+4.169j |
| off |
off |
cos |
cosine
cos(2-3j)=-4.19+9.109j |
| off |
off |
tan |
tangens
tan(2-3j)=-0.004-1.003j |
| off |
on |
sinh |
sine-hyperbolicus
sinh(2-3j)=-3.591-0.531j |
| off |
on |
cosh |
cosine-hyperbolicus
cosh(2-3j)=-3.725-0.512j |
| off |
on |
tanh |
tangens-hyperbolicus
tanh(2-3j)=0.965+0.01j |
| on |
off |
asin |
arcsine
arcsin(2-3j)=0.571-1.983j |
| on |
off |
acos |
arccosine
arccos(2-3j)=1+1.983j |
| on |
off |
atan |
arctangens
arctan(2-3j)=1.41-0.229j |
| on |
on |
asinh |
arcsine-hyperbolicus
arcsinh(2-3j)=1.969-0.965j |
| on |
on |
acosh |
arccosine-hyperbolicus
arccosh(2-3j)=1.983-1j |
| on |
on |
atanh |
arctangens-hyperbolicus
arctanh(2-3j)=0.147-1.339j |
| off |
- |
abs |
absolute value
abs(j)=1
abs(2-3j)=3.606 |
| on |
- |
sign |
signum
sign(2-3j)=0.555-0.832j
abs(0.555-0.832j)=1 |
| off |
- |
ln |
natural logarithm
ln(2-3j)=1.282-0.983j |
| off |
- |
lg |
base10-logarithm
lg(2-3j)=0.557-0.427j |
| off |
- |
sqr |
square root
sqr(2-3j)=1.674-0.896j |
| off |
- |
conj |
Conjugate
conjugate(2-3j)=2+3j |
| - |
- |
Im |
imaginary part
im(2-3j)=-3j |
| - |
- |
Re |
real part
re(2-3j)=2 |
In those cases, where there are more than one possible result of a function,
the base value is calculated. For instance, if you are calculating
C^(1/n), C element of complex, n natural number,
for instance (pol(1, 90)^(1/4)), there would be three results:
pol(1,90)=rad(90)^(1/4)*(cos((rad(90)+2*pi*k)/4 + j * sin ((rad(90)+2*pi*k)/4))
with k = 0, 1, 2.
Be careful what kind of mode you select! Usually, the calculation should be
executed in deg-mode, but you can also select rad- and grad-mode. This is
especially important if you are using the polar form to define a complex number.
The angle will be evaluated as deg, rad or grad, depending on your selected mode.
Furthermore, if using the available trigonometrical function like sin, cos, tan,
the parameter is interpreted in the selected mode.
Back to top of page
With the help of the function calculator, you can do a complete curve sketching.
Last but not least, the function calculator is able to calculate symbolic derivatives.
This calculator is quite similar to the scientific calculator and the function plotter.
But there is no memory-handling and the mode button (deg/rad/grad) is disabled.
Symbolic function derivation
By selecting "derive (symbolic)" from the combo box, the input expression will be
derived after pressing the result button. With the derivation calculator, it is
possible to calculate the symbolic derivative of expressions like
| function |
result |
| sin(2x^2) |
4x*cos(2x^2) |
| 4x^2+6x |
8x+6 |
Symbolic function simplifier
By selecting "Simplify (symbolic)" from the combo box, the input expression will
be simplified after pressing the result-button. With that function it is possible
to simplify expressions like
| function |
result |
| (x+1)(x-1) |
x^2-1 |
| (2x^4-9x^3-20x^2+9x+18)/(x+1) |
2x^3-11x^2-9x+18 |
Symbolic function calculations
By selecting "Calculate (symbolic)" from the combo box, the input expression will
be calculated after pressing the result-button. With that function it is possible
to calculate expressions like
| function |
result |
| (x+1)^2 |
x^2+2+2x |
| (2x^4-9x^3-20x^2+9x+18)/(x+1) |
2x^3-11x^2-9x+18 |
The main difference between the last two functions is, that the simplifier does
not change the input expression "(x+1)^2" in the result, because that expression
cannot be simplified any further.
Polynomdivision
Furthermore, if a polynom is divided through an expression like ("ax+b"), a polynomdivision
takes place. Therefore, it is possible to enter an expression like "(2x^4-9x^3-20x^2+9x+18)/(x+1)"
and the result will be "2x^3-11x^2-9x+18". Please recognize, that this division
tooks only place if a polynom is divided throug a linear function (e.g. 2x+3).
Calculate polynom parts
By selecting "Calculate polynom parts" from the combo box, the input expression will
be calculated after pressing the result-button. With that function it is possible
to calculate expressions like
| function |
result |
| x^2-1 |
(x+1)(x-1) |
Of course, this is also possible for much greater polynoms, e.g. "2x^4-9x^3-20x^2+9x+18"
will be calculated to "(x+1.5)(x+1)(x-1)(x-6)(2)". With this calculation, the
zero-points of the polynom can easily be calculated.
It is not guaranteed, that the polynom is divided into his parts completly. Maybe a
part is left which could be divided further. Furthermore, it is only searched within
the range of [-100;100]. Therefore, an expression like "((x+200)^3)" would not
give back the correct solution "(x+200)(x+200)(x+200)".
Polynomdivision
If you select "Polynumdivision" from the combobox, a Polynomdivision can take
place.
An expression P(x)/Q(x) will be transfered to an expression S(x) + R(x)/Q(x).
This is done even for nonlinear Q(x).
Example:
Enter "(4x^5-x^4+2x^3+x^2-1)/(x^2+1)", select Polynomdivision from the combobox
and press "=". The result will be "4x^3-x^2-2x+2+(2x-3)/(x^2+1)".
Numeric function solver
By selecting "Solve f(x)=0 (numeric)" from the combo box, the input function will
be solved, that means there is a search for points where f(x)=0. This will be done
numerically, so you have to define the boundaries (the area that is searched for zero-points)
in the dialog which then appears.
This dialog is the same for some of the other numeric function calculations.
Numeric function derivation
By selecting "Derivate (numeric)" from the combo box, the derivation at a point of
f(x) is calculated. Therefore, you have to define the point x where to calculate
f'(x) in the dialog which then appears.
Numeric extrema calculation
By selecting "Extrema (numeric)" from the combo box, the extrema of a function
are calculated. You have to define the boundaries in the dialog which then
appears. The boundary defines the area that is searched for extremas.
Local minima are displayed in the form "Min(point)", local maxima are displayed
in the form "Max(point)".
Numeric saddle point calculation
By selecting "Saddle points (numeric)" from the combo box, the saddle points of
a function are calculated. You have to define the boundaries in the dialog which
then appears. The boundaries define the area that is searched for saddle points.
Numeric discontinues calculation
By selecting "Discontinuities (numeric)" from the combo box, the points of a
function are calculated where f(x) is undefined (has a vertical asymptote), e.g.
1/x --> undefined at x=0
You have to enter the boundaries in the dialog which then appears. The boundaries
define the area that is searched for for discontinuities.
Calculation of f(0)
By selecting "Calculating f(0)" from the combo box, the value of f(x) at the
point x=0 is calculated.
Calculation of f(x)
By selecting "Calculating f(x)" from the combo box, the values of f(x) at
points x=[from;to;stepwidth] are calculated. You have to specify the boundaries
in the dialog which then appears. The result is displayed in a grid.
Calculation of an integral
By selecting "Integrate (numeric)" from the combo box, a definite integral of f(x)
is calculated.
You have to define the boundaries (the area the integral is
calculated for) and the width of the rectangles used for calculating the integral
in the dialog which then appears. You can also specify, if the integral should be
calculated as an absolute value (area calculation) and which method to use for
the calculation of the integral. At the moment, three methods are possible: Rectangular
Trapez and Simpson. Please remind, that this is a numeric solution, so the result may differ
from the exact result. If you choose a small step width (e.g. 1/5000), the result gets
better, but the calculation takes longer.
Back to top of page
General
The equation solver is a calculator with which you can solve equations numerically.
Equations can have an inlimmited number of parameters. For solving, for an
expression with n unknown parameters, n-1 parameters must be entered in the
matrix.
Examples
Let's take the well known formular a^2+b^2=c^2. You can enter this in the equation
solver as a^2+b^2=c^2 (the "=" sign is available in the first button line at the left side).
In the matrix, enter "a", "b" and "c" in the parameter-row, "2" below "a" and "4" below "c".
Then, the two possible solutions for b are calculated.
The equation-sover is also very important to calculate the intersections of 2 funtions.
Let's take f1(x)=x^2+1 and f2(x)=x+3. You can enter them as "x^2+1=x+3", enter "x" in
the first column and first row as the unknown parameter and you will get the 2 solutions -1 and 2.
Loading and storing equations
Up to 10 equations can be stored and retrieved to/from the registry. For storing
an equation, specify it inclusive parameters and press the "store"-button. In the
appearing dialog, you have to enter the name of the equation and select the slot
where to store it in the registry. For loading an equation, press the "load"-button.
In the appearing dialog, you have to select the equation you want to be copied to
the inputfield and the parameter-matrix.
Calculation of solutions
With the "sl"-button, it is tried to solve the equation. If no solutions is found, a
dialog appears where you have to enter the range in which the solutions should be searched.
With the "swp"-button, this dialog appears immediatelly. Normally, for standard functions the
"sl"-button works quite well.
Be aware, that this is only a numeric calculation. It is not guaranteed, that all solutions are
found. If you know the area, where there may be solutions, you should use the "slp"-button.
This is specially true, if there are more than one solution within a small area.
If there are more than 5 solutions and you have start the calculation with the "sl"-button,
you have to specify the exact region. If there are more than 5 solutions in the specified
region, an error-message "Too much solutions found!" is displayed.
The solutions are shown in the mode and with the significant digits you have selected from the
Edit-Option-dialog.
Back to top of page
This calculator helps you to make calculations with hexadecimal, binary, octal
and decimal numbers. Last but not least, it is very easy to convert numbers between
two modes f.e. from binary to octal.
As within other calculators, you can select your own defined functions and constants
by pressing the "btns" button. Be aware, that e.g. sin() makes no sense for the
computer calculator and therefore an error will occur.
Be aware, that the greatest number you can calculate has 8 bytes (DWORD): 0xFFFFFFFF.
All calculations which would have a result greater than this number are leading to an
overflow and an error message.
Changing the mode
With the "mde"-button at the left side in the first button row, you can change the
mode between hexadecimal, binary, octal and decimal. The possibility for the input
of numbers and characters depends on the selected mode.
Available Functions
The following table lists all functions that are available
| Fnct |
Meaning |
Example |
| and |
logical and |
and(10,101)=0 |
| or |
logical or |
or(10,100)=110 |
| xor |
logical exclusive or |
xor(10,110)=100 |
| not |
logical not |
not(101)=10 |
| nand |
logical nand (not and) |
nand(10,111)=101 |
| nor |
logical nor (not or) |
nor(101,1)=10 |
| lsh |
left shift |
lsh(1010)=10100 |
| rsh |
right shift |
rsh(1010)=101 |
Conversions
You can convert a result (hex, bin, oct, dec) to another mode (hex, bin, oct, dec)
by selecting another mode from the combo box. Furthermore, if your present mode is
binary for instance, and the selected mode in the combo box is hexadecimal, the
result is shown as a hexadecimal number. There is no need for an additional
conversion.
Back to top of page
The statistic calculator helps to perform statistical calculations. Un unlimitted
count of data points can be entered. Both one-variable (x) and two-variable (x and y)
statistics are supported.
Changing the mode
By selecting the "x/xy" button, you can switch between 1-variable statistics and
2-variable statistics. Additionally, you can enter the number of data points in the
dialog which appears.
If you select the two-variable statistics, the matrix will contain rows for the x- and the y- values.
In case of one-variable statistics, the matrix does only contain a row for the x- values.
Available functions
In the following table, all available functions are listed (from top to bottom and
from left to right):
| inv |
btn |
meaning |
| off |
Sx |
Sum of all x-values |
| off |
Sx^2 |
Sum of the square of all x-values |
| off |
Sxy |
Sum of the product of the x- and y-values |
| off |
Mx |
Arithmetic mean of the x-values |
| off |
Mxg |
Geometric mean of the x-values |
| off |
MDx |
Median of the x-values |
| off |
Qx |
a-Quantil of the x-values |
| off |
Vx |
Sample variance of x-values |
| off |
SDx |
Sample standard deviation of x-values |
| off |
Vpx |
Population variance of x-values |
| off |
SDpx |
Population standard deviation of x-values |
| off |
minx |
Minimal value of all x-values |
| off |
maxx |
Maximal value of all x-values |
| off |
VCsx |
Sample x-coefficient of variance |
| off |
VCpx |
Population x-coefficient of variance |
| on |
Sy |
Sum of all y-values |
| on |
Sy^2 |
Sum of the square of all y-values |
| on |
n |
Count of data points |
| on |
My |
Arithmetic mean of the y-values |
| on |
Myg |
Geometric mean of the y-values |
| on |
MDy |
Median of the y-values |
| on |
Qy |
a-Quantil of the y-values |
| on |
Vy |
Sample variance of y-values |
| on |
SDy |
Sample standard deviation of y-values |
| on |
Vpy |
Population variance of y-values |
| on |
SDpy |
Population standard deviation of y-values |
| on |
miny |
Minimal value of all y-values |
| on |
maxy |
Maximal value of all y-values |
| on |
VCsy |
Sample y-coefficient of variance |
| on |
VCpy |
Population y-coefficient of variance |
Explanation of some of the functions
- Arithmetic mean: This is just the sum of all values divided by the data count.
- Geometric mean: (Product of all values)^(1/Data Count)
- Median: Middle of all values
- a-Quantil (Percentiles): At least a-percent of all x-values are smaller than the result.
- Variance: auxiliary measure
- Standard deviation: square root of variance
- Coefficient of variance: standard deviation / arithmetic mean
There is a difference in the formulars between calculation of samples and
calculations of the whole population. Therefore, some of the functions above
are available for sample calculations and population calculations.
Regression
With RealCalculator it is possible to make regressions. With this, it is
possible to calculate a function (e.g. f(x)=a+bx) which fits best the values which
has been entered in 2-variable statistics. By pressing the "Regr"-button, the function
is calculated, and at the same time, follwing values are calculated:
- R²: Goodness of Fit / Coefficient of Determination R²
- cov: Correlation of metrically scaled variables
- r: Correlation coefficient (Bravais-Pearson)
Before the function and the values are calculated, you have to select a function
type from a combobox. At the moment, following functions are available:
After that RealCalculator tries to find values for the parameters a and b such that
the square error is minimized. Please recognize, that the non-linear regression
(e.g. y=a*e^(bx)) is transferred to a linear type (here: ln(y)=ln(a)+bx).
Plotting
With the plot-button, it is possible to plot the statistic data. The first plotting region
is selected in such a way, that all data elements are visible within the plot. Of course,
you can zoom in, zoom out, change the region etc. in the plotting window as it is possible
in the "normal" function plotter.
Furthermore, if you have made a regression analysis before, the regression functions is plotted, too.
Therefore it is easy to evaluate how good the regression function fits the statistic data.
Loading and storing statistic data
With the load- and store-button, you can load and store statistic data. The data
you have entered in the matrix is stored as a semicolon separated list. For instance,
if you have entered 1, 5, 3, 8 as the x-values, this is stored in a csl-file as
"1;5;3;8". If you have selected 2-dimensional values ((x,y)-mode) while loading this file,
there would be 2 value-pairs: (x:1,y:5),(x:3,y:8).
The data for the regression analysis can be entered directly in RealCalculator
or can be imported e.g. from Excel(TM).
Back to top of page
The metrics converter is quite a simple one: just convert a number or the result
of an expression from one metric to another.
The combo box at the top is for selecting a type of metrics (f.e. speed, weight).
At the moment, there are seven different standard metric kinds:
- Distance (e.g. meters, yards, miles)
- Weight (e.g. gramm, lps, ounce)
- Volumina (e.g. liter, gallon, quart)
- Speed (e.g. meters/second, feets/second)
- Area (e.g. square meter, acre, square mile)
- Power (e.g. watt, kp, ps)
- Temperature (Celcius, Kelvin, Fahrenheit, Reamur, Rankine)
- Time (e.g. Day, Minute, Hour)
If you don't select a value from that combo box, the other 2 combo boxes will be
filled with all metrics. If you select a value from that combo box, the other 2
comboboxes will be filled only with metrics of the selected type. If a conversion
is not available (e.g. from miles/hour to gram) an error message will be displayed
in the result line.
How it works
It is important that you understand the way how the calculation tooks place
within the metrics converter, especially if you want to add metrics or metrics
kinds.
Every metric kind (e.g. distance) has an international base metric. For distance,
this is meter. All other metrics of the kind distance are based on the base metric
meter. For instance, on mile is 1609.3 meter. So, if you want to calculate a
conversion between mile and inch, the inch-value is calculated to meter and the meter value
to feet (one feet is 0.3048 meter).
Adding and deleting metric kinds
The buttons "Mk+" and "Mk-" are for adding and deleting metric kinds. If you
want to add a new metric kind (e.g. radioactivity), you have to press the "Mk+"
buggon.
You have to enter the name of the metric kind and the base metric. The base metric
always has the value 1.
By pressing the "Mk-" button, you can delete one of your own defined metric kinds
or even one of the predefined metric kinds.
Adding and deleting metrics
By pressing "M+" you are able to add a new metric in one of the available kinds.
You have to specify the kind, the name and the value of the metric.
Because all calculations in the metrics converter are made over a base metric, the value
also must be entered in the relationship to the base metric. For instance, if you want to
add "decimeter", you have to select the "distance"-type. It is shown in the dialog, that
the base metric of distance is meter. So the value for decimeter must be 0.1, because
0.1 meter is one decimeter.
For deleting a metric, just press the button "M-". Select the metric you want to delete.
Reseting metrics
If there is a problem with the metrics, or you want to delete all your added metrics,
there is the possibility to reset the metrics by pressing the button "MR" (Metrics reset).
Every metric or metric kind you have added will be lost! Only the predefined metrics
and metrics kinds are available after that.
Back to top of page
