User Manual

Version: 1.1
Date: 2013-05-11
Revision: 0

Calculation modes

So that the operations are carried out in the easiest way possible, the calculator should be configured so that the calculations may be processed in certain modes. You should select the appropriate calculation mode according to the type of operation that will take place.

  • Comp mode (Computational Mode)

    mode +

    General calculations where values ​​are entered manually, including scientific function calculations.

  • SD mode (Statistical Data Mode)

    mode x

    Input data mode for statistical purposes (statistics with two variables).

  • LR mode (Linear Regression Mode)

    mode /

    Regression calculations (statistics with two variables).

  • CPLX mode (Complex Numbers Mode)

    mode -

    Calculations with complex numbers (including scientific function calculations).

Manual calculations

Example:

(4.5 x 1075) x (-2.3 x 10-79)

Type: 4.5 E 75 x ( - 2.3 E - 79 ) ENTER
Result:-0.001035

Retrieving the result of the last calculation

Once obtained the result of a calculation by pressing the ENTER key, if the result is visualized can be used in later calculations.

Example:

3 x 4 = 12, followed by / 3.14

Type: 3 x 4 ENTER
Result:12
(followed by) / 3.14 ENTER
Result:3.821656051

It is also possible to retrieve the last result obtained and use it within a calculation formula. To insert the result of the last calculation on a calculation formula press...

shift1 ans(ENTER button)

Example:

Perform the calculation of 123 + 456, followed by 789 - 579 (that is the result of the previous calculation).

Type: 123 + 456 ENTER
(followed by) 789 - shift1 ans ENTER
Result:210

Constants and functions

Functions

To open the list of available functions to use in calculations with real and complex numbers, press...
func

In the opened functions list, click on the function to be used and it will be inserted at the current cursor position of the formula being edited.

Constants

To open the list of available constants, press...
shift1 func

History list of calculations

All calculations made by the user are being written in a sequential list with formulas and results. These calculations and formulas can be retrieved and inserted into the new calculations where necessary.

To view the history list of calculations press...
hist

You can also edit any value from this list, such as changing the formula and its result, delete it from the list or get basic statistics of the results of the calculations (sum, average, standard deviation, etc.).

To erase all calculations from the history list, press...
shift1 Mcl (DEL button)

The history list is also cleared whenever the application is restarted.

Data input for statistical processing with 2 variables

This is the mode to select for entering data for statistical regression models with two variables.

Select the SD mode (statistical data mode)
mode x

Example:

Enter the following X/Y data for statistical processing:

X Y
50 122
53 118
54 128
55 121
56 125
59 136
62 144
65 142
67 149
71 161

In SD mode press...

50 ENTER 122 ENTER
53 ENTER 118 ENTER
54 ENTER 128 ENTER
...

and so on until all the data is entered.

To view the complete list of data entered, in SD mode press...
shift1 XY data (hist button)

To erase all statistic data from the list, press...
shift1 Scl (AC button)

Unlike what happens with the list of historical calculations, the statistical data list is persistent whenever the application is closed and restarted again.

Linear regression analysis

With the data of the two statistical variables introduced you will be able to do a linear regression analysis, observing graphically the regression line with his confidence interval limits for a given level of confidence and study the regression data in a tabular form. You can also validate the regression model by the T-Test method and by the Analysis Of Variance (ANOVA) method.

To execute the regression analysis do the following steps:

  • Press the second application bar button

  • In the XY data list page press
    Regression Analysis

or

  • Select the SD mode (statistical data mode)
    mode x

  • Open the statistical data list page by pressing
    shift1 XY data (hist button)

  • In the XY data list page press
    Regression Analysis

T-Test validation

To run the T-Test to validate the regression model, press the application menu bar and select 'T-Test'. The T-Tests are used to conduct hypothesis tests on the regression coefficients obtained in simple linear regression. A statistic based on the t-distribution is used to test the two-sided hypothesis that the true slope, 'B', equals some constant value, B0. The statements for the hypothesis test are expressed as:

H0 : B = B0
H1 : B ≠ B0

Failure to reject H0 : B = B0 implies that no linear relationship exists between 'X' and 'Y'.
The T-Test is carried out on the basis of a confidence interval (defined by a significance level).

For more information on the web about the T-Test click here...

Analysis of variance (ANOVA)

To run the ANOVA test to validate the regression model, press the application menu bar and select 'Analysis of variance'. The analysis of variance (ANOVA) is another method to test for the significance of regression. As the name implies, this approach uses the variance of the observed data to determine if a regression model can be applied to the observed data. The observed variance is partitioned into components that are then used in the test for significance of regression. To test the hypothesis H0 : B = 0 (means null slope), the statistic used is based on the F-distribution. Remember again that the H0 hypothesis must be rejected, so that the model can be considered valid. ('B' is the real slope of the regression line)

For more information on the web about the ANOVA method click here...

Working with the regression data

You can embed the regression parameters in any calculation formula, such as the regression coefficient (' r '), the slope of the regression line (' b '), the interception of the regression line with the Y axis (' a '), the sum of X or Y, etc..

To do that you have to select the LR mode (liner regression mode)

mode /

In LR mode, use the shift1 or shift2 keys to incorporate the regression parameters in the calculation formula currently being edited.
(The next examples results are based on the data entered in the previous example.)

Example:

Multiply the slope of the regression line by 5 (B x 5)
(here 'B' is the estimated slope of the regression line)

Type: shift1 8 x 5 ENTER
Result:9.935653

Example:

Add the [sum of X] to (5 x [sum of Y])
(∑X + 5 x ∑Y)

shift2 2 + 5 x shift2 5 ENTER
Result:7322

Calculate estimated values based on the regression line

If not already in LR mode, select the LR mode
mode /

To calculate estimated values of X press...
shift1 x

To calculate estimated values of Y press...
shift1 /

Example:

Calculate the estimated value of X for Y = 130
(Y = 130)

Type: shift1 x 130 ENTER
Result:56.88510434

Example:

Calculate the estimated value of Y for X = 60
(X = 60)

Type: shift1 / 60 ENTER
Result:136.18970448

Calculations with complex numbers

A Complex number is a number that has a real part and an imaginary part, and can be represented in the form ' a + bi ', where ' a ' is called the real part, ' b ' the imaginary part and ' i ' is called the imaginary unit, being i 2 = -1. The calculator also supports the introduction of Complex numbers in polar form ' rAθ ', where ' r ' is the magnitude and ' θ ' is the angle of the vector in degrees with the axis of the Real numbers in the two-dimensional Complex plane.

Note: Complex numbers in polar form introduced in the calculation expression, are assumed to have the angle in degrees.

The available functions for calculations with Complex numbers have the same name of its homologous functions for Real numbers, preceded by the prefix 'c' ('c' from complex). For example, the function ' sin ' for Real numbers is called ' csin ' for Complex numbers and so on. Until version 1.0.0, the functions for real numbers only supported parameters of type real number, so it is necessary to use the functions for complex numbers to use parameters of type complex number. In versions later than 1.0.0 the functions for real numbers start to support both types of parameters (real numbers and complex numbers).

Note: In versions later than 1.0.0 it is no longer necessary to use two different functions depending on the parameter type.
In complex mode you can view the results of the operations with Complex numbers in polar form 'rAθ'. To do this, select the shift1 button followed by the ∠ button. Since then all results will be expressed in polar form. To return to the form ' a + bi ', select shift1 and press the ∠ button again.
The angle or argument of the Complex number is expressed in the currently selected angle unit. The available units for angles are degrees, radians (default) and grads.

To switch to another unit angle press...
∠

To perform calculations with complex numbers select the complex mode
mode -

Example:

Calculate (3 + 5.2i) x (-2 + 5i) and express the result in polar form with the angle in degrees

Type: ( 3 + 5.2 i ) x ( - 2
+ 5 i ) ENTER
Result:-32 + 4.6i
(followed by) shift1 ∠
Result:32.32893441A2.99882071(-32 + 4.6i)

Assuming you have radians as the current selected angle unit, press the angle button twice, as shown below

Type: ∠ ∠
Result:32.32893441A171.81977012°(-32 + 4.6i)

Example:

Calculate the produt of a complex number with magnitude 2.1 and argument 30 degrees by 5
(2.1A30) x 5

If still not in complex mode, select the complex mode
mode -

Type: ( 2.1 shift2 x-1 30 ) x 5 ENTER
Result:1.61964022 - 10.37433205i

Example:

Calculate the sin of a complex number with magnitude 2.1 and argument 30 degrees
sin(2.1A30)

If still not in complex mode, select the complex mode
mode -

Type: sin ( 2.1 shift2 x-1 30 ) ENTER
Result:1.28734395 - 3.71513951i

Functions and equations

You can create various types of functions, to trace them in graphic, calculate its roots, maxima and minima, points of interception, etc..

Three main types of equations are supported:

  • cartesian equations (Y = f(x) or Z = f(x, y));
  • parametric equations with one or two parameters (X = f(u, v); Y = g(u, v); Z = h(u, v));
  • polar equations (r = f(θ)).

Cartesian equations (Y = f(x) or Z = f(x, y))

These represent equations of which the result depends on a parameter 'X' (ex: Y=sin(X)) or two parameters 'X' and 'Y' (ex: Z=sin(X)+cos(Y/2)).

To work with this kind of equations, press...
f(x)

Parametric equations (f(u, v); g(u, v); h(u, v))

These represent equations of which the result for each dimension (X, Y, Z) depends on a parameter 'u' or two parameters 'u' and 'v' (ex: X=sin(u); Y=cos(u/2) or X=sin(u) x cos(v); Y = u/v; Z = u).

To work with parametric equations, press...
shift2 f(x)

Polar equations (r = f(θ))

These represent equations of which the result radius if calculated as a function of an angle 'θ' (ex: r=sin(θ)).

To work with polar equations, press...
shift1 f(x)

Introducing a new equation

After selecting the type of equation you want to edit (cartesian, parametric or polar), enter the expression of the equation and press the save button Save or press the enter button ENTER(plot).
On the new page, fill the form fields with the configuration data for the calculations and plotting the graph (function name, increment, interval domain for each dimension, etc.) and save.

After returning to the main page, to display the graph of the equation(s) press...
ENTER (plot)

For 2D equations you can draw up to a maximum of 10 equations on the same graph.

Selecting an existing equation to plot in a graph or edit

All equations previously saved can be selected and used as the basis for later editing of new functions or for plotting in a graph.
The stored equations are grouped into two distinct lists:

  • user-defined equations list;
  • gallery of pre-defined equations list.

The user-defined list contains all the equations saved by the user.
The list of the gallery contains some of the 2D and 3D equations more commonly known.

You can select any equation of these lists and use it to plot in a chart or as a starting point for editing a new equation.

To open these lists press... (if not already selected)
f(x)

in f(x) mode press...
Fx list
Goto index