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Quick Start Guide      Plotting

Quick Start Guide

 Pg.1  (Keypad)      Pg.2  (Auto-calculation)      Pg.3  (Plotting) 

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Plotting


The Plot Tab Plotting is available by selecting the "Plot" tab found in the lower left of the program window.

Plot Button This is the 'Plot' button.


To plot an expression from the editor, simply select it using the mouse, select one of the coloured tabs to the right of the plotting area, and press the 'Plot' button (see the example below).

Plot Button

The 'Plot' button is located on the vertical toolbar to the right of the plotting area (see the below figure: 'Plotting Area - Labelled') or on the popup menu of the mathematics editor - to access it, right click inside the selection area of the expression to be plotted.



  IMPORTANT:

Parameters within Plotted Expressions will be Assigned Values Automatically.
The real power of the plotting module in AnalyticMath lies in the fact that it can plot expressions containing up to 8 parameters.

In the example above, 2cos(kx+Bm)) is plotted y vs. x and so both k and Bm are, therefore, considered to be parameters of this expression. The plotting module will set values for these parameters automatically (usually a value of 1.0, unless this causes indeterminacy) and will set up sliders for them on the tab-pane of the plot in question so that their values can be altered if desired (see the labelled figure below). The plotting module will do this for up to 8 parameters no matter where they are situated in a given expression.

Parameters within plotted expressions may be denoted by any Latin or Greek letter that is available from the keyboard or from the program key-pad and may contain subscripts, superscripts, or both. In addition, they may be embellished using the 'Hat', 'Bar' etc. buttons found on the primary key-pad.

The plotting module defines a parameter as any variable that is neither the horizontal plotting variable (the independent variable) or the vertical plotting variable (the dependent variable). The plotting variables can be set by the user from the 'Plot' menu and are visible at the bottom of the program window labelled: 'Horiz. Var:' and 'Vert.  Var:' (the defaults are x and y respectively).


Plotting Area - Labelled:


Plotting Example




Things to Know About the Plotting Module:


Plot Button This is the Plot button. Select the expression to be plotted in the editor; select one of the tabs found to the right of the plotting area (there are 8 tabs allowing 8 simultaneous plots); press the plot button.


Clr Button - Clear Tab This button will Clear the plot on the tab that is selected when the button is pressed. For example, if the #2 (blue) tab were selected, then pressing the <Clr> button would clear the plot on this tab only. The program will always request confirmation before clearing a plot.


All Button - Clear All Tabs This button will clear All plots on all tabs. Again, the program will request confirmation before carrying out this command.


Change Horizontal Variable

This text-field displays the Horizontal Plotting Variable and exists at the bottom-right of the program window. This variable can be changed from the 'Plot' menu (see: Change Horizontal Plotting Variable) or by double left-clicking inside its text-field. Either method will bring up a dialogue box that will allow the variable in question to be changed (the defaults are x for the horizontal variable and y for the vertical variable).
Note: The horizontal plotting variable can be defined as anything, from single variables such as 'x', 't' or 'zm' to functional expression such as 'log(x)' - subscripts, superscripts, character embellishments etc. can all be used.
(There is a similar text-field that displays the vertical plotting variable and the discussion above applies equally well to it.)



Change Tick Interval - One or Pi Major tick interval ( 1 or pi ) There are two of these, one for the horizontal axis and one for the vertical axis. The 'pi' interval is useful when examining trigonometric functions and their inverses.



Change Horizotal Range
Every plot tab has a range display that is found at the bottom of the tab pane in question. The range over which a particular plot (on a particular tab) is displayed can be limited to a subset of the normal horizontal axis range, which is {-7.0 <= x <= 7.0}, by either double-clicking in the light-blue text-field displaying the range or by clicking the button on the bottom of this display. Doing so will display a dialogue box that will allow a new min. and/or max. to be defined for the range of the plot in question.



Displaying Plot Coordinates
A left-click inside the plotting area will bring up the 'Plot Coordinates' dialogue box that will allow the examination of (x,y) plot coordinates for the plot on the selected tab (see the above image).



Specifying y is not necessary for explicit plots.
Either of the above selections is sufficient to plot sin(x).

It is not necessary to specify the vertical plotting variable ('y' in the example above) when plotting explicit expressions.



Not having to specify the dependent vertical variable by selecting just f(x)-type expressions such as sin(x) is convenient when examining larger expressions, piece by piece. For example, the expression, ex ~ 1 + x + x2/2! + x3/3!, represents the first 4 terms of the Maclaurin series for ex. It could be examined as follows (Note: 'Select' => 'Select with the mouse'):
1) Select just the '1' part of this expression; choose the #1 tab; press <P>lot.
2) Select '1 + x'; choose the #2 tab; press <P>lot.
3) Select '1 + x + x2/2!'; choose the #3 tab; press <P>lot.
4) Select 1 + x + x2/2! + x3/3! (i.e. all 4 terms); choose the #4 tab; press <P>lot.
5) Finally, select ex from the left side of this expression; choose the #5 tab; press <P>lot.
This is an interesting exercise that demonstrates how the Maclaurin series increases in accuracy as more terms are added.




Lock / Unlock Buttons.

Normally, plots are re-calculated and repainted immediately after a slider adjustment is made. This behaviour can be temporarily postponed by selecting the <Lock> button. Any number of slider adjustments can then be made without the having the plot area repainted. When your finished select the 'Unlock' button (the default state). This will cause an immediate repaint to occur and the newly painted plot will correctly reflect any adjustments made to its parameter sliders.

The 'Lock' button should be used in the following situations:
  1. When 'fine-tuning' a parameter slider (i.e. adjusting it to very precise value). To achieve this, click on either side of the slider 'thumb'. Hold the mouse button down in these locations to move the slider continuously at this very small incremental value.

  2. When multiple slider adjustments must be made.
( Be sure to re-select the 'Unlock' button once your slider adjustments are complete. )


 Tip: Fine-tuning a Parameter Slider.
To 'fine-tune' a parameter slider (i.e. adjust it to a very precise value):
  1. Press the 'Lock' button.

  2. Click on either side of the slider 'thumb'. Holding the mouse button down in one of these locations will move the slider continuously at a very small incremental value.

  3. Finish by pressing the 'Unlock' button.




Implicit expressions such as the hyperbola x2 - y2 = 1 can be plotted in this version of the program, although they take longer to calculate than the same expression (or expressions) written in explicit form - if this is indeed possible.
Until a quicker plotting algorithm is found, try to write expressions in explicit form, they will plot more accurately and in considerably less time than the same expression(s) written in implicit form.
Please consider implicit plotting to be at a beta stage in terms of its development.



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