{ Walter Milner }

Descartes

This is a Windows application for drawing graphs of mathematical functions. See screenshots below for an idea of what it can do. You do not choose from a limited set of offered functions - an expression evaluator can deal with an extremely wide range of expressions from simple polynomials, trigonometric, hyperbolic, exponential terms, differentials and integrals, and sums and products of series.

Requirements : 32 bit Windows

Since its release in April 2006 Descartes had over 4800 downloads from this site.
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This package is free

Versions

Current release is version 1.2. New features in this release are:

File.. New and File..Save
Memo - this is some text saved with a file, giving an explanation or notes about the idea behind the file contents. The memo is displayed when the file loads, and can be reviewed/edited from the menu Memo option.
Files remember the 'context' of what was saved eg polar or parametric functions, and the appropriate dialog box is displayed when the file opens.


Mouse right-click on the graph background offers various options, some of which are obvious - zoom in and out, centre, and reset graph limits to the original : +/- 5. The non-obvious options will display a chord on a function, showing the 'rise and run', and the slope of the chord as 'rise over run'. With appropriate zoom in, continuous functions become locally straight, and the chord slope becomes the function differential coefficient. The other options enable the user to select where (what x value) the chord is shown at, or to use the next function, if several functions are being displayed.

Two implicit relations can be displayed. This is to enable simultaneous equations to be written in conventional form.

If a mouse wheel is available, it does zoom in and out.

Some 'example' files are supplied to show what can be done.

Download and install

The download is here

Unzip it into a suitable directory - c:/descartes or wherever you like. Then create a shortcut on your desktop to descartes.exe. Drag a copy to the Start menu if you like. Simple. Descartes does not alter the system registry, install or change any dlls, or anything else which would alter the operating system.


ScreenshotsThumb

Click on the thumbnail for a full-size version

This shows the basic idea - plotting 3 functions





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Inequalities can be shown. This is the region defined by

sin(x) >0

and

y > x


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Functions can be plotted using polar co-ordinates, with any variable representing the angle. Here we are plotting

f( t ) = 4 sin ( a t )

with a = 2


ThumbThis shows the chord feature. A chord is displayed together with the slope value. Combined with zoom in, this can be used to show ideas of limits, tangents and differentiation





ThumbA built-in function which performs numerical differentiation is also available. Here one function is displayed ( x sin x ) together with its differential coefficient. In fact the nth differential coefficient can be shown.





ThumbThere is a command window where variables can be given values, expressions calculated, functions defined and evaluated and so on.





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Parametrically-defined curves can be drawn, using any variable as the parameter. Here we are looking at

x = sin( 2 t )
y = cos( 3 t )





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Implicitly-defined functions can be plotted. Here we are looking at a quadratic curve

ax^2 + bxy + cy^2 = 1

Values of a b and c can be altered