An equation describing how some quantity varies at a given point in time in terms of other quantities (or their derivatives) at that point in time. Ubiquitous in science.

Employed by programmers with math backgrounds or by programmers assisted by a mathematics specialist. It is often necessary for a programmer to employ their use along with other such areas as probability and statistics, fuzzy logic, and numerical analysis. 
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DifferentialEquation''''''s are used to solve physical relationships between mass, energy, charge, space, position, time, and temperature. This makes them useful in:

	* ElectroMagnetic''''''s
	* WavePropagation
	* ProcessControl
	* Physical Science
	* Chemistry

Mathlab and Maple are two software packages designed to manipulate DifferentialEquation''''''s.

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'''Sources of additional information:'''

Electronic Journal of Differential Equations - http://ejde.math.txstate.edu/ 

Mathematics And Programming - A Revolution in the art of Reasoning. 
http://www.cs.nott.ac.uk/~rcb/inaugural.pdf
* "Roland Backhouse Inaugural Lecture, 24th October, 2001; Abstract: The modern world is highly dependent on the reliable functioning of computer software. The sheer scale of software systems makes their design and implementation a highly demanding intellectual activity. Meeting these demands has inspired a revolution in the way that mathematics, the art of effective reasoning, is conducted and presented. Continued effort is needed in education and research in the mathematical construction of programs, based on the controlled manipulation of mathematical formulae."
* Nice paper (talk transcript), but it has '''absolutely''' nothing whatsoever to do with differential equations, so it should be moved to some other page. I can't imagine what motivated it being put here in the first place.
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The ExponentialFunction can be coded thusly:

  function expFun($x0,$k,$t)
  { 
    $x = $x0*exp($k*$t);
    return $x;
  }
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CategoryMath