https://calculus.subwiki.org/w/index.php?title=Discrete_derivative&feed=atom&action=historyDiscrete derivative - Revision history2020-10-28T11:52:39ZRevision history for this page on the wikiMediaWiki 1.29.2https://calculus.subwiki.org/w/index.php?title=Discrete_derivative&diff=1778&oldid=prevVipul: Created page with "==Definition== The term '''discrete derivative''' is a loosely used term to describe an analogue of derivative for a function whose domain is discrete. The idea is typica..."2012-06-04T17:46:44Z<p>Created page with "==Definition== The term '''discrete derivative''' is a loosely used term to describe an analogue of <a href="/wiki/Derivative" title="Derivative">derivative</a> for a function whose domain is discrete. The idea is typica..."</p>
<p><b>New page</b></p><div>==Definition==<br />
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The term '''discrete derivative''' is a loosely used term to describe an analogue of [[derivative]] for a function whose domain is discrete. The idea is typically to define this as a [[difference quotient]] rather than the usual ''continuous'' notion of derivative, which is defined as a limit of a difference quotient.<br />
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The typical case of interest is a function defined on the set of integers, or some contiguous subset of the set of integers (for instance, all integers from <math>a</math> to <math>b</math>, where <math>a < b</math> are integers). There are two related notions:<br />
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* The '''forward difference operator''', sometimes denoted <matH>\Delta</math>, is defined as follows for a function <math>f</math>:<br />
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<math>\Delta f = n \mapsto f(n + 1) - f(n)</math><br />
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This can be thought as a [[difference quotient]] between <math>n</math> and <matH>n + 1</math>. Note that it is analogous to the right hand derivative.<br />
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* The '''backward difference operator''' is defined as:<br />
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<math>n \mapsto f(n) - f(n - 1)</math><br />
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This can be thought as a [[difference quotient]] between <math>n</math> and <matH>n - 1</math>. Note that it is analogous to the left hand derivative.<br />
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In practice, we simply choose one of these as the notion of discrete derivative and stick with it. The reason is that the forward difference operator of <math>f</math> at <math>n</math> equals the backward difference operator of <math>f</math> at <math>n + 1</math>, so we do not in fact lose any information by considering only one of these operators as the discrete derivative.</div>Vipul