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| | I'm Fabian and I live in a seaside city in northern Poland, Lublin. I'm 20 and I'm will soon finish my study at English Literature.<br><br>Look at my webpage; [http://touredition.com/uncategorized/%d0%b4%d0%b8%d0%b5%d1%82%d1%8b-%d0%ba%d0%b0%d0%ba-%d0%bf%d0%be%d1%85%d1%83%d0%b4%d0%b5%d1%82%d1%8c-%d1%80%d1%83%d0%ba%d0%b8-%d0%b8-%d0%b4%d0%b8%d0%b5%d1%82%d1%83-%d1%87%d1%82%d0%be%d0%b1%d1%8b/ поджелудочная железа диета] |
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| The '''Weierstrass–Erdmann condition''' is a technical tool from the [[calculus of variations]]. This condition gives the sufficient conditions for an [[extremal]] to have a corner.
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| == Conditions ==
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| The condition says that, along a [[piecewise smooth]] extremal ''x''(''t'') (i.e. an extremal which is smooth except at a finite number of corners) for an [[integral]] <math>J=\int f(t,x,y)\,dt</math>, the [[partial derivative]] <math>\partial f/\partial x</math> must be [[Continuous function|continuous]] at a corner ''T''. That is, if one takes the [[Limit of a function|limit]] of partials on both sides of the corner as one approaches the corner ''T'', the result must be the same answer.
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| == Applications ==
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| The condition allows one to prove that a corner exists along a given extremal. As a result, there are many applications to [[differential geometry]]. In calculations of the [[Weierstrass's elliptic functions|Weierstrass E-Function]], it is often helpful to find where corners exist along the curves. Similarly, the condition allows for one to find a minimizing curve for a given integral.
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| {{DEFAULTSORT:Weierstrass-Erdmann Condition}}
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| [[Category:Calculus of variations]]
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Latest revision as of 10:53, 29 May 2014
I'm Fabian and I live in a seaside city in northern Poland, Lublin. I'm 20 and I'm will soon finish my study at English Literature.
Look at my webpage; поджелудочная железа диета