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| {{Orphan|date=February 2013}}
| | 29 year-old Taxation Accountant Clifford Mahl from Saint-Jerome, likes to spend some time pinochle, venapro and scrabble. Likes to visit unfamiliar places like Vézelay.<br><br>Feel free to visit my web-site; [http://Buyvenapro.org/venapro-works-treat-hemorrhoids/ buyvenapro.org] |
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| In the [[mathematics|mathematical]] theory of [[partial differential equations]], a '''Monge equation''', named after [[Gaspard Monge]], is a [[first-order partial differential equation]] for an unknown function ''u'' in the independent variables ''x''<sub>1</sub>,...,''x''<sub>''n''</sub>
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| :<math>F\left(u,x_1,x_2,\dots,x_n,\frac{\partial u}{\partial x_1},\dots,\frac{\partial u}{\partial x_n}\right)=0</math>
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| that is a [[polynomial]] in the partial derivatives of ''u''. Any Monge equation has a [[Monge cone]].
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| Classically, putting ''u'' = ''x''<sub>0</sub>, a Monge equation of degree ''k'' is written in the form
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| :<math>\sum_{i_0+\cdots+i_n=k} P_{i_0\dots i_n}(x_0,x_1,\dots,x_k) \, dx_0^{i_0} \, dx_1^{i_1} \cdots dx_n^{i_n}=0</math> | |
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| and expresses a relation between the [[differential of a function|differentials]] ''dx''<sub>''k''</sub>. The Monge cone at a given point (''x''<sub>0</sub>, ..., ''x''<sub>''n''</sub>) is the zero locus of the equation in the tangent space at the point.
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| The Monge equation is unrelated to the (second-order) [[Monge–Ampère equation]].
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| [[Category:Partial differential equations]]
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| {{mathanalysis-stub}}
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Latest revision as of 02:37, 25 July 2014
29 year-old Taxation Accountant Clifford Mahl from Saint-Jerome, likes to spend some time pinochle, venapro and scrabble. Likes to visit unfamiliar places like Vézelay.
Feel free to visit my web-site; buyvenapro.org