翻訳と辞書 Words near each other ・ Differential gain ・ Differential Galois theory ・ Differential game ・ Differential games with random time horizon ・ Differential geometry ・ Differential geometry of curves ・ Differential geometry of surfaces ・ Differential GPS ・ Differential graded algebra ・ Differential graded category ・ Differential graded Lie algebra ・ Differential graded scheme ・ Differential grasshopper ・ Differential group delay ・ Differential heat treatment ・ Differential ideal ・ Differential inclusion ・ Differential inheritance ・ Differential interference contrast microscopy ・ Differential invariant ・ Differential item functioning ・ Differential Manchester encoding ・ Differential mobility detector ・ Differential nonlinearity ・ Differential norming ・ Differential object marking ・ Differential of a function ・ Differential of the first kind ・ Differential operator ・ Differential optical absorption spectroscopy Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Differential ideal ： ウィキペディア英語版 Differential ideal In the theory of differential forms, a differential ideal ''I'' is an ''algebraic ideal'' in the ring of smooth differential forms on a smooth manifold, in other words a graded ideal in the sense of ring theory, that is further closed under exterior differentiation ''d''. In other words, for any form α in ''I'', the exterior derivative ''d''α is also in ''I''. In the theory of differential algebra, a differential ideal ''I'' in a differential ring ''R'' is an ideal which is mapped to itself by each differential operator. == Exterior differential systems and partial differential equations == An exterior differential system on a manifold ''M'' is a differential ideal :$I\backslash subset\; \backslash Omega^$ *(M) . One can express any partial differential equation system as an exterior differential system with independence condition. Say that we have ''k''th order partial differential equation systems for maps $f:\; \backslash mathbb^m\; \backslash rightarrow\; \backslash mathbb^n$, given by :$F^r(x,\; u,\; \backslash frac)=0,\; \backslash quad\; 1\backslash le\; |I|\backslash le\; k$. The solution of this partial differential equation system is the submanifold $\backslash Sigma$ of the jet space consisting of integral manifolds of the pullback of the contact system to $\backslash Sigma$. This idea allows one to analyze the properties of partial differential equations with methods of differential geometry. For instance, we can apply Cartan's method on partial differential equation systems by writing down the exterior differential system associated with it. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Differential ideal」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.