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SEO Keyword summary for en.wikipedia.org/wiki/exterior_derivative
Keywords are extracted from the main content of your website and are the primary indicator of the words this page could rank for. By frequenty count we expect your focus keyword to be wedge
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Short Tail Keywords wedge displaystyle partial |
long Tail Keywords (2 words) exterior derivative cdots wedge wedge beta if displaystyle displaystyle alpha |
long Tail Keywords (3 words) dalpha wedge beta move to sidebar if displaystyle alpha dxi1wedge cdots wedge dxi2wedge cdots wedge terms of axioms leftdxi1wedge cdots wedge |
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exterior derivative wikipedia
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wikipedia free encyclopedia displaystyle int abftdtfbfa alpha beta daalpha bbeta adalpha bdbeta dalpha wedge kalpha dbeta ddalpha dfwedge dfg dfgdfggdf gamma klalpha dgamma varphi gdxigdxi dxi cdots dxik dvarphi dgwedge dxikfrac partial gpartial xjdxjwedge omega fidxi beginaligneddvarphi dleftgdxi dxikrightdgwedge leftdxi dxikrightgdleftdxi dxikgsum dxip xipwedge dxikdgwedge xidxiwedge dxikendaligned domega frac fipartial ijpartial iomega jpartial jomega dxikrightleftfrac ldots xikright xikrightfrac vksum iviomega widehat vildots ijomega vivjv vjldots vkomega beginaligneddomega over sum vkendaligned beginaligneddsigma duwedge leftsum nfrac upartial xidxirightwedge nleftfrac rightendaligned dxrightleftsum vpartial dyrightleftfrac xdxwedge dxfrac ydywedge dxrightleftfrac dyfrac dyright ydxwedge leftfrac xfrac yrightdxwedge dyendaligned mdomega momega langle nabla fcdot rangle dfsum fpartial xidxi fdfsharp xileftdxirightsharp beginalignedomega leftdx dxnrightv dxnrightcdots vnleftdx dxn rightsum vileftdx dxiwedge dxnrightendaligned voperatorname div vleftdx dxnright eta vndxn deta vomega operatorname curl beginarrayrcccloperatorname grad fequiv fleftdfrightsharp cdot fstar dstar mathord leftfflat rightoperatorname times fleftstar dmathord rightrightsharp delta dfnabla fleftdstar rightstar endarray wikimedia foundation powered mediawiki
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calculus
fundamental theorem of calculus
limit of a function
continuous function
rolles theorem
mean value theorem
inverse function theorem
differential calculus
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differentiablesmooth manifold
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lie cartan
exterior calculus
gausss theorem
flux
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maps
1form
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pointwise
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work
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exterior covariant derivative
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https://wikimedia.org/api/rest_v1/media/math/render/svg/869d723e075db892559c539b23060086e231ea45 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}d\sigma &=\left(\sum _{i=1}^{2}{\frac {\partial u}{\partial x^{i}}}dx^{i}\wedge dx\right)+\left(\sum _{i=1}^{2}{\frac {\partial v}{\partial x^{i}}}\,dx^{i}\wedge dy\right)\\&=\left({\frac {\partial {u}}{\partial {x}}}\,dx\wedge dx+{\frac {\partial {u}}{\partial {y}}}\,dy\wedge dx\right)+\left({\frac {\partial {v}}{\partial {x}}}\,dx\wedge dy+{\frac {\partial {v}}{\partial {y}}}\,dy\wedge dy\right)\\&=0-{\frac {\partial {u}}{\partial {y}}}\,dx\wedge dy+{\frac {\partial {v}}{\partial {x}}}\,dx\wedge dy+0\\&=\left({\frac {\partial {v}}{\partial {x}}}-{\frac {\partial {u}}{\partial {y}}}\right)\,dx\wedge dy\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/945945319b3949e79bb9d23b58f0937c41141b63 height: height attribute not set width: width attribute not set description: {\displaystyle \int _{m}d\omega =\int _{\partial {m}}\omega } |
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https://upload.wikimedia.org/wikipedia/commons/b/bf/exteriorderivnatural.png height: 110 width: 195 description: no alt description found |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/1f75d8a5905d837fe167e995f37848fc4d43cdeb height: height attribute not set width: width attribute not set description: {\displaystyle \langle \nabla f,\cdot \rangle =df=\sum _{i=1}^{n}{\frac {\partial f}{\partial x^{i}}}\,dx^{i}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/6e8382ed383109a5a90ea12bfceb4a270e4147c1 height: height attribute not set width: width attribute not set description: {\displaystyle \nabla f=(df)^{\sharp }=\sum _{i=1}^{n}{\frac {\partial f}{\partial x^{i}}}\,\left(dx^{i}\right)^{\sharp },} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/cea77f7a8c54c5c3b84746b31429813e98489ef3 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{aligned}\omega _{v}&=v_{1}\left(dx^{2}\wedge \cdots \wedge dx^{n}\right)-v_{2}\left(dx^{1}\wedge dx^{3}\wedge \cdots \wedge dx^{n}\right)+\cdots +(-1)^{n-1}v_{n}\left(dx^{1}\wedge \cdots \wedge dx^{n-1}\right)\\&=\sum _{i=1}^{n}(-1)^{(i-1)}v_{i}\left(dx^{1}\wedge \cdots \wedge dx^{i-1}\wedge {\widehat {dx^{i}}}\wedge dx^{i+1}\wedge \cdots \wedge dx^{n}\right)\end{aligned}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/b67eae31c334c40f99ef1b2e7fcf93442c8315c3 height: height attribute not set width: width attribute not set description: {\displaystyle {\widehat {dx^{i}}}} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/28bc1c1e4a173031d36f8cbcbd50055607d449c5 height: height attribute not set width: width attribute not set description: {\displaystyle d\omega _{v}=\operatorname {div} v\left(dx^{1}\wedge dx^{2}\wedge \cdots \wedge dx^{n}\right).} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a7a8b22045be59289907281fd5ee1c19d93b9b30 height: height attribute not set width: width attribute not set description: {\displaystyle \eta _{v}=v_{1}\,dx^{1}+v_{2}\,dx^{2}+\cdots +v_{n}\,dx^{n}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/d8ee630651aa93ae4878e019c589be49cf5870d0 height: height attribute not set width: width attribute not set description: {\displaystyle d\eta _{v}=\omega _{\operatorname {curl} v}.} |
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https://wikimedia.org/api/rest_v1/media/math/render/svg/a3e50370cdcc920aabe57346d3dc6299622045d6 height: height attribute not set width: width attribute not set description: {\displaystyle {\begin{array}{rcccl}\operatorname {grad} f&\equiv &\nabla f&=&\left(df\right)^{\sharp }\\\operatorname {div} f&\equiv &\nabla \cdot f&=&{\star d{\star }{\mathord {\left(f^{\flat }\right)}}}\\\operatorname {curl} f&\equiv &\nabla \times f&=&\left({\star }d{\mathord {\left(f^{\flat }\right)}}\right)^{\sharp }\\\delta f&\equiv &\nabla ^{2}f&=&{\star }d{\star }df\\&&\nabla ^{2}f&=&\left(d{\star }d{\star }{\mathord {\left(f^{\flat }\right)}}-{\star }d{\star }d{\mathord {\left(f^{\flat }\right)}}\right)^{\sharp },\\\end{array}}} |
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https://login.wikimedia.org/wiki/special:centralautologin/start?type=1x1 height: 1 width: 1 description: no alt description found |
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http://en.wikipedia.org/static/images/footer/wikimedia-button.svg height: 29 width: 84 description: wikimedia foundation |
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http://en.wikipedia.org/w/resources/assets/poweredby_mediawiki.svg height: 31 width: 88 description: powered by mediawiki |
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