@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-RLHKF4PS-0
  skos:inScheme psr: ;
  a skos:Concept ;
  skos:prefLabel "théorème de Stokes"@fr, "generalized Stokes theorem"@en ;
  skos:altLabel "Stokes-Cartan theorem"@en, "Stokes' theorem"@en, "théorème de Stokes-Cartan"@fr ;
  skos:narrower psr:-DKRGCZ1S-Z ;
  skos:broader psr:-BQTC43FX-J ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Generalized_Stokes_theorem> ;
  dc:modified "2023-08-24"^^xsd:date ;
  skos:definition """In vector calculus and differential geometry the <b>generalized Stokes theorem</b> (sometimes with apostrophe as <b>Stokes' theorem</b> or <b>Stokes's theorem</b>), also called the <b>Stokes–Cartan theorem</b>, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.  In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {R} ^{2}}">
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<br/>            <mi mathvariant="double-struck">R</mi>
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<br/>            <mn>2</mn>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{2}}</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e150115ab9f63023215109595b76686a1ff890fd" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:2.732ex; height:2.676ex;" alt="\\\\R^2"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {R} ^{3},}">
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<br/>      <mstyle displaystyle="true" scriptlevel="0">
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<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
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<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mn>3</mn>
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<br/>        <mo>,</mo>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{3},}</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/deb17c1074c77de2cf88d45bcd6d7a795b0f5d44" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:3.379ex; height:3.009ex;" alt="{\\\\displaystyle \\\\mathbb {R} ^{3},}"></span> and the divergence theorem is the case of a volume in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\mathbb {R} ^{3}.}">
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<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <msup>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="double-struck">R</mi>
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<br/>            <mn>3</mn>
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<br/>        <mo>.</mo>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {R} ^{3}.}</annotation>
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<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b00b2b4fd27c2cbffa02df568472f77b194a6db9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:3.379ex; height:2.676ex;" alt="{\\\\displaystyle \\\\mathbb {R} ^{3}.}"></span> Hence, the theorem is sometimes referred to as the <b>Fundamental Theorem of Multivariate Calculus</b>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Generalized_Stokes_theorem">https://en.wikipedia.org/wiki/Generalized_Stokes_theorem</a>)"""@en .

psr:-BQTC43FX-J
  skos:prefLabel "analyse vectorielle"@fr, "vector calculus"@en ;
  a skos:Concept ;
  skos:narrower psr:-RLHKF4PS-0 .

psr:-DKRGCZ1S-Z
  skos:prefLabel "théorème de Green"@fr, "Green's theorem"@en ;
  a skos:Concept ;
  skos:broader psr:-RLHKF4PS-0 .