About: Stokes' theorem

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Stokes's theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, is a theorem in vector calculus on R3. Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The classical Stokes' theorem can be stated in one sentence: The line integral of a vector field over a loop is equal to the flux of its curl through the enclosed surface.

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rdfs:label	مبرهنة كلفن-ستوكس (ar) Teorema del rotore (it) ケルビン・ストークスの定理 (ja) Stokes' theorem (en)
rdfs:comment	In matematica, il teorema del rotore, anche detto teorema di Kelvin o teorema di Kelvin-Stokes, il cui nome è dovuto a Lord Kelvin e George Stokes, afferma che il flusso del rotore di determinati campi vettoriali attraverso superfici regolari dotate di bordo è uguale alla circuitazione del campo lungo la frontiera della superficie. Si tratta pertanto di un caso particolare del teorema di Stokes. Il teorema di Green è un caso speciale del teorema del rotore che considera superfici appartenenti a . (it) ケルビン・ストークスの定理（ケルビン・ストークスのていり、英: Kelvin–Stokes' theorem）は、3次元ベクトル場の2次元曲面上での面積分に関する定理であり、本定理は、与えられたベクトル場の回転を面積分したものと、前記面積分の積分領域の境界での線積分とを関連付ける。本定理は、一般化されたストークスの定理の特殊なケースの一つであり、3次元ベクトル場が、上の一次微分形式と見なした場合に対応する（この場合外微分dがrotに対応する）。本定理は、回転定理ともいわれる。 (ja) مبرهنة كلفن–ستوكس، سميت نسبةً للرياضياتيين لورد كلفن وجورج ستوكس، معروفة أيضًا باسم مبرهنة ستوكس، أو المبرهنة الأساسية للدوران أو ببساطة مبرهنة الدوران، هي مبرهنة في حساب المتجهات على . بالنظر إلى حقل متجهي، تربط المبرهنة تكامل دوران الحقل المتجهي على بعض السطح، بالتكامل الخطي للحقل المتجهي حول حدود السطح. إذا كان الحقل المتجهي معرفة في منطقة ذات سطح ناعم موجه وله مشتقات جزئية مستمرة من الدرجة الأولى، فإن: حيث هي حدود المنطقة ذات سطح ناعم . يمكن ذكر مبرهنة كلفن-ستوكس الكلاسيكية المذكورة أعلاه في جملة واحدة: التكامل الخطي لحقل متجه على عُرْوة (Loop) يساوي تدفق دورانه عبر السطح المغلق. (ar) Stokes's theorem, also known as the Kelvin–Stokes theorem after Lord Kelvin and George Stokes, the fundamental theorem for curls or simply the curl theorem, is a theorem in vector calculus on R3. Given a vector field, the theorem relates the integral of the curl of the vector field over some surface, to the line integral of the vector field around the boundary of the surface. The classical Stokes' theorem can be stated in one sentence: The line integral of a vector field over a loop is equal to the flux of its curl through the enclosed surface. (en)
rdfs:seeAlso	Maxwell's equations Curl
foaf:depiction
dct:subject	Vectors (mathematics and physics) Electromagnetism Mechanics Vector calculus
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Wikipage revision ID	1124959760 (xsd:integer)
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