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  2. Stokes' theorem - Wikipedia

    en.wikipedia.org/wiki/Stokes'_theorem

    An illustration of Stokes' theorem, with surface Σ, its boundary ∂Σ and the normal vector n.The direction of positive circulation of the bounding contour ∂Σ, and the direction n of positive flux through the surface Σ, are related by a right-hand-rule (i.e., the right hand the fingers circulate along ∂Σ and the thumb is directed along n).

  3. Generalized Stokes theorem - Wikipedia

    en.wikipedia.org/wiki/Generalized_Stokes_theorem

    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 or , and the divergence theorem is the case of a volume in . [2] Hence, the theorem is sometimes referred to as the fundamental theorem of multivariate calculus.

  4. Discrete exterior calculus - Wikipedia

    en.wikipedia.org/wiki/Discrete_exterior_calculus

    In this notation, Stokes' theorem reads as = . In finite element analysis, the first stage is often the approximation of the domain of interest by a triangulation, T. For example, a curve would be approximated as a union of straight line segments; a surface would be approximated by a union of triangles, whose edges are straight line segments ...

  5. Surface integral - Wikipedia

    en.wikipedia.org/wiki/Surface_integral

    Assume that f is a scalar, vector, or tensor field defined on a surface S.To find an explicit formula for the surface integral of f over S, we need to parameterize S by defining a system of curvilinear coordinates on S, like the latitude and longitude on a sphere.

  6. Circulation (physics) - Wikipedia

    en.wikipedia.org/wiki/Circulation_(physics)

    By Stokes' theorem, the flux of curl or vorticity vectors through a surface S is equal to the circulation around its perimeter, [4] = = = Here, the closed integration path ∂S is the boundary or perimeter of an open surface S , whose infinitesimal element normal d S = n dS is oriented according to the right-hand rule .

  7. Stokes problem - Wikipedia

    en.wikipedia.org/wiki/Stokes_problem

    Stokes boundary layer due to the sinusoidal oscillation of the far-field flow velocity. The horizontal velocity is the blue line, and the corresponding horizontal particle excursions are the red dots.

  8. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum – a continuous substance rather than discrete particles. Another necessary assumption is that all the fields of interest including pressure , flow velocity , density , and temperature are at least weakly differentiable .

  9. Orthologic triangles - Wikipedia

    en.wikipedia.org/wiki/Orthologic_triangles

    Anticomplementary triangle; Orthic triangle; The triangle whose vertices are the points of contact of the incircle with the sides of ABC; Tangential triangle; The triangle whose vertices are the points of contacts of the excircles with the respective sides of triangle ABC; The triangle formed by the bisectors of the external angles of triangle ABC

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