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  2. Curl (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Curl_(mathematics)

    The curl of a 3-dimensional vector field which only depends on 2 coordinates (say x and y) is simply a vertical vector field (in the z direction) whose magnitude is the curl of the 2-dimensional vector field, as in the examples on this page. Considering curl as a 2-vector field (an antisymmetric 2-tensor) has been used to generalize vector ...

  3. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    C: curl, G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do not exist.

  4. Divergence - Wikipedia

    en.wikipedia.org/wiki/Divergence

    In physical terms, the divergence of a vector field is the extent to which the vector field flux behaves like a source or a sink at a given point. It is a local measure of its "outgoingness" – the extent to which there are more of the field vectors exiting from an infinitesimal region of space than entering it.

  5. 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).

  6. Multivariable calculus - Wikipedia

    en.wikipedia.org/wiki/Multivariable_calculus

    Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables (multivariate), rather than just one.

  7. Generalized Stokes theorem - Wikipedia

    en.wikipedia.org/wiki/Generalized_Stokes_theorem

    For example, if the domain of integration is defined as the plane region between two -coordinates and the graphs of two functions, it will often happen that the domain has corners. In such a case, the corner points mean that Ω {\displaystyle \Omega } is not a smooth manifold with boundary, and so the statement of Stokes' theorem given above ...

  8. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist.

  9. List of mathematical abbreviations - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    R – real numbers. ran – range of a function. rank – rank of a matrix. (Also written as rk.) Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field.