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  2. Divergence - Wikipedia

    en.wikipedia.org/wiki/Divergence

    In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.

  3. Del - Wikipedia

    en.wikipedia.org/wiki/Del

    Del is a very convenient mathematical notation for those three operations (gradient, divergence, and curl) that makes many equations easier to write and remember. The del symbol (or nabla) can be formally defined as a vector operator whose components are the corresponding partial derivative operators.

  4. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    As the name implies, the divergence is a (local) measure of the degree to which vectors in the field diverge. The divergence of a tensor field T {\displaystyle \mathbf {T} } of non-zero order k is written as div ⁡ ( T ) = ∇ ⋅ T {\displaystyle \operatorname {div} (\mathbf {T} )=\nabla \cdot \mathbf {T} } , a contraction of a tensor field ...

  5. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.

  6. Divergence theorem - Wikipedia

    en.wikipedia.org/wiki/Divergence_theorem

    The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus.

  7. Notation for differentiation - Wikipedia

    en.wikipedia.org/wiki/Notation_for_differentiation

    Divergence: The divergence of the vector field A is a scalar, which is ... Earliest Uses of Symbols of Calculus, maintained by Jeff Miller ...

  8. Operator (mathematics) - Wikipedia

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

    Div , (with operator symbol ) is a vector operator that measures a vector field's divergence from or convergence towards a given point. Curl , (with operator symbol ∇ × {\displaystyle \nabla \!\times } ) is a vector operator that measures a vector field's curling (winding around, rotating around) trend about a given point.

  9. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The divergence of an antisymmetric tensor ... The principal symbol of the ... [Results in Mathematics and Related Areas (3)], 10. Springer-Verlag, Berlin ...