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  2. 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.

  3. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    The figure to the right is a mnemonic for some of these identities. The abbreviations used are: D: divergence, 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.

  4. Gradient - Wikipedia

    en.wikipedia.org/wiki/Gradient

    The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.

  5. List of formulas in Riemannian geometry - Wikipedia

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

    The gradient of a function is obtained by raising the index of the differential , whose components are given by: =; =; =, = = The divergence of a vector field with components is

  6. Grade (slope) - Wikipedia

    en.wikipedia.org/wiki/Grade_(slope)

    The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line is either the elevation angle of that surface to the horizontal or its tangent.

  7. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    [c] The right hand side is symmetric in v and w, so the shape operator is self-adjoint on the tangent space. The eigenvalues of S x are just the principal curvatures k 1 and k 2 at x . In particular the determinant of the shape operator at a point is the Gaussian curvature, but it also contains other information, since the mean curvature is ...

  8. Track geometry - Wikipedia

    en.wikipedia.org/wiki/Track_geometry

    The allowable gradients may be based on the ruling gradient which is the maximum gradient over which a tonnage train can be hauled with one locomotive. In some countries, momentum gradient which is a steeper but shorter gradient may be allowed. This is usually when a track gradient connects to a leveled tangent track long enough and with no ...

  9. Surface gradient - Wikipedia

    en.wikipedia.org/wiki/Surface_gradient

    In other words, the surface gradient is the orthographic projection of the gradient onto the surface. The surface gradient arises whenever the gradient of a quantity over a surface is important. In the study of capillary surfaces for example, the gradient of spatially varying surface tension doesn't make much sense, however the surface gradient ...