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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.
Del operator, represented by the nabla symbol. Del, or nabla, is an operator used in mathematics (particularly in vector calculus) as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes the standard derivative of the function as defined in calculus.
As a second-order differential operator, the Laplace operator maps C k functions to C k−2 functions for k ≥ 2.It is a linear operator Δ : C k (R n) → C k−2 (R n), or more generally, an operator Δ : C k (Ω) → C k−2 (Ω) for any open set Ω ⊆ R n.
This formula does not explicitly depend on the definition of the scalar product. It is therefore sometimes chosen as a definition of the adjoint operator. When is defined according to this formula, it is called the formal adjoint of T. A (formally) self-adjoint operator is an operator equal to its own (formal) adjoint.
The vector of coordinates forms the coordinate vector or n-tuple (x 1, x 2, …, x n). Each coordinate x i may be parameterized a number of parameters t . One parameter x i ( t ) would describe a curved 1D path, two parameters x i ( t 1 , t 2 ) describes a curved 2D surface, three x i ( t 1 , t 2 , t 3 ) describes a curved 3D volume of space ...
Since this article is about the del operator, not the differential operator, the formulas should be replaced by the correct ones. The terms of each formula are judiciously arranged in the form of a matrix corresponding to the matrix of the tensor. To preserve this form pairs of corresponding off-diagonal coefficients should be transposed.
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In trigonometry, the Snellius–Pothenot problem is a problem first described in the context of planar surveying.Given three known points A, B, C, an observer at an unknown point P observes that the line segment AC subtends an angle α and the segment CB subtends an angle β; the problem is to determine the position of the point P.