Encyclopedia > Del in cylindrical and spherical coordinates
This is a list of some vector calculus formulae of general use in working with standard coordinate systems. Vector calculus (also called vector analysis) is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. ... In mathematics as applied to geometry, physics or engineering, a coordinate system is a system for assigning a tuple of numbers to each point in an n-dimensional space. ...
Table with the del operator in cylindrical and spherical coordinates
or In vector calculus, del is a vector differential operator represented by the nabla symbol: ∇. Del is a mathematical tool serving primarily as a convention for mathematical notation; it makes many equations easier to comprehend, write, and remember. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ... For other uses, see Gradient (disambiguation). ... In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... In vector calculus, curl is a vector operator that shows a vector fields rate of rotation: the direction of the axis of rotation and the magnitude of the rotation. ... In mathematics and physics, the Laplace operator or Laplacian, denoted by Δ, is a differential operator, specifically an important case of an elliptic operator, with many applications. ...
In vector calculus, the Laplace operator or Laplacian is a differential operator equal to the sum of all the unmixed second partial derivatives of a dependent variable. ... For the crossed product in algebra and functional analysis, see crossed product. ...
Remarks
This page uses standard physics notation; some (American mathematics) sources define φ as the angle from the z-axis instead of θ.
The function atan2(y, x) is used instead of the mathematical function arctan(y/x) due to its domain and image. The classical arctan(y/x) has an image of (-π/2, +π/2), whereas atan2(y, x) is defined to have an image of (-π, π].
Atan2 is a two-parameter function for computing the arctangent in the C programming language. ...
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