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In vector calculus, del is a vector differential operator represented by the symbol ∇. This symbol is sometimes called the nabla operator, after the Greek word for a kind of harp with a similar shape (with related words in Aramaic and Hebrew). (Another, less-common name is Atled, because it is a reversed Delta.) Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in 2 or more dimensions. ...
This article is about operators in mathematics, for other kinds of operators see operator (disambiguation). ...
The harp is a chordophone whose strings are positioned perpendicular to the soundboard. ...
In geometry, two sets of points are of the same shape precisely if one can be transformed to another by dilating (i. ...
Aramaic is a Semitic language with a 3,000-year history. ...
The Modern Hebrew language is a Semitic language of the Afro-Asiatic language family. ...
Delta (upper case Δ, lower case δ) is the 4th letter of the Greek alphabet. ...
It is a shorthand for the vector: In physics and engineering, the word vector typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but this...
The symbol ∇ was introduced by William Rowan Hamilton. William Rowan Hamilton Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematician, physicist, and astronomer. ...
The operator can be applied to scalar fields (φ) or vector fields F, to give: In mathematics and physics, a scalar field associates a single number (or scalar) to every point in space. ...
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 Euclidean space. ...
In differential geometry, the nabla symbol is also used to refer to a connection. In vector calculus, the gradient of a scalar field is a vector field which points in the direction of the greatest rate of change of the scalar field, and whose magnitude is the greatest rate of change. ...
In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ...
cURL is a command line tool for transferring files with URL syntax, supporting FTP, FTPS, HTTP, HTTPS, Gopher, Telnet, DICT, FILE and LDAP. cURL supports HTTPS certificates, HTTP POST, HTTP PUT, FTP uploading, Kerberos, HTTP form based upload, proxies, cookies, user+password authentication, file transfer resume, http proxy tunneling and...
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. ...
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ...
In differential geometry, a connection (also connexion) or covariant derivative is a way of specifying a derivative of a vector field along another vector field on a manifold. ...
See also
In mathematics, a set of symbols is frequently used in mathematical expressions. ...
Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...
This is a list of some vector calculus formulae of general use in working with standard coordinate systems. ...
Further reading - Div, Grad, Curl, and All That, H. M. Schey, ISBN 0-393-96997-5
- Jeff Miller, Earliest Uses of Symbols of Calculus (http://members.aol.com/jeff570/calculus.html) (Aug. 30, 2004).
- Cleve Moler, ed., "History of Nabla (http://www.netlib.org/na-digest-html/98/v98n03.html#2)", NA Digest 98 (Jan. 26, 1998).
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