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Divergence

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal neighborhood of each point. (In 2D this "volume" refers to area.) More precisely, the divergence at a point is the rate that the flow of the vector field modifies a…

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Overview

Physical interpretation of divergence

Definition

Definition in coordinates

Properties

Decomposition theorem

Relation to the exterior derivative

In curvilinear coordinates

The divergence of tensors

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Divergence

Nodes81
Edges80
Triples93
Avg. degree1.98
Density0.024691
Components1

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Divergence

Top relations

related to References · 35
Divergence → Academic Press, Advanced Calculus, An Introduction, Archived, Brewer, Continuum Mechanics, Definitions, Dover, Dover Publications, Edwards, Engineers, Formulas, Granino Arthur, Gurtin, ISBN, January, Jess, Korn, Mathematical Handbook, McGraw-Hill
related to Physical interpretation of divergence · 11
Divergence → Any, If, In, It, Similarly, So, The, There, Therefore, This, Thus
related to External links · 10
Divergence → Academy, Archived, EMS Press, Encyclopedia, Grant, June, Mathematics, Maxwell's, The, YouTube
related to In curvilinear coordinates · 6
Divergence → Generalising, Lie, Lorentzian, R3, Riemannian, The
related to Relation to the exterior derivative · 5
Divergence → Define, It, Its, One, R3
is a · 4
Divergence → codifferential in disguise, linear operator, same in any coordinate system, vector operator that operates on a vector field
related to Cylindrical coordinates · 4
Divergence → For, If, In, The
related to General coordinates · 4
Divergence → Here, The, The Voss-Weyl, Using Einstein
related to In arbitrary finite dimensions · 3
Divergence → Euclidean, If, The
related to The divergence of tensors · 3
Divergence → Fμ, In, In Einstein

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Important terminology

vector field volume displaystyle velocity point coordinates flux gas mathbf div coordinate surface zero derivative right thus tensor local closed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Divergenceis avector operator that operates on a vector field0.90text
Divergenceis asame in any coordinate system0.90text
Divergenceis alinear operator0.90text
Divergenceis acodifferential in disguise0.90text
Divergencerelated to Cartesian coordinatesIn0.60section
Divergencerelated to Cartesian coordinatesCartesian0.60section
Divergencerelated to Cylindrical coordinatesFor0.60section
Divergencerelated to Cylindrical coordinatesThe0.60section
Divergencerelated to Cylindrical coordinatesIf0.60section
Divergencerelated to Cylindrical coordinatesIn0.60section
Divergencerelated to DefinitionThe0.60section
Divergencerelated to DefinitionIt0.60section

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