Divergence


 
 

In vector calculus, the divergence is an operator that measures a vector field's tendency to originate from or converge upon a given point. For instance, for a vector field that denotes the velocity of water flowing in a draining bathtub, the divergence would have a negative value over the drain because the water vanishes there (if we only consider two dimensions); away from the drain the divergence would be zero, since there are no other sinks or sources.

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A vector field which has zero divergence everywhere is called solenoidal.

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Vector calculus: Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. It consists of a suite of formulas and problem solving techniques very useful for engineering and physics....

Vector field: In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space....

Tendency: The word tendency may have a number of meanings. It may refer to:...

~ Table of Content ~

Introduction
Definition
rac{partial F_x}{partial x}
a;operatorname{div}( mathbf{F} )
operatorname{grad}( arphi) cdot mathbf{F}
( abla arphi) cdot mathbf{F}
operatorname{curl}(mathbf{F})cdotmathbf{G}
( abla imesmathbf{F})cdotmathbf{G}
 


 

~ Related Subjects ~

Dimension (2) - Mathematics (2) - Vector (2) - Vector calculus (2) - Formula (1) - Engineering (1) - Euclidean space (1) - Physics (1) - Bathtub (1) - Velocity (1) - Tendency (1) - Real analysis (1) - Vector field (1) -
 

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