Divergence Theorem - Revision history

SamHB: No. Limiting to only the smallest category may be right for some topics, but not for mathematics and science. See talk.

2021-03-02T04:51:14Z

No. Limiting to only the smallest category may be right for some topics, but not for mathematics and science. See talk.

Quidam65: update to more specific category

2021-03-01T23:16:48Z

update to more specific category

DavidB4-bot: /* top */Category

2016-07-29T20:17:49Z

top: Category

DavidB4-bot: /* top */clean up & uniformity

2016-07-13T11:43:37Z

top: clean up & uniformity

Aschlafly: add dates of origination

2012-09-09T20:35:37Z

add dates of origination

BradleyS at 17:18, July 9, 2011

2011-07-09T17:18:57Z

Aschlafly: clarified further

2009-12-26T20:18:29Z

clarified further

Aschlafly: only Conservapedia explains math concepts well. This theorem: the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface

2009-12-26T18:48:48Z

only Conservapedia explains math concepts well. This theorem: the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface

Aschlafly: a start

2009-12-26T16:10:10Z

a start

New page

The '''divergence theorem''' establishes the volume integral (triple integral) of a function over a three-dimensional shape ''equals'' the double integral of the same function over the two-dimensional surface that encloses the space.

For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.

This is also known as the Gauss Theorem, and it is the simplest of the three main integral theorems in advanced or multivariable calculus, the other two being [[Green's Theorem]] and [[Stokes' Theorem]].
[[Category:vector analysis]]
[[Category:calculus]]
[[Category:mathematics]]

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	[[Category:Calculus]]		[[Category:Calculus]]
		+	[[Category:Mathematics]]

← Older revision		Revision as of 23:16, March 1, 2021
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	[[Category:Calculus]]		[[Category:Calculus]]
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 This is also known as the Gauss Theorem (1813), and it is the simplest of the three main integral theorems in advanced or multivariable calculus, the other two being [[Green's Theorem]] (1825) and [[Stokes' Theorem]] (1850).
-[[Category:Vector analysis]]
+[[Category:Vector Analysis]]
 [[Category:Calculus]]
 [[Category:Mathematics]]

@@ Line 8: / Line 8: @@
 This is also known as the Gauss Theorem (1813), and it is the simplest of the three main integral theorems in advanced or multivariable calculus, the other two being [[Green's Theorem]] (1825) and [[Stokes' Theorem]] (1850).
-[[Category:vector analysis]]
+[[Category:Vector analysis]]
-[[Category:calculus]]
+[[Category:Calculus]]
-[[Category:mathematics]]
+[[Category:Mathematics]]

@@ Line 1: / Line 1: @@
 The '''divergence theorem''' states that the overall (net) flux through the surface of an object equals the summation of all the changes in flux inside the object.  Stated more formally, the net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface.
-In mathematical terms, the '''divergence theorem''' establishes that the volume integral (triple integral) of the derivative (divergence) of a vector function over a three-dimensional shape ''equals'' the double integral of the perpendicular component of same function with respect to a two-dimensional surface that encloses the space.
+In mathematical terms, the '''divergence theorem''' establishes that the volume integral (triple integral) of the derivative (divergence) of a vector function over a three-dimensional shape (V) ''equals'' the double integral of the perpendicular component of same function with respect to a two-dimensional surface that encloses the space (S):
 For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.

← Older revision		Revision as of 18:48, December 26, 2009
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−	The '''divergence theorem''' establishes the volume integral (triple integral) of a function over a three-dimensional shape ''equals'' the double integral of the same function ~~over the~~ two-dimensional surface that encloses the space.	+	The '''divergence theorem''' establishes the volume integral (triple integral) of the derivative (divergence) of a vector function over a three-dimensional shape ''equals'' the double integral of the perpendicular component of same function with respect to a two-dimensional surface that encloses the space.
		+
		+	Simply put, the overall net flux through a closed surface equals the sum of all the changes in flux throughout the volume enclosed by the surface.

	For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.		For example, the volume integral of the electric field caused by a charge within an electric sphere equals the surface integral of that same field.