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Meaning of partial differential in limits of integration?

0

$begingroup$

I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_{partial z} $

What exactly does it represent/mean? When is it used?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 26 at 10:13

Simplex1Simplex1

745

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It might be the boundary of some domain.
  $endgroup$
  – Gibbs
  Mar 26 at 10:14
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ohh...ok... i get it... Q is a region that denotes an "area", whereas $partial{Q}$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
  $endgroup$
  – DiscreteMath
  Mar 28 at 15:26
  
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_{partial z} $

What exactly does it represent/mean? When is it used?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 26 at 10:13

Simplex1Simplex1

745

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  It might be the boundary of some domain.
  $endgroup$
  – Gibbs
  Mar 26 at 10:14
  
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  ohh...ok... i get it... Q is a region that denotes an "area", whereas $partial{Q}$ is the "circumference" around this 2-dimensional area. The "boundary" of the "area". Right or wrong?
  $endgroup$
  – DiscreteMath
  Mar 28 at 15:26
  
  
  

  
  
  
  

add a comment | 

$begingroup$

I have seen some maths problems where there is a partial differential in the limits of integration, for example: $int_{partial z} $

What exactly does it represent/mean? When is it used?

calculus integration definite-integrals

share|cite|improve this question

asked Mar 26 at 10:13

Simplex1Simplex1

745

$endgroup$

share|cite|improve this question

asked Mar 26 at 10:13

Simplex1Simplex1

745

share|cite|improve this question

asked Mar 26 at 10:13

Simplex1Simplex1

745

asked Mar 26 at 10:13

Simplex1Simplex1

745

asked Mar 26 at 10:13

Simplex1Simplex1

745

2 Answers
2

active

oldest

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1

$begingroup$

If you provide more context, it may be clearer but it may mean "the boundary of $z$".

This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.

share|cite|improve this answer

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

$endgroup$

add a comment | 

1

$begingroup$

The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.

share|cite|improve this answer

answered Mar 26 at 10:16

5xum5xum

92.9k395162

$endgroup$

add a comment | 

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1

$begingroup$

If you provide more context, it may be clearer but it may mean "the boundary of $z$".

This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.

share|cite|improve this answer

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

$endgroup$

add a comment | 

1

$begingroup$

If you provide more context, it may be clearer but it may mean "the boundary of $z$".

This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.

share|cite|improve this answer

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

$endgroup$

add a comment | 

$begingroup$

If you provide more context, it may be clearer but it may mean "the boundary of $z$".

This makes sense if $z$ represents some region, e.g. a disc, and then the integral over $partial z$ means you integrate over its boundary, in the case of the example the circle bounding the disc.

share|cite|improve this answer

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

$endgroup$

share|cite|improve this answer

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

answered Mar 26 at 10:14

StackTDStackTD

24.3k2254

1

$begingroup$

The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.

share|cite|improve this answer

answered Mar 26 at 10:16

5xum5xum

92.9k395162

$endgroup$

add a comment | 

1

$begingroup$

The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.

share|cite|improve this answer

answered Mar 26 at 10:16

5xum5xum

92.9k395162

$endgroup$

add a comment | 

$begingroup$

The symbol $partial$ is often used to denote the boundary of a set. So, for example, if $D$ is some (nice enough) set in $mathbb C$, then $partial D$ is the boundary of $D$, and this means that the integral over $partial D$ is simply a line integral.

share|cite|improve this answer

answered Mar 26 at 10:16

5xum5xum

92.9k395162

$endgroup$

share|cite|improve this answer

answered Mar 26 at 10:16

5xum5xum

92.9k395162

answered Mar 26 at 10:16

5xum5xum

92.9k395162

answered Mar 26 at 10:16

5xum5xum

92.9k395162