Gauss' Theorem -- Why two different notations are used?

  • #1
sams
Gold Member
84
2
In Mathematical Methods for Physicists, Sixth Edition, Page 60, Section 1.11, the Gauss' theorem is written as:
Gauss' Theorem.PNG

In Mathematical Methods for Physicists, Fifth Edition, Page 61, Section 1.11, the Gauss' theorem is written as:
Gauss' Theorem 2.jpeg

Kindly I would like to know please:
1. What is the difference between the two relations?
2. What does ##\partial{V}## in Equation (1.101a) stands for? In physics, I realized that ##\partial{V}## is usually not included when Gauss' theorem is used, why is that?

Thanks a lot for your help...
 

Attachments

Last edited by a moderator:

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
16,171
8,204
In Mathematical Methods for Physicists, Sixth Edition, Page 60, Section 1.11, the Gauss' theorem is written as:
View attachment 231423
In Mathematical Methods for Physicists, Fifth Edition, Page 61, Section 1.11, the Gauss' theorem is written as:
View attachment 231424
Kindly I would like to know please:
1. What is the difference between the two relations?
2. What does ##\partial{V}## in Equation (1.101a) stands for? In physics, I realized that ##\partial{V}## is usually not included when Gauss' theorem is used, why is that?

Thanks a lot for your help...
Do these books not make their notation clear? The only difference is notational.

##\partial V## is sometimes used for the surface of a region ##V##. In the second equation, simply ##S## is used for the surface of the region ##V##.
 
  • Like
Likes sams
  • #3
12,499
6,286
The notation used by the sixth edition was to remind the reader that the left hand side is a double integral over the surface of the region and the right hand side is a triple integral over the volume of the region. They likely changed it as someone brought it to their attention or an editor schooled as a physicist took issue and decided it was best to change it.
 
  • Like
Likes dextercioby and sams
  • #5
Usually un physics triple or double integrals $$\int \int$$ $$\int \int \int$$
Are changed by only one simbol $$\int$$, so that is the same equation.

The simbol $$\partial v$$ means that the integral Is computed on boundary superfice of $$v$$ or on boundary of $$v$$.
$$\partial v=S$$
 
  • Like
Likes sams
  • #6
sams
Gold Member
84
2
Thank you all for your help and for your explanations
 

Related Threads on Gauss' Theorem -- Why two different notations are used?

Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
Replies
30
Views
1K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
13
Views
4K
  • Last Post
Replies
4
Views
14K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
2
Views
8K
Top