A doubt on total differentials

  • Thread starter Thread starter Rishabh Narula
  • Start date Start date
  • Tags Tags
    Differentials Doubt
Click For Summary
The discussion centers on understanding total differentials in the context of a horizontal plane through point P. The rectangle PDEF is confirmed to be flat and not sloped, which is crucial for the analysis. Participants are encouraged to clarify their statements for better feedback. The question posed is whether the short proof regarding the relationship between partial derivatives and small changes in dimensions accurately defines the total differential. Overall, the conversation emphasizes the importance of clear communication and the correct interpretation of mathematical concepts.
Rishabh Narula
Messages
61
Reaction score
5
Please refer to the images and my handwritten note(i tried my best handwriting) for the question
 

Attachments

  • pf doubt 1.jpg
    pf doubt 1.jpg
    39.7 KB · Views: 205
  • pf doubt 2.jpg
    pf doubt 2.jpg
    37.5 KB · Views: 230
  • 20200116_150022.jpg
    20200116_150022.jpg
    68.1 KB · Views: 216
Physics news on Phys.org
There is a horizontal plane (z constant) through the point P. They are identifying a rectangle in it as PDEF. There is nothing there that one can argue with. It is not "sloped". With that in mind, you should reconsider your thinking.

PS. If you type your statements in, then it is easier for people to comment on specific parts of it.
 
Last edited:
  • Like
Likes Rishabh Narula and berkeman
Thanks,will do that next time onwards.Is the short proof right,that the different partials multiplied by small changes in different dimensions,when added up give the total small change?
 
That is what is defined as the "total differential".
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Finding the differential equation of motion
  • · Replies 4 ·
Replies
4
Views
2K
I don't understand how the author calculated the pullback of the 1 form (differential geometry)
  • · Replies 5 ·
Replies
5
Views
2K
Notion of an integral as a summation
  • · Replies 4 ·
Replies
4
Views
1K
Chemistry A confusion about conductance of weak electrolytes
  • · Replies 6 ·
Replies
6
Views
3K
LaTeX Writing Notes LaTeX: Benefits vs Handwritten Notes
  • · Replies 2 ·
Replies
2
Views
2K
Given unit impulse response, obtain differential equation
  • · Replies 7 ·
Replies
7
Views
2K
Study Function: Continuity, Derivatives & Differentiability
  • · Replies 6 ·
Replies
6
Views
2K
Reduction of order for Second Order Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Why can't a critical point of a system of DEs be complex?
  • · Replies 27 ·
Replies
27
Views
2K
Doubt about the derivative of a Taylor series
  • · Replies 42 ·
2
Replies
42
Views
4K