Partial Derivatives: What are They and Why Are They Used?

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Homework Help Overview

The discussion revolves around the concept of partial derivatives, particularly in the context of functions of multiple variables, such as the magnetic field represented by B. Participants are exploring the conditions under which partial derivatives can be considered continuous.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question how to determine the continuity of a function's first and second partial derivatives. There is an exploration of evaluating these derivatives if a formula for the function is available, as well as a discussion on the implications of empirical laws in physics regarding the continuity of derivatives.

Discussion Status

The discussion is active, with participants seeking clarification on the continuity of partial derivatives and sharing insights about the nature of functions in physics. Some guidance has been offered regarding the evaluation of derivatives and assumptions about their continuity based on empirical observations.

Contextual Notes

There is an underlying assumption that naturally occurring phenomena, such as the magnetic field, are infinitely differentiable, which is being discussed in relation to the continuity of derivatives.

sparkle123
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Why can you do this?
6f2ca8b6.png

thanks!
 
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It can be done if B, as a function of x & t, and its first and second partial derivatives are all continuous.
 
Thanks!
How would you know if a function's first and 2nd partial derivatives are continuous?
 
sparkle123 said:
Thanks!
How would you know if a function's first and 2nd partial derivatives are continuous?

If you have a formula for B, you can try and evaluate them.

If B is the magnetic field, you can assume so, because our empirical laws of physics say so.
(Most naturally occurring phenomena are infinitely differentiable.)
 
Yes, B is the magnetic field! Thanks! :)
 

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