Partial Differentiation [Subscript]

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Homework Help Overview

The discussion revolves around the notation used in partial differentiation, specifically the meaning of subscripts in expressions like \(\left(\frac{\partial x}{\partial y}\right)_z\). Participants are exploring the implications of this notation in different contexts, particularly in relation to its use in fields such as Thermodynamics.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the significance of the subscript in partial derivatives and whether it differs from standard notation. There is a discussion on its usage in various fields and its implications for understanding functions of multiple variables.

Discussion Status

The conversation is ongoing, with some participants providing insights into the meaning of the subscript and its relevance in specific disciplines. There is a recognition of the notation's rarity in Mathematics compared to its prevalence in other fields.

Contextual Notes

Some participants note that the notation indicates holding certain variables constant while differentiating, which may not be immediately clear to those encountering it for the first time.

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What does the subscript outside a partial differentiation mean? For example:

\left(\frac{\partial x}{\partial y}\right)_z

What does the z mean above?
 
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It means "holding z constant".
 
Is that any different from a regular partial derivative though? I've started to encounter the notation in literature and am finding it strange.
 
Amos Axiom said:
Is that any different from a regular partial derivative though? I've started to encounter the notation in literature and am finding it strange.

It is rarely used in Mathematics, but is used often in some fields such as Thermodynamics. Basically, it indicates that we are considering x to be a function of y and z, without using notation like x(y,z).

RGV
 

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