- #1
Understanding the Equation in f'(x) Notation
- Context: Undergrad
- Thread starter luckis11
- Start date
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Discussion Overview
The discussion revolves around the interpretation of an equation presented in f'(x) notation, specifically in the context of fluid dynamics and Bernoulli's equation. Participants seek clarification on the meaning of the notation and its implications for the variables involved.
Discussion Character
- Conceptual clarification
- Technical explanation
Main Points Raised
- One participant asks for clarification on the meaning of an equation in f'(x) notation.
- Another participant presents the equation vv' = (v2)'/2, which seems to relate to the discussion but lacks context.
- A participant requests an explanation in Lagrange's notation f'(x) and questions the assumption that u=u(x) in the context of steady flow.
- It is noted that writing u=u(x) serves to clarify the dependency of the function on x, and that it is common to omit the explicit function notation.
- A clarification is made that v' refers to v'(x) and v refers to v(x), leading to the expression v(x)v'(x)=(v(x)2)'/2.
Areas of Agreement / Disagreement
Participants appear to have differing views on the interpretation of the notation and the implications of the equations presented. No consensus is reached regarding the meanings or assumptions underlying the equations.
Contextual Notes
The discussion includes assumptions about the dependency of variables on x, which may not be universally accepted. The implications of steady flow and the notation used are also points of contention.
- #2
epenguin
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vv' = (v2)'/2
- #3
luckis11
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In Lagrange's notation f'(x), please, as I asked? 
They also say there: "In steady flow u=u(x), so..."...so the equation I asked about. What do they mean? How can it not be that u=u(x)?
http://en.wikipedia.org/wiki/Bernoulli's_equation#Derivations_of_Bernoulli_equation
They also say there: "In steady flow u=u(x), so..."...so the equation I asked about. What do they mean? How can it not be that u=u(x)?
http://en.wikipedia.org/wiki/Bernoulli's_equation#Derivations_of_Bernoulli_equation
Last edited:
- #4
Office_Shredder
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When you write u=u(x) you're simply clarifying that the function is dependent on x. It's very common to just stop writing u(x) because everybody knows that it's a function of x (for example, epenguin's post)
v' is v'(x) in epenguin's post, and v is v(x) so it's v(x)v'(x)=(v(x)2)'/2
v' is v'(x) in epenguin's post, and v is v(x) so it's v(x)v'(x)=(v(x)2)'/2
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