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Summary:
 Isn't it incorrect or at least sloppy to write a function as having multiple arguments when one or more of the arguments are not independent?
Main Question or Discussion Point
Hi,
This is on the wikipedia entry for the Euler Lagrange equation. Here is a link.
https://en.wikipedia.org/wiki/Calculus_of_variations#Euler–Lagrange_equation
The notation I am confused about is this:
Aren't the y(x) and the y'(x) unnecessary to list as arguments when x is already one of the arguments? Or to reverse the question: Wouldn't the x be unnecessary to list as an argument if y(x) and y'(x) are already listed as the 2 arguments? But listing all three of them together like that doesn't seem right. It implies all three of them need to be given as input in order to uniquely determine L, which clearly is incorrect, right?
This is on the wikipedia entry for the Euler Lagrange equation. Here is a link.
https://en.wikipedia.org/wiki/Calculus_of_variations#Euler–Lagrange_equation
The notation I am confused about is this:
Aren't the y(x) and the y'(x) unnecessary to list as arguments when x is already one of the arguments? Or to reverse the question: Wouldn't the x be unnecessary to list as an argument if y(x) and y'(x) are already listed as the 2 arguments? But listing all three of them together like that doesn't seem right. It implies all three of them need to be given as input in order to uniquely determine L, which clearly is incorrect, right?
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