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Mathematics
Differential Equations
Change of variable - partial derivative
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[QUOTE="andrewkirk, post: 5493364, member: 265790"] I would put it down to careless writing on the authors' part. I expect they have something in mind that makes sense, but they have made mistakes in translating that into mathematical notation and ended up with something that makes no sense. If you are familiar with the subject matter of the paper you may be able to guess what it is that they were trying to say. Alternatively, you could contact the authors and ask them what they meant. One other comment: The manuscript appears to be using a version of the Total Derivative formula, that if ##y## is a function of ##t## and ##x_1,...,x_n##, and each of the ##x_k## is a function of ##t##, then: $$\frac{dy}{dt}=\frac{\partial y}{\partial t}+\sum_{k=1}^n\frac{\partial y}{\partial x_k}\frac{dx_k}{dt}$$ However in the manuscript, the total derivatives (items using ##d## instead of ##\partial##) are replaced by partials. That is not necessarily valid or even well-defined and can lead to circularity or ambiguity. [/QUOTE]
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Mathematics
Differential Equations
Change of variable - partial derivative
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