I Stationary Field: Why Professor and Books Differ

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The discussion centers on the definition of a stationary field, highlighting a discrepancy between a professor's lecture and textbook explanations. The professor asserts that a stationary field implies the total derivative \(\frac{du}{dt}=0\), while textbooks indicate it means \(\frac{\partial u}{\partial t}=0\). Participants argue that the total derivative is not applicable unless the function is solely dependent on time. Clarification is sought on the correct interpretation of a stationary field, emphasizing that it should not depend on time at all. The conversation underscores the importance of precise terminology in understanding stationary fields in physics.
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So, I got a question about stationary field.
In the lecture the professor said, that our field is stationary, so we have \frac{du}{dt}=0, but from what I read in books, it only means, that \frac{\partial u}{\partial t} =0. Who is right and why ?
 
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The total derivative makes no sense unless you have a function of ##t## only. A stationary field is a field that does not depend on ##t## and therefore ##\partial_t u = 0##.
 
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