I'm trying to study some basic tensor analysis on my own for practical purposes, but I'm having some problems. More specifically I'm rather puzzled over the concept of total derivative in curvilinear coordinates (well, to be exact, as I've got little experience with differential geometry, it's all a bit hazy).(adsbygoogle = window.adsbygoogle || []).push({});

I have a function f, which depends on the position vectorr, which in turn is a function of time t i.e. f = f(r(t)). Now what I'd want to do is to take the time derivative of f: df/dt. Normally I'd write it as [tex]\frac{df}{dt} = \sum_i \frac{\partial f}{\partial \mathbf{r}_i}\frac{d\mathbf{r}_i(t)}{dt}[/tex]. I however have doubts in my mind whether this is the right way to go about when I'm dealing with curvilinear coordinates. Should I replace the partial derivative with the gradient (covariant derivative)?

I hope my question is making any sense. Please direct me to a good book on tensors if it is not (I'd prefer mathematical ones, but I'm in a hurry to apply the mathematics, so one for engineers/physicists would be well appreciated).

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# Total derivative

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