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GR191511

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GR191511

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PAllen

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malawi_glenn

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There is a comma indeed.

This notation is introduced in the book (2nd edition) in equation (3.19)

This notation is introduced in the book (2nd edition) in equation (3.19)

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PeterDonis

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Because the derivative operator acts like a covector, i.e., a thingie with a lower index. For example, you can contract the derivative operator with a vector to get a number (this number is usually called the "divergence" of the vector).

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PeterDonis

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Yes, I've always preferred that as well, even though my favorite GR textbook, MTW, insists on using commas and semicolons instead of partials and nablas. I've never really understood why: it's not as though partials and nablas are scarce resources.

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malawi_glenn

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I never understood the need of the ## \dot y## notation for ## \dfrac{\mathrm{d}y}{\mathrm{d}t} ##I've never really understood why

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PeterDonis

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Perhaps it's meant to induce eyestrain. It certainly does a good job of that for me.I never understood the need of the ## \dot y## notation for ## \dfrac{\mathrm{d}y}{\mathrm{d}t} ##

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PAllen

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I’ll usually mention that the comma/semicolon notation exists and then happily go on using partials and nablas. It is just clearer to me.

This, on the other hand, I have no particular issue with for some reason.I never understood the need of the ## \dot y## notation for ## \dfrac{\mathrm{d}y}{\mathrm{d}t} ##

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Compactness. Also, I think there's a degree of sense to it because "the partial derivative of ##T##" is one "thing", so I understand the desire to notate it as one "thing" without having to introduce some arbitrary new letter for it. It's kind of analogous to the ##\dot x## notation, in fact, which I do use.I've never really understood why

But I personally find the commas too easy to lose among the other indices. I wonder if this particular notational preference is well correlated with the strength of the physicist's astigmatism.

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Because there's nothing else above the letter for the dot to become visually lost in, I suspect. I'd avoid ##\dot i## and ##\dot j##, though. 😁This, on the other hand, I have no particular issue with for some reason.

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PAllen

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But second derivatives might be fine ... but maybe not in German (?)Because there's nothing else above the letter for the dot to become visually lost in, I suspect. I'd avoid ##\dot i## and ##\dot j##, though. 😁

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##\ddot{\ddot{e}}## 😁But second derivatives might be fine ... but maybe not in German (?)

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$$

u_{tt} -c^2 u_{xx}=0.

$$

It is quite convenient and fine as long as you only ever deal with scalars. The problems start to arise when you want to combine that with tensors in index notation …

Context is important.

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That's the old quarrel between Newton and Leibniz. The intoduction of Leibniz's notation in England by Maxwell was anrevolution ;-).I never understood the need of the ## \dot y## notation for ## \dfrac{\mathrm{d}y}{\mathrm{d}t} ##

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It is said that they both worked independently, but I find both their works a bit … derivative …That's the old quarrel between Newton and Leibniz. The intoduction of Leibniz's notation in England by Maxwell was anrevolution ;-).

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malawi_glenn

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And now it has been integrated into our standard math curriculum. If only the people responsible would know their limits...It is said that they both worked independently, but I find both their works a bit … derivative …

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I don’t know … I may be partial …And now it has been integrated into our standard math curriculum. If only the people responsible would know their limits...

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malawi_glenn

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maybe, but I need to get to the kernel with thisI don’t know … I may be partial …

(that was lame, even for my standards)

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It seems we reach these types of conversations atmaybe, but I need to get to the kernel with this

(that was lame, even for my standards)

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PAllen

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On a more serious note, I looked through a French calculus textbook from circa 1725 once - I read no French. I could follow it easily, the notation and even order of presentation of topics was already similar to texts of my era. I wonder whether this is a good thing.

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- #23

PeterDonis

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Where's the :groan: emoji?

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