What Does Derivation Mean in a General Relativity Context?

[bmb2009]

Homework Statement

This seems like a simple question but I've never asked it and I'm stuck haha
For my general relativity course we are asked to derive the change in a vector under parallel transport. My professor references his lecture notes on his course web page in the statement of the problem...he says "In the notes, derive all the steps in eq. 1.8"

But in the lecture notes the equation 1.8 seems to be the derivation itself. I.e. he has several steps of tensor analysis and arrives at the conclusion and says the final answer, that a vector does not change under parallel transport. This is what I would have considered a derivation.

Do you think he wants to re-write the steps already laid out for us and maybe write some side comments to show we understand what's going on in each step? Or is a derivation something else entirely?

and yes I did try to ask him about this but no luck on an email response. thanks!

Homework Equations

The Attempt at a Solution

 

[kurros]

Are there lots of steps missing in the notes? Maybe he just wants you to fill in all the gaps needed to get to this eq. 1.8. Usually lecture notes only have really brief and sketchy ("hand-waving") derivations of things, so he probably just wants you to do it more thoroughly.

 

[bmb2009]

Are there lots of steps missing in the notes? Maybe he just wants you to fill in all the gaps needed to get to this eq. 1.8.

That's what I thought... but the equalities and substitutions to derive further results are very well laid out and "easy" to follow. (easy meaning comprehensive)

 

[kurros]

Well, then I'm out of ideas :p.

 

[HalfLostAndSearching]

A derivation is a mathematical process of deriving or obtaining a result or equation from known principles or assumptions. In this context, deriving the change in a vector under parallel transport means using the principles and equations of general relativity to mathematically show how the vector changes when transported along a curved path in spacetime. This involves manipulating tensors and equations to arrive at the final result. It is possible that your professor wants you to go through the steps and fully understand each step of the derivation, rather than just looking at the final result. This will help you understand the underlying principles and assumptions that lead to the result. It is also possible that your professor wants you to show your understanding by re-writing the steps and adding side comments. In any case, a derivation is a rigorous mathematical process that involves using known principles and equations to obtain a result.