How is the covariant derivative derived?
You mean, "How is the covariant derivative defined?", don't you?
Step 1: Open an internet browser.
Step 2: Go to Google.
Step 3: Search for "covariant derivative".
You will see entries from both Wikipedia and MathWorld.
No. This thread has been continued in 'Calculus and Analysis' under 'Mathematics'.
If you weren't so terse in your replies and actualy explained fully what you meant then you might get somewhere more quickly. A more careful choice of words would help as well. You don't mean derive, closer is why on taking the limit of something along certain paths or whatever this is (trying too recall prevect's post in the calc thread) is it equivalent to this statement? How about "how does one pass from the phrase 'is the limit along some parallel transport of something' to that formula?" That to my mind isn't deriving, it is simply moving from words to symbols. One derives the fundamental theorem of calculus by starting with the axioms and definitions of continuity etc and proving the result.
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