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Original post by Timkin
Actually, it''s a one-form, not a vector. We just teach undergrads (particularly engineers) that it''s a vector, because it turns out that in 3 dimensions, one-forms and vectors have the same properties and there''s no point in confusing them!

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Good point! The higher-dimension manifold thing comes up very frequently in optimization problems, which we''ve dealt with.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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Original post by cedricl
Graham, I'm working on the "total derivative" right now. We call it the divergence. Your statement:
"grad(f) = del * f" - from grhodes_at_work

that looks a lot like the divergence.

div(f) = del . f

When we write about the gradient vector, the del operator is directly in front of f

grad(f) = del f (without the space)

Anyway, that's just notation. You forgot to mention the curl and the Laplacian

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Ha ha! Glad to have a bunch of regulars to fill in the blanks, correct my mistakes, etc.!

The "del f" notation is probably more consistent. I actually wasn't thinking about divergence when I wrote that last night. Which is why I wrote the total derivative using a sort of DotProduct formula instead of "del . f". Its hard to know how people interpret attempts at ASCII-formatted math.

The total derivative has the divergence term in there (representing change due to advection/convection of a property with mass movement), but it also includes the time derivative (representing a local change in a property). Its called total since it includes changes that are occurring locally and changes that are happening since the new properties are being carried in with fluid mass that comes from another location.

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

[edited by - grhodes_at_work on October 21, 2002 10:42:06 PM]