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there is a section that starts from:

Define the exterior derivative by $Dt ≡ \frac{\partial}{\partial x} \wedge t$

First of all, what does this first part quoted mean, in relation to the previous parts?

I then want to know what the rest of the section is talking about.

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Egads, what horrible notation. Wolfram Mathworld is okay as a reference, but it really isn't where you should be learning stuff from. Instead try one of the standard texts on differential topology: Madsen and Tornehave, Lee, or Morita. – Willie Wong Jun 27 '12 at 8:54
If you want to learn differential form, I would recommend the book of Do Carmo "Differential Forms and Applications" – Paul Jun 27 '12 at 10:40

The notation between the dollar sign is LaTeX ( mathematics notation. It is meant to be very descriptive of mathematical expressions; it is not intended to "look" like standard mathematical notation.

The closest equivalent in Mathematica itself is:

Dt [Congruent] ([PartialD]/[PartialD]x)[Wedge]t

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Welcome to MSE! Was this intended to be an answer to the posted question? Regards – Amzoti May 5 '13 at 16:37

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