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In http://mathworld.wolfram.com/ExteriorDerivative.html,

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.

  • 4
    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](http://www.amazon.com/Calculus-Cohomology-Rham-Characteristic-Classes/dp/0521589568), [Lee](http://www.amazon.com/Introduction-Smooth-Manifolds-John-Lee/dp/0387954481), or [Morita](http://www.amazon.com/Geometry-Differential-Translations-Mathematical-Monographs/dp/0821810456).2012-06-27
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    If you want to learn differential form, I would recommend the book of Do Carmo "Differential Forms and Applications"2012-06-27

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