exterior derivative

Hello, you have come here looking for the meaning of the word exterior derivative. In DICTIOUS you will not only get to know all the dictionary meanings for the word exterior derivative, but we will also tell you about its etymology, its characteristics and you will know how to say exterior derivative in singular and plural. Everything you need to know about the word exterior derivative you have here. The definition of the word exterior derivative will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofexterior derivative, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

English Wikipedia has an article on:
Wikipedia

Pronunciation

  • Audio (US):(file)

Noun

exterior derivative (plural exterior derivatives)

  1. (calculus) A differential operator which acts on a differential k-form to yield a differential (k+1)-form, unless the k-form is a pseudoscalar, in which case it yields 0.
    The exterior derivative of a “scalar”, i.e., a function where the ’s are coordinates of , is .
    The exterior derivative of a k-blade is .
    The exterior derivative may be though of as a differential operator del wedge: , where . Then the square of the exterior derivative is because the wedge product is alternating. (If u is a blade and f a scalar (function), then , so .) Another way to show that is that partial derivatives commute and wedge products of 1-forms anti-commute (so when is applied to a blade then the distributed parts end up canceling to zero.)