On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
The exterior derivative of a k-form is a (k+1)-form. For example, for a differential k-form ... Algebra. Applied Mathematics. Calculus and Analysis. Discrete Mathematics.
The exterior derivative allows the fundamental theorem of calculus to be generalized to integrals over areas and volumes and higher dimensional analogues.
In mathematics, the exterior covariant derivative is an analog of an exterior derivative that takes into account the presence of a connection
The exterior derivative is uniquely speci ed by the following requirements: rst, it satis es d(df) = 0 for all functions f. Second, it is a graded derivation of
Does anyone know where I can see a motivation for defining the exterior derivative antisymmetrically instead of just using the *normal* derivative of forms?
Hi, actually I have several related questions, not worth opening different threads: What is the of the exterior derivative intuitively? What is its geometric meaning?
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Define the exterior derivative of a function and of a differential form; Show that d(dw) = 0 for any differential form w; Be able to manipulate exterior derivatives ...
The take-home message here, though, is that the exterior derivative ... Introduction to Exterior Calculus — Part ... and Dirty Introduction to Exterior Calculus ...