Line Integral and Curl

Abstract: Flux and divergence introduced the concept of flux and the surface integral associated with it. Flux uses the directional property of a vector field to have it pierce an element of area. The directional property can also naturally assign a varying direction along a line. One can consider how a vector field changes direction as it moves along a curve in space. This change can also lead to a new kind of integration and differentiation of vector fields. The integration leads to the notion of a line integral and the associated differentiation to the concept of curl.
(The paper)

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