Geometric Calculus
Geometric calculus extends the formalism to include differentiation and integration including differential geometry and differential forms.
Essentially, the vector derivative is defined so that the GA version of Green's theorem is true,
and then one can write
as a geometric product, effectively generalizing Stokes theorem (including the differential forms version of it).
In when A is a curve with endpoints and, then
reduces to
or the fundamental theorem of integral calculus.
Also developed are the concept of vector manifold and geometric integration theory (which generalizes Cartan's differential forms).
Read more about this topic: Geometric Algebra
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