8 GEOMETRIC DIFFERENTIATION

Differentiation is the process of computing with changes in quantities. When the changes are small, those computations can be linear to a good approximation, and it is not too hard to develop a calculus for geometry by analogy to classical analysis.

When formulated with geometric algebra, it becomes possible to differentiate not only with respect to a scalar (as in real calculus) or a vector (as in vector calculus), but also with respect to general multivectors and k blades. The differentiation operators follow the rules of geometric algebra: they are themselves elements that must use the noncommutative geometric product in their multiplication when applied to other elements. As you might expect, this has precisely ...

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