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Maths - Clifford Calculus

Prerequisites

If you are not familiar with quaternion algebra you may like to look at the following pages first:

Clifford Differentiation with respect to Scalar

To differentiate a multivector with respect to a scalar, say 'x', we individually differentiate each element with respect to 'x'. So if:

f(x) = a + b e1 + c e2+ d e1^e2

then:

d f(x) / dx = d(a /dx) + d(b /dx) e1 + d(c /dx) e2+ d(d /dx) e1^e2

So this is quite simple, provided that we can differentiate the elements of a multivector, we can differentiate the whole multivector.

Multivector Differentiation with respect to another Multivector

 

What are the rules of such differentiation? What applications does it have?

 


Multivector Integration

As with differentiation we can integrate a whole multivector by individually integrating each element. So if:

f(x) = a + b e1 + c e2+ d e1^e2

then:

intergral f(x) dx = intergrala dx + intergralb dx e1 + intergralc dx e2+ intergrald dx e1^e2


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