Maths - Clifford Calculus

Prerequisites

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

• clifford algebra

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:

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

EuclideanSpace

home