Amplitwist

In mathematics, the amplitwist is a concept created by Tristan Needham in the book Visual Complex Analysis (1997) to represent the derivative of a complex function visually.

Definition

The amplitwist associated with a given function is its derivative in the complex plane. More formally, it is a complex number such that in an infinitesimally small neighborhood of a point in the complex plane, for an infinitesimally small vector . The complex number is defined to be the derivative of at .[1]

Uses

The concept of an amplitwist is used primarily in complex analysis to offer a way of visualizing the derivative of a complex-valued function as a local amplification and twist of vectors at a point in the complex plane.[1]

Examples

Define the function . Consider the derivative of the function at the point . Since the derivative of is , we can say that for an infinitesimal vector at ,

References

  1. Tristan., Needham (1997). Visual complex analysis. Oxford: Clarendon Press. ISBN 0198534477. OCLC 36523806.
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