Amplitwist
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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[]
- Functions and mappings
- Complex analysis