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.
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]
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] [2]
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 , .
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.
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]
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] [2]
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 , .