Functional Derivatives

Martin Vieten
University of Wisconsin-Milwaukee
PhD Graduate Student

“The concept of the derivative of a single-variate function is one of the first concepts   students are exposed to in elementary calculus. Typically, it is introduced using the ‘classical’ limit definition. To attain full understanding of derivatives of multi-variate functions or even functions on infinite-dimensional vector spaces, it however is crucial to embrace the derivative as a component of the linearization of such functions.
In this talk, I will present different notions of differentiability and illustrate how they can be connected to the idea of linearization. Then, this concept is generalized to functionals on infinite-dimensional vector spaces – in other words, we will learn how to differentiate with respect to a function.”