A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population’s growth rate is typically ...

In this paper we derive the explicit, closed-form, recursion-free formulae for the arbitrary-order Fréchet derivatives of the exponential and logarithmic functions in unital Banach algebras (complex ...