In the Introduction to the Derivative video we introduce the notion of the derivative of a function and explain how the derivative captures the instantaneous rate of change of a function. In the ...

This is a single variable calculus course with applications to the life sciences. Review of basic algebra, trigonometry, functions and graphs. Limits and derivatives, including differentiation rules, ...

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 ...

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 ...

In this paper we prove the following general exponential law for holomorphic functions in infinite dimensions: He(U × V, G) ≅ He(U, He(V, G)). This generalizes exponential laws for holomorphic ...