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 ...

Let f be a smooth function on the unit n-dimensional ball, with the C0-norm, equal to one. We prove that if for some k ⩾ 2, the norm of the kth derivative of f is bounded by 2-k - 1, then the set of ...

Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...

This example illustrates some properties of splines. Splines are curves, which are usually required to be continuous and smooth. Splines are usually defined as piecewise polynomials of degree n with ...