Vector and tensor analysis in euclidean space

Abstract

In the following we consider a vector-valued function x(t) and a tensor-valued function A(t) of a real variable t. Henceforth, we assume that these functions are continuous such that (Formula Presented) for all t0 within the definition domain. The functions x(t) and A(t) are called differentiable if the following limits (Formula Presented) exist and are finite. They are referred to as the derivatives of the vector- and tensor-valued functions x(t) and A(t), respectively.