Total Differentiation, Differential Operators

Abstract

So far, we have considered only partial derivatives or directional derivatives for functions in several variables. In addition to these special derivation terms, there is also the total derivative. This total derivative is explained as a local approximation of a function f by a linear function and finally leads to the total differential, which allows a linearized error estimate.

Finally, we present a clear overview of the differential operators gradient, Laplace, divergence and rotation, which are important in the following chapters, and partly their interpretations.