What are vector valued functions

Vector-valued functions

write. We first define the continuity of a vector-valued function by considering the continuity of all of its components demand. The derivative of a vector-valued function provides such a function and is defined as

Let's press again through the components, it follows

We postpone a further discussion of vector-valued functions to the exercises.
The derivation of a vector-valued function must not be confused with the derivation of a function that depends on a vector - and can itself be vector-valued (fields) - according to this vector, i.e. the formation of the gradient, the divergence or the rotation. We will go into these in the following.