In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and ...

This paper covers the concept of a conservative vector field, and its application in vector physics and Newtonian mechanics. Conservative vector fields are defined as the gradient of a scalar-valued ...

In this chapter, we will describe the curves in $\mathbb{R}^2$ or $\mathbb{R}^{3}$ as the image of a function. $$\vec{r}(t) = \big(r_{1}(t), r_{2}(t),\dots ,r_{n}(t ...

Suppose I have a vector-valued function f(x) = y, where x and y are both vectors of some length (same or different length). f could be evaluated over a regular grid of x values, producing a set of y ...