Concept of derivative Increment Definition - Increment of a variable. An increment of a variable $x$ is a change in the value of the variable; it is denoted $\Delta x$. The increment of a variable $x$ along an interval $[a,b]$ is given by $$\Delta x = b-a.

Vector functions of a single real variable Definition - Vector function of a single real variable. A vector function of a single real variable or vector field of a scalar variable is a function that maps every scalar value $t\in D\subseteq \mathbb{R}$ into a vector $(x_1(t),\ldots,x_n(t))$ in $\mathbb{R}^n$:

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