# Tag Archives: vector field

## Math2111: Chapter 2: Vector fields and the operator ∇. Section 2: Divergence and Curl

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

We discuss now derivatives of vector fields. To that end we introduce the del operator ∇. Throughout we assume that the vector field $\boldsymbol{F}:\mathbb{R}^3\to\mathbb{R}^3$ and the scalar field $f:\mathbb{R}^3\to\mathbb{R}$ are $\mathcal{C}^1$, i.e. have at least one continuous partial derivative in each coordinate (similarly we write $\mathcal{C}^2$ if the functions are assumed to have continuous partial derivative of order at least two). Continue reading