Notation

Appendix A Notation

The following table defines the notation used in this book. Page numbers or references refer to the first appearance of each symbol.

Symbol	Description	Location
$x \cdot y$	scalar product of two vectors $x, y \in R^{N}$	Definition 1.4
$‖ x ‖$	norm (or length or magnitude) of a vector $x \in R^{N}$	Paragraph
$x \times y$	cross product of two vectors $x, y \in R^{3}$	Definition 1.20
$\frac{\partial f}{\partial x_{i}}$	partial derivative with respect to $x_{i}$	Definition 4.2
$grad (f)$	gradient of a scalar valued function	Definition 4.4
$\nabla f$	gradient of a scalar valued function	Definition 4.4
$J_{f} (x)$	Jacobian matrix	Definition 4.18
$\frac{\partial}{\partial v} f (a)$	directional derivative	Definition 4.25
$curl (f)$	curl of a vector field $f$ on a subset of $R^{3}$	Definition 8.14
$\nabla \times f$	curl of a vector field $f$ on a subset of $R^{3}$	Definition 8.14
$\nabla = (\frac{\partial}{\partial x_{1}}, \dots, \frac{\partial}{\partial x_{N}})$	Nabla operator	Definition 8.15
$Δ u = \sum_{k = 1}^{N} \frac{\partial^{2} u}{\partial x_{k}^{2}}$	Laplace operator	Definition 12.6