Notation

Appendix A Notation

Symbol	Description	Location
$x \in A$	set membership	Definition 0.1.1
$A \subseteq B$	set inclusion	Definition 0.1.3
$A \cup B$	set union	Definition 0.1.8
$A \cap B$	set intersection	Definition 0.1.8
$A - B$	set difference	Definition 0.1.8
${}, \emptyset$	the empty set	Definition 0.1.9
$R$	the real numbers	Definition 0.1.9
$Z$	the integers	Definition 0.1.9
$Q$	the rational numbers	Definition 0.1.9
$A \times B$	Cartesian product	Definition 0.1.10
$f : A \to B$	a function from $A$ to $B$	Definition 0.1.13
$f (A)$	image of the set $A$ under $f$	Definition 0.1.18
$im f$	image of a function $f$	Definition 0.1.18
$f \circ g$	the composition of $f$ and $g$	Definition 0.1.21
$‖ P ‖$	norm of a partition	Definition 1.1.1
$\iint_{R} f (x, y) d A$	double integral over region $R$	Definition 1.3.2
${avg}_{R} (f)$	average value of $f$ over $R$	Definition 1.4.4
$\underset{D}{∭} f (x, y, z) d V$	double integral over region $D$	Definition 1.5.3
${avg}_{R} (f)$	average value of $f$ over $R$	Definition 1.5.16
$\frac{\partial (g_{1}, g_{2}, \dots, g_{n})}{\partial (x_{1}, x_{2}, \dots, x_{n})}$	Jacobian of $G = (g_{1}, g_{2}, \dots, g_{n})$	Definition 1.6.2
$\nabla \times F$	curl of vector field $F$	Definition 2.3.12
$curl F$	curl of vector field $F$	Definition 2.3.12
$\nabla \cdot F$	divergence of vector field $F$	Definition 2.4.9
$\iint_{S} f (x, y, z) d σ$	surface integral of scalar function	Definition 2.6.1