Symbols and Notation

Symbol	Description
\(\N\), \(\Z^{+}\)	the set of natural (positive integer) numbers \(\{1, 2, 3, \ldots\}\)
\(\Z\)	the set of integer numbers \(\{\ldots, -2, -1, 0, 1, 2, 3, \ldots\}\)
\(\N_0\), \(\Z^{+}_0\)	the set of whole (non-negative integer) numbers \(\{ 0, 1, 2, 3, \ldots\}\)
\(\R\)	the set of real numbers
\(\mathbf{\hat{i}}\)	the imaginary unit, \(\mathbf{\hat{i}}^2=-1\)
\(z\)	a complex number
\(|z|\)	the modulus of \(z\)
\(\arg(z)\)	the argument of \(z\)
\(\Re(z)\), \(\mathrm{Re}(z)\)	the real component of \(z\)
\(\Im(z)\), \(\mathrm{Im}(z)\)	the imaginary component of \(z\)
\(\theta\)	angle
\(\mathbb{C}\)	the set of complex numbers \(\{z | z=x+\mathbf{\hat{i}} y~, ~ x \in \R, y \in \R\}\)
\(\{y_n\}_{n=0}^{+\infty}\)	a sequence defined on \(\N_0\)
\(\D\)	differential operator
\(\Delta\)	forward difference operator
\(\nabla\)	backward difference operator
\(\E\)	forward shift operator
\(\E^{-1}\)	backward shift operator
\(I\)	interval of definition
\(t\)	time variable
\(h\)	step size, step length
\(k\)	number of steps
\(\alpha_i\), \(\beta_i\)	the coefficients of a linear multistep method (\(i=0, 1, 2, \ldots, k\))
\(\epsilon\)	error
\(T\), LTE	local (truncation) error
\(\L(\D)\)	linear differential operation
\(\L(\E)\)	linear shift operation
\(\L(z)\)	characteristic polynomial
\(\L(z, h\lambda)\), \(\pi(z, h\lambda)\)	characteristic polynomial, stability polynomial
\(\rho(z)\)	first characteristic polynomial
\(\sigma(z)\)	second characteristic polynomial
\(\begin{pmatrix} n \\ k \end{pmatrix}\), \(^n C_r\)	binomial coefficient
\(\forall\)	for all
\(\exists\)	there exists
\(\implies\)	implies; if … then
iff, \(\iff\)	if and only if, equivalent to
\(\because\)	because, since
\(\therefore\)	therefore
\(\subset\)	is a proper subset of
\(\subseteq\)	is a subset of
\(\in\)	is an element of
\(\notin\)	is not an element of
\(\angle\)	angle, argument
\(i\), \(j\), \(k\), \(m\), \(n\), \(p\)	whole numbers
\(r\), \(s\)	real numbers