Appendix B: Mathematical Notation and Useful Formulas

Table B.1: Mathematical Notation
Notation	Meaning	Remark
?	Real numbers
?	Integers
?	Complex numbers
j		Imaginary number
?	For every, for all
?	There exists
?	Element of
:=	Defined as being equal to
N!	N!:= N ( N - 1) 3 2 1	Factorial, 0! = 1
?( t), ?[ n]	CT, DT unit impulse
u( t), u[ n]	CT, DT unit step signal	Except for state-space systems for which u( t), u[ n] are the inputs, notably in Chapters 10 and 17
q( t), q[ n]	CT, DT unit step signal	In Chapters 10, 11 and 17
h( t), h[ n]	CT, DT impulse response
s( t), s[ n]	CT, DT step response
	(dx/dt)
? _n	Undamped natural frequency	Second-order systems
?	Damping ratio	Second-order systems
?	Continuous-time frequency	Units of rad/s
?, ?	Discrete-time frequency	Units of rad
? _i( A)	i ^theigenvalue of square matrix A
?( A)	Spectral radius of N N matrix A
	Four-quadrant arctan ?. ? ? ? are displayed with their own sign