Notations
x, X
Scalar variable or function (italics)
x
Vector (lowercase, bold)
x i
Vector element
X
Matrix (upper case, bold)
X ij
Matrix element
x
T , X
T
Vector or matrix transpose
|x|
Absolute value
|X|, det(X) Matrix determinant
tr(X)
Matrix trace
x
Complex conjugate
_
x; € x
Time derivatives
x′, x′′
Spatial derivatives
x
(i)
ith spatial derivative
x
[i] , x [i]
ith iterate
O(x)
Order of magnitude
∇/∇
2
Gradient/Laplacian operator
D i
j
Multiple scales differential operator ¼ @
j
=@T
j
i
À
Á
d ij
The Kronecker delta ( = 1 for i = j; = 0 for i 6 ¼ j)
d(x)
Dirac’s delta-function
R þ 1
À1 d x
ð Þdx ¼ 1
i
Counter index or √–1 (as appears from context)
ln/log
Base-e / base-10 logarithm
Assigning equality
cc
Complex conjugates of preceding terms
hh(n)
Harmonics of nth and higher order
j = 1, n
j= 1, 2,…, n
xxi