Page 3 - Advanced engineering mathematics

Guide to Notation

L[ f] Laplace transform of f
L[ f](s) Laplace transform of f evaluated at s
L [F] inverse Laplace transform of F
−1
H(t) Heaviside function
f ∗ g often denotes a convolution with respect to an integral transform, such as the Laplace
transform or the Fourier transform
δ(t) delta function
< a,b,c > vector with components a, b, c
ai + bj + ck standard form of a vector in 3-space
V norm (magnitude, length) of a vector V
F · G dot product of vectors F and G
F × G cross product of F and G
R n n-space, consisting of n-vectors < x 1 , x 2 ,··· , x n >
[a ij ] matrix whose i, j-element is a ij . If the matrix is denoted A,this i, j element may also be
denoted A ij
n × m zero matrix
O nm
n × n identity matrix
I n
A t transpose of A
reduced (row echelon) form of A
A R
rank(A) rank of a matrix A
.
.
[A.B] augmented matrix
A −1 inverse of the matrix A
|A| or det(A) determinant of A
p A (λ) characteristic polynomial of A
often denotes the fundamental matrix of a system X = AX

T often denotes a tangent vector
N often denotes a normal vector
n often denotes a unit normal vector
κ curvature
∇ del operator
∇ϕ or grad ϕ gradient of ϕ
D u ϕ(P) directional derivative of ϕ in the direction of u at P

fdx + gdy + hdz line integral

C
F · dR another notation for fdx + gdy + hdz with F = f i + gj + hk
C
C

C 1 C 2 ··· C n join of curves C 1 ,C 2 , ··· ,C n

f (x, y, z)ds line integral of f over C with respect to arc length
C
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October 14, 2010 15:48 THM/NEIL Page-1 27410_00_IFC_p01-02