Remarks to the Notation
347
From Chap. 25 onwards multiple component quantities are summed using identical
indices according to the Einsteinian summation convention,
a · b = a r b r ,
a · ε
k
= a r ε rk , ε · · σ = ε rs σ sr ,
a × b
i
= irs a r b s .
From Chap. 23 onwards, a comma is used to describe the partial derivative,
∂ f
∂x k
= f, k .
The vectorial operator ∇ = (∇ 1 , ∇ 2 , ∇ 3 ) is also written as grad and defined by
∇ k =
∂
∂x k
.
One thus notes
div a = ∇ · a , (curl a) k = (∇ × a) k = krs a s , r , grad f = ∇ f = ( f, 1 , f, 2 , f, 3 ) .
The Laplacian is defined as
= div grad = ∇ · ∇ =
∂
2
∂x 2 +
∂
2
∂ y 2 +
∂
2
∂z 2 .
The notation exp[x] is used for the function e
x if complicated exponents are
included.