Mathematical Physics Vol 1

Chapter 2. Vector analysis

46

or, if t i − a i = ∆ t i , for i = 1 , 2 ,..., n

∂ v ∂ t 1

∂ v ∂ t n

∆ t 1 + ··· +

∆ t n

d v ( T , A )=

(2.51)

or, for ∆ t i = d t i

∂ v ∂ t 1

∂ v ∂ t n

d v ( T , A )=

d t 1 + ··· +

d t n .

(2.52)

Definition The expression (2.52) is called the total differential of the function v , and the expres sion

∂ v ∂ t i

d t i ( i = 1 , 2 , ··· , n )

(2.53)

the partial differential .