Лекции по векторному и тензорному анализу. Лосик М.В. - 5 стр.

UptoLike

ВУЗ: 

СГУ им. Чернышевского | Саратов

Составители: 

Рубрика: 

k(t) U
~a(t) +
~
b(t) k(t)~a(t) [~a(t),
~
b(t)]
(~a(t),
~
b(t) ) (~a(t) ,
~
b(t) ,~c(t) )
U (~a,
~
b )
[~a,
~
b] (~a ,
~
b ,~c)
~a(t)
~
b(t) ~c(t) k(t)
t
0
t
0
~a(t) +
~
b(t) k(t)~a(t) [~a(t),
~
b(t)] (~a(t)
~
b(t)) (~a(t) ,
~
b(t) ,~c(t))
t
0
lim
t→t
0
(~a(t) +
~
b(t) ) = lim
t→t
0
~a(t) + lim
t→t
0
~
b(t)
lim
t→t
0
( k(t)~a(t) ) = lim
t→t
0
k(t) lim
t→t
0
~a(t)
lim
t→t
0
(~a(t),
~
b(t) ) = ( lim
t→t
0
~a(t), lim
t→t
0
~
b(t) )
lim
t→t
0
[~a(t),
~
b(t) ] = [ lim
t→t
0
~a(t), lim
t→t
0
~
b(t) ]
lim
t→t
0
(~a(t),
~
b(t),~c(t)) = (lim
t→t
0
~a(t), lim
t→t
0
~
b(t)) lim
t→t
0
~c(t))
~
i,
~
j,
~
k ~a(t)
~
b(t)
~a(t)( a
x
(t), a
y
(t), a
z
(t) )
~
b(t)( b
x
(t), b
y
(t), c
z
(t) )
~a(t) +
~
b(t) k(t)~a(t) (~a(t),
~
b(t) ) [~a(t),
~
b(t)]
(~a(t) +
~
b(t))( a
x
(t) + b
x
(t), a
y
(t) + b
y
(t), a
z
(t) + b
z
(t) ),
(k(t)~a(t))( k(t) a
x
(t), k(t) a
y
(t), k(t)a
z
(t) ),
(~a(t),
~
b(t) ) = a
x
(t)b
x
(t) + a
y
(t)b
y
(t) + a
z
(t)b
z
(t),
[~a(t),
~
b(t)]
a
y
(t) a
z
(t)
b
y
(t) b
z
(t)
,
a
z
(t) a
x
(t)
b
z
(t) b
x
(t)
,
a
x
(t) a
y
(t)
b
x
(t) b
y
(t)
(~a ,
~
b ,~c) = ([~a,
~
b], ~c)
~a(t) t
0

Страницы