Клевчихин - Матан II семестр

D RN

x0

x01, . . . , x0N

D

F

x0

lim F x

F x0 .

x

x0

ε 0 δ 0 x : x x0

δ

F x

F x0

ε.

x

x0 0

ε 0 δ 0 F Uδ x0

Uε F x0

Uδ x0 F 1 Uε F x0 .

x0

y =

F

(x)

y0

D

F

D G

RM

x F 1 G

F x G

G

ε

0

Uε F x

G

Uε F x

G

Uδ x

Uδ x

F 1

G

x

F 1

G

x

F 1 G

x

D

F

x

ε 0

F x

Uε

F x

x

x

x

F

F : D

RM

K D

Gi

F 1 G

F K

V

i

i

Gi

F 1 G

K

F

i

K

Vi

Vi1 , Vi2 , . . . , Vin .

y F x

D RN RM

E

D

AF , BF

F E

F 1 AF F 1 BF

E

A

B

E

x

x t

A

B

E

x a A

x b B t

a, b x t

E

y F x t , t

a, b

AF , BF

F E

F E

RN

RM

L

lj

1 i N

x

x1, . . . , xN

i

1 j M

N

l1xk

k

1

1

1

x

1

k

1

l1

l2

. . . lN

N

l2

l2

. . . l2

x2

l2xk

x

1

2

N

k

k

1

lM

lM

. . . lM

xN

N

1

2

N

lM xk

k

k

1

~e1, . . . , ~eN

RN

~e1

1, 0, 0 . . . , 0 , ~e2

0, 1, 0, . . . , 0 , . . . , ~eN

0, 0, 0, . . . , 1 .

x x1~e1 x2~e2

xN ~eN .

x x1

~e1 x2

~e2

xN ~eN .

~ek

RM

RM

j

~εj

0, . . . , 0, 1, 0, . . . , 1 ,

M

M

~e

lj

~ε

k

k

j

j 1

M

M

x x

1

~e1

x

2

~e2

x

N

N

1

j

x

N

j

~εj .

~e

x

l1~εj

lN

j 1

j 1

~ε1 ~ε2, . . . , ~εM

N

N

N

x

l1xk~ε

l2xk~ε

lM xk~ε .

k

1

k

2

k

M

k

1

k 1

k 1