3.
Y , f Y, .. , Y y = . Y : ( ), , .. . , , - , . Y - , f ; . Y , - , , -.
- - , , - . , , ( - ) , . -, .
-.
-,
1.1.
, - (t), .. , - = (t).. x (t), y(t) z (t) (t) , - . , x (t), y(t) z (t) - , , - (t) , :
= (x (t), y (t), z (t)).
x (t), y(t) z (t) - (t). , - (t), (x (t), y(t), z (t)) () - .
, : (x (t), y (t), z (t)) - - , , - (t) : . , - - .
, (t), , , .. . , : , (t) Ox Oy . , T, , - (t) T - : . , , , T , T. - .
|
|
- .- (t) - , : (x (t), y (t), z (t)). t, , T, , (. . 1). - (t). t , x = x (t), y = y (t), z = z (t)
, - , , , - .
1. = = , . O D , , . t - : . D . - ,
- .
1.2. -
t0 , - - - , , - .
. - t, - t0 , ε> 0 δ> 0 , t, - δ t0, ε..
, : = ( t, t0 ) ( t, t0 ).
, :
,
| t- t0 | , | - | - (. . 2)
. : φ (t) = . , φ (t) - , , (. )
, .., (. ε-δ). , , - t t0:
. (1)
1 -
1. ( ) - - t0 , t0 , x (t), y (t) z (t) - - . , , - , , . - , :
►: =( ) . :
. ; , , ..
() , :
() (2) (1) (2). ◄
. = , =| |. ► = = = | |. ◄
. =| |, = . , :
|
|
= = 0
- (1) = .
-, .
2. ( ) - - , .
► , - : =( ) =( ). ≠ , - . , , ≠ . - x (t) , ; - . ◄
3. ( -) t0 , t0 , - λ (t), : , λ (t) λ. :
1) ; 2) ;
3) ; 4) .
► , - . - 4).
, , , - :
, ,
, . , - :
= =
= :
;
;
. , :
= = . ◄
. ; . - , , , - , , .
- (α,β), - .
. - t, α ( t, β ), ε> 0 δ> 0 , t, (α, α + δ) - () , - ε.
- (α,β), x (t), y (t) z (t) - . , , - , , . , - :
;
.
- .
4. ( - )
- t0 , t0 ,, - . , , , t, t0 , t, t0 :
( = ) ( = = ).
► x (t), y (t) z (t) - - , , - .
. = . , , . : , , . : = .
- . ◄
1.3. -
. - t0 , t0 , , .
5. ( ) - . t0 . , t0, - , .
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► x (t), y(t) z (t) - - : : 0 = (t 0), 0 = y(t 0), z0 = z (t 0); .
. , - t 0, . ◄
t t0 t t0 Δ t h. : t = t0 + Δ t= t0 + h. - = - = - - t0 - Δ Δ (h), - h = Δ t t. : .
6 ( -) - . t0 . , t0, , : .
► , 0 = (t 0), 0 = y(t 0), z0 = z (t 0); - = (x (t)- x (t0), y(t)- y(t0), z (t) - z (t0)), ..
Δ (h) = - = (x (t0+h)- x (t0), y(t0+h)- y(t0), z (t0+h) - z (t0)) =
= (
() (, , ). 5 6, , , t0 ◄
. - (α,β), . - [α,β], (α,β) , , α (.. ) β (.. ).