Аналитическая геометрия. Часть III. Многомерные пространства. Гиперповерхности второго порядка. Шурыгин В.В. - 60 стр.

UptoLike

ВУЗ: 

КФУ | Казань

Составители: 

Рубрика: 

1
◦
17
◦
2) A
3
1
◦
17
◦
I ϕ
(v
1
)
2
+ (v
2
)
2
± (v
3
)
2
1
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
= 1
2
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
= −1
3
◦
. (x
1
)
2
+ (x
2
)
2
+ (x
3
)
2
= 0
4
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
= 1
5
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
= −1
6
◦
. (x
1
)
2
+ (x
2
)
2
− (x
3
)
2
= 0
II ϕ
(v
1
)
2
± (v
2
)
2
eϕ det(a
αβ
) 6= 0
7
◦
. (x
1
)
2
+ (x
2
)
2
= 2x
3
8
◦
. (x
1
)
2
− (x
2
)
2
= 2x
3
III ϕ (v
1
)
2
±
(v
2
)
2
eϕ det(a
αβ
) = 0
9
◦
. (x
1
)
2
+ (x
2
)
2
= 1
10
◦
. (x
1
)
2
+ (x
2
)
2
= −1
11
◦
. (x
1
)
2
+ (x
2
)
2
= 0
12
◦
. (x
1
)
2
− (x
2
)
2
= 1
13
◦
. (x
1
)
2
− (x
2
)
2
= 0
IV ϕ (v
1
)
2
14
◦
. (x
1
)
2
= 2x
2
15
◦
. (x
1
)
2
= 1
16
◦
. (x
1
)
2
= −1
17
◦
. (x
1
)
2
= 0
A
n
p
X
i=1
(x
i
)
2
−
q
X
i=p+1
(x
i
)
2
− 2ax
p+q+1
+ b = 0,
¦ pia }fjkbmbau 1◦ 17◦ €
                                          nv                 v
    2)  km egkmfrbghia kigfgxg egft j k A3 j``abbg z kakjombibc igp
xnj a igo‚vg igxnjw vgxnj k bmvgigfcr j``abbcr hahimdjr vggf nabji
gba ljnj{iht gnbad a imd ym }fjkbmbamd al heahvj 1◦ 17◦ €
                                                                ) „
    I < *,7356>,A* .-B*3C,-/70 < //-½003-B5,,58 1B5D3570 ,58 -3:5 ϕ
.30B-D07/8 1 B0D2 (v1)2 + (v2)2 ± (v3)2 <
                                                ‹
    1◦ . (x1 )2 + (x2 )2 + (x3 )2 = 1 •¨660./-0D <
                                                            ‹
    2◦ . (x1 )2 + (x2 )2 + (x3 )2 = −1 •:,0:A” ¨660./-0D <
                                                      ‹
    3◦ . (x1 )2 + (x2 )2 + (x3 )2 = 0 •:,0:A” 1-,2/ <
                                                                   ‹
    4◦ . (x1 )2 + (x2 )2 − (x3 )2 = 1 •-D,-.-6-/7,A” 90.*3+-6-0D <
                                                                    ‹
    5◦ . (x1 )2 + (x2 )2 − (x3 )2 = −1 •DB2.-6-/7,A” 90.*3+-6-0D <
                                                           ‹
    6◦ . (x1 )2 + (x2 )2 − (x3 )2 = 0 •B*ˆ*/7B*,,A” 1-,2/ <
                                                   ) „
    II < ’535+-6-0DA < //-½003-B5,,58 1B5D3570 ,58 -3:5 ϕ .30B-D07/8
1 B0D2 (v1)2 ± (v2)2 < Á-3:5 ϕe ,*BA3-“D*,5 •det(aαβ ) 6= 0‹<
                                           )                 ‹
    7◦ . (x1 )2 + (x2 )2 = 2x3 •¨660.70 */10” .535+-6-0D <
                                             )                 ‹
    8◦ . (x1 )2 − (x2 )2 = 2x3 •90.*3+-60 */10” .535+-6-0D <
                                      ) „
    III < //-½003-B5,,58 1B5D3570 ,58 -3:5 ϕ .30B-D07/8 1 B0D2 (v 1 )2 ±
          Á                                   ‹
(v 2 )2 < -3:5 ϕe BA3-“D*,5 •det(aαβ ) = 0 <
                                        )               ‹
    9◦ . (x1 )2 + (x2 )2 = 1 •¨660.70 */10” ½060,D3 <
                                                   )              ‹
    10◦ . (x1 )2 + (x2 )2 = −1 •:,0:A” ¨660.70 */10” ½060,D3 <
                                                                         ‹
    11◦ . (x1 )2 + (x2 )2 = 0 •.535 :,0:AC .*3*/*15‡ˆ0C/8 .6-/1-/7*” <
                                            )             ‹
    12◦ . (x1 )2 − (x2 )2 = 1 •90.*3+-60 */10” ½060,D3 <
    13◦ . (x1 )2 − (x2 )2 = 0 •.535 B*ˆ*/7B*,,AC .*3*/*15‡ˆ0C/8 .6-/1-
/7*”‹<
                                      ) „
    IV < //-½003-B5,,58 1B5D3570 ,58 -3:5 ϕ .30B-D07/8 1 B0D2 (v 1 )2 <
                                     )              ‹
    14◦ . (x1 )2 = 2x2 •.535+-60 */10” ½060,D3 <
                                                                       ‹
    15◦ . (x1 )2 = 1 •.535 B*ˆ*/7B*,,AC .53566*6>,AC .6-/1-/7*” <
                                                                  ‹
    16◦ . (x1 )2 = −1 •.535 :,0:AC .53566*6>,AC .6-/1-/7*” <
                                                                      ‹
    17◦ . (x1 )2 = 0 •.535 B*ˆ*/7B*,,AC /-B.5D5‡ˆ0C .6-/1-/7*” <
         .3-/735,/7B* An  BA+0358 .-DC-D8ˆ0” 3*.*3  235B,*,0* B/81-” 90
.*3.-B*3C,-/70 :-“,- .30B*/70 1 B0D2
                 p
                 X              q
                                X
                        i 2
                       (x ) −           (xi )2 − 2axp+q+1 + b = 0,
                 i=1            i=p+1
                                           ÀÑ

Страницы