Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 164 стр.

UptoLike

ВУЗ: 

МФТИ | Москва

Составители: 

Рубрика: 


Ë} ÒÒ}ÈÁË ¯©m©° Ë®äÈËäÈÒ}Òlnj
ÙkÓÈãÒÒË°}È«˺äË¯Ò«ÒãÒÓË®ÓÈ«ÈãË¯Èµ

äÓºmkp
ÒÓˮӺË¹¯º°¯ÈÓ°mº
cÈÏä˯
Óº°
¯Òä˯ÈÏÒ°È
Îtvnxzkvkxn}éjlqyx
knrzvévktjwsvxrvxzq

ȯÈÓË}ºããÒÓËȯө²mË}º¯ºmÓÈ¹ãº°}º°Ò
Îtvnxzkvkxn}knrzv
évkkwévxzéjtxzkn

¯º®}È Óº¯äÒ¯ºmÈÓÓ©² ¹º¹È¯Óº º¯ººÓÈãÓ©²
mË}º¯ºm
Îtvnxzkv kxn}
n
rvuwvtntzt}xzvsi|vk
n
n
FºãºmmÒÈ
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
...
;
...
;
...
; ...
...

Îtvnxzkvkxn}utvmv
·sntvkxznwntqtnk
¡n·nu
n
n+1
n+1
ºÓºãËÓmÒÈ
PP P P
PP
n
n
n
n
12 3
2
4
3
1
1
1();();() ;() ;
... ; ( ) ; ( ) .
τττττττ
ττ ττ
=== =
==
−
+
Îtvnxzkvkxn}ujz
éq|éjounéj
nm×
nm
nm
m°ËmºÏäºÎÓ©² ¯ÈÏãÒÓ©² äÈ¯Ò ¯ÈÏä˯È
nm
×
 m°Ë ªãËäËÓ© }ºº¯©² ¯ÈmÓ© Óã }¯ºäË
ºÓºº¯ÈmÓºº
Îtvnxzkvkxn}{ytr
|qptnwénékt}tj
[a,b]
∞
rÈÏÒ°ÓË°Ë°mË

Îtvnxzkv én¡ntqp
vltvévltvp xqxznu
m
yéjktntqp x
n
tnqo
knxztuqqéjtmvu
r

n
r
sº¯äÈãÓÈ«ÁÓÈäËÓÈãÓÈ«°Ò°ËäÈ¯ËËÓÒ®
Òjisq|j
{ÈãÒË¹¯ÒmËËÓ©¹¯Òä˯©m©º¯ÈÈÏÒ°ÈmãÒÓˮӺä¹¯º°¯ÈÓ°mË

 ºË°ã«ãººÓÈ¯ÈãÓºº
n
mÈÓÓºäãÒÓˮӺä¹¯º°¯ÈÓ°mËÓÈ®Ë°«
n
+1ãÒÓˮӺ
ÓËÏÈmÒ°Òä©®ªãËäËÓÓȹ¯Òä˯°Ò°ËäÈÁÓ}Ò®mÒÈ
}cos,...,3cos,2cos,cos,1{
ττττ
n

 Ë }  Ò Ò    } È Á Ë  ¯ ©   m © °  Ë ®   ä È ˆ Ë ä È ˆ Ò } Ò   l n ‘ j 
ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



                                         
                                                                                                
                                    cÈÏä˯
  ÒÓˮӺ˹¯º°ˆ¯ÈÓ°ˆmº                                                         ¯Òä˯­ÈÏÒ°È
                                      Óº°ˆ 
                 
                                               
                                               
 Îtv nxzkvkxn}éjlqyx                        È¯ÈÓË}ºããÒÓËȯө²mË}ˆº¯ºmÓȹ㺰}º°ˆÒ
 knrzvévktjwsvxrvxzq
                                               
 Îtv nxzkvkxn}knrzv                         ‘¯º®}È Óº¯äÒ¯ºmÈÓÓ©² ¹º¹È¯Óº º¯ˆººÓÈã Ó©²
 évkkwévxzéjtxzkn                             mË}ˆº¯ºm
 
                                                                                1              0              0                      0
                                         
                                          
                                                                                  0              1              0                      0
 Îtv nxzkv kxn} n
 rvuwvtntzt€}xzvsi|vk                  n      nFˆºã­ºmmÒÈ 0 ;                            0 ;            1 ; ...                0 
                                                                                         ...          ...          ...                ...
                                                                                          0            0            0                  1
                                                           
                                                         
 Îtv nxzkvkxn}utvmv                         n+1        n+1ºÓºãËÓmÒÈ
 ·sntvkxznwntqtnk€                                     
 ¡n·nun                                                    P1 (τ ) = 1 ;      P2 (τ ) = τ ;      P3 (τ ) = τ 2 ;       P4 (τ ) = τ 3 ;
                                                                                                                                              
                                                                   ...       ;    Pn (τ ) = τ n −1 ;        Pn +1 (τ ) = τ n   .
                                                           
                                                         
 Îtv nxzkvkxn}ujz                            nm        nm m°ËmºÏäºÎÓ©² ¯ÈÏãÒÓ©² äȈ¯Ò ¯ÈÏä˯È
 éq|éjounéj m× n                                        m× n  m°Ë ªãËäËӈ© }ºˆº¯©² ¯ÈmÓ© ӂã  }¯ºäË
                                                           ºÓºº¯ÈmÓºº
                                                         
 Îtv nxzkvkxn}{ytr      ∞                              rÈÏÒ°ÓË°‚Ë°ˆm‚ˈ 
 |qptnwéné€kt€}tj
 [a,b]
                                                         
 Îtv nxzkv     én¡ntqp nr                              sº¯äÈã ÓÈ«Á‚ÓÈäËӈÈã ÓÈ«°Ò°ˆËäÈ¯Ë ËÓÒ®
 vltvévltvp xqxznu€ m
 yéjktntqp x n tnqo
 knxzt€uqqéjtmvur
 
        
                                        Òjisq|j


{ˆÈ­ãÒ˹¯ÒmËËÓ©¹¯Òä˯©m©­º¯È­ÈÏÒ°ÈmãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmË


      ‘ºË°ˆ ã«ã ­ººÓȈ‚¯Èã Óºº nmÈÓÓºäãÒÓˮӺ乯º°ˆ¯ÈÓ°ˆmËÓÈ®ˈ°« n+1ãÒÓˮӺ
        ÓËÏÈmÒ°Òä©®ªãËäËӈÓȹ¯Òä˯°Ò°ˆËäÈÁ‚Ó}Ò®mÒÈ{1,cos τ ,cos 2τ ,cos 3τ ,..., cos nτ } 

Страницы