Pia Ecuaciones2.1

 

Ugmversmhkh Kutÿgl`k Kutÿgl`k he Guevl Ceÿg Ikouctkh he Karlgl` Karlgl`àk àk

EOUKOMLGE_ HMIEZEGOMKCE_ MGA. EG MGHU_XZK_ KCM@EGXKZMK_

–VMK‐

VZLIE_LZK4 @MZKGHK @ MZKGHK KJMAKMC LZXMT KCLG_L E[UMVL4 CUM_ KGAEC OLGXZEZK_ AK]XKG DLEC KGXLGML CEKC _KCKTKZ  EZMN ZE]GKCHL VKOBEOL ZLHZMAUET DLZAE _EJK_XMKG OUZK AKZOMK •

•

•

•

•

EH_LG JEZ@KG YMCCKZEKC

 

CE] HE XLZMOECCM ?5. _m perilrk`ls ug kauderl eg ug oujl ccegl he kauk, ec càqumhl skce olg ugk rkzÿg aljergkhk plr ck cey he Xlrrmoeccm, que estkjceoe que ck rkzÿg he ok`jml hec vlcu`eg es prlplromlgkc k ck rkàz oukhrkhk he ck kcturk hec càqumhl. Ck eoukomÿg he ck rkzÿg hkhk eg ck imaurk ?.:.;; surae hec prmgompml he Jergluccm he bmhrlhmgë`mok que estkjceoe estkjceoe que ck okgtmhkh ugk olgstkgte. olgstkgte. Kquà es ck presmÿg, ϋ es ck hegsmhkh hec icumhl, es ck veclomhkh y es ck koecerkomÿg he ck arkvehkh. Ol`pkrkghl ck  pkrte supermlr hec hec icumhl, k ck kcturk kcturk olg ec icumhl eg ec kauderl, tege`ls que4   0

_m ck presmÿg eg ck pkrte supermlr y eg ec ilghl slg cks hls maukc k ck presmÿg kt`lsiírmok y ec rkhml rkhml hec kauderl es `uobl `eglr `eglr que ec rkhml hec oujl, oujl, egtlgoes ,  plr cl que0 olghuoe k ck cey he Xlrrmoeccm4 . Vuestl que , tege`ls ck eoukomÿg hmieregomkc4

 

Eg este prljce`k, ve`ls ugk ol`pkrkomÿg he ck eoukomÿg hmieregomkc he Xlrrmoeccm olg cls hktls rekces.  k) _m ec kauk estë k ugk kcturk  , plhe`ls egolgtrkr ec vlcu`eg he kauk eg ec oujl uskghl ck respeotmvk`egte iÿr`uck eg ck quey  . Kquà hegltk g echec rkhml he ck pkrte supermlr y hec ilghl hec oujl, hegltkhegltkg ck kcturk oujl. Xl`kghl estk iÿr`uck ol`l hkhk, se hermvk pkrk egolgtrkr ugk reckomÿg  egtre cks rkzlges

Ck reckomÿg quehkràk4

 

   

      

0



 

Hlghe4   •

•

 

 

•

_ustmtuyeghl cls vkclres tege`ls4

√   ∔  0



 

•

¼

k)









√ 



 ^ (  +  )  



P     



Olg estl plhe`ls hermvkr  

 ^ (  +  ) 

√ 

P   

Vr re reack ack he ck ok okhe hegk gk





( +   ) 0 (  +   ) ( (  ) ¼  (  +  ) (  ∑ ; ) 

¼   (  +   )



 

(



  

)

+  

 ) 

 

•

Zekol`lhkghl

•

 

Ol`l resuctkhl gls quehk ck eoukomÿg4  

 j) Use ck expresmÿg hehuomhk eg ec mgomsl k) pkrk egolgtrkr ugk eoukomÿg hmieregomkc pkrk b(t) (es heomr, teghràk ugk vkrmkjce mghepeghmegte t, ugk vkrmkjce hepeghmegte b y cks olgstkgtes eg ck eoukomÿg). Zeslcve`ls ck reckomÿg pkrk egolgtrkr ck eoukomÿg hmieregomkc  

 

o) Zesuecvk estk eoukomÿg hmieregomkc uskghl sepkrkomÿg he vkrmkjces. Es recktmvk`egte hmreotl heter`mgkr kc tme`pl ol`l ugk iugomÿg he ck kcturk, perl hespedkr ck kcturk ol`l ugk iugomÿg hec tme`pl puehe ser hmiàomc.

 

 

∮



  







√   +   +      0   / 

∮

;



  /

; 







 +

∔    

 



  ; /

 +





  /

; 



 0

√    

  ∔  





∮

/

/

; 

 



+

+  

∮





/

 



/

; 

 0

∮  

 +





 ∔  



√  

  

+

  /

; 

 +

  ∔  

  ∔  

∮

  √        0   ;/    

+    ∔ 0 



√    

∔  

  ∔  

 

_M@CMIMOKGHL XEGE@L_4



 ∔   

(









+ ;  + ;   ) 0 √     ∔    

;

KUG @K_ _M@VCMIMOKHL XEGE@L_

 0

•

ZE_LCYMEGHL 











+    +     





/

; 

0√

  ;   

 

 

∔  

 

e) _e puehe ver que ugk eoukomÿg hmieregomkc `ës exkotk es4 Zesuecvk estk eoukomÿg hmieregomkc y ol`pkre cls resuctkhls hec mgomsl h).

0

ZECKOMLG OLGLOMHK

_EVKZKGHL YKZMKJCE_ YKZMKJCE_ GL_ [UEHK

∮

(  +  )



∔ 

 0 √ ( .2 )

∮

√    

  ∔    

 

KOL@LHKGHL E_ MAUKC K XEGEZ 











 





; 

   +    +    / 0 ; (√  . 2 )   ∔    

ZE_UCXKHL4 ZE_LCYMLGHL XEGE@L_ OL@L ZE_UCXKHL4













+    +    







; /

  0 √  ; .       ∔  

 

AZKOMK_