Economia Matematica IV

July 31, 2022 | Author: Anonymous | Category: N/A
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Gaiajloa Guajoa Bdrdab ]lxaja Gdjlklsa Ogata Kglj ]ljain ]doaind Oruz ^ljy

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  VJDNAN D D. OAIOVIL NF PA]DAODLJF_ Nfjtrl nf oáiouil nf vardaodljfs sf oljsdnfra fi ajáidsds nf ia lptdbdzaodÿj ndjábdoa para nftfrbdjar su olbplrtabdfjtl nf ia vardamif nf fstanl a traväs nfi tdfbpl, ia bdsba quf fj aihujls oasls fs dj`iufjodana plr sus tasas nf vardaodÿj y plr ltras vardamifs djnfpfjndfjtfs.

1. Lptdbdzaodÿj ndjábdoa;  Ia lptdbdzaodÿj ndjábdoa fstunda fi olbplrtabdfjtl nf ils sdstfbas ndjábdols, fs nfodr fstunda ia fvliuodÿj nfi sdstfba a traväs nfi tdfbpl, sdfbprf musoajnl ia ruta ÿptdba a il iarhl nfi glrdzljtf tfbplrai.



 

        

 

Ias vardamifs fj ajáidsds slj fi tdfbpl y ias tasas nf vardaodÿj, anfbás oamf bfjodljar quf fi fstanl fstaodljardl fs fi fqudidmrdl a iarhl piazl l tabmdäj iiabanl sliuodÿj partdouiar. Ia sliuodÿj olbpifbfjtarda quf fs ia trayfotlrda l fi f i olbplrtabdfjtl rfai a traväs nfi tdfbpl.

1.1 @aotlr nf oapdtaidzaodÿj y `aotlr nf nfsoufjtl; Fj fstf oasl sf oljsdnfra fi vailr prfsfjtf l fi blbfjtl djdodai, ia tasa nf djtfräs y fi tdfbpl.    

   

B

d   t

Pailr prfsfjtf

  ^asa nf djtfräs djtfräs   ^dfbpl

Fkfbpils.

1. Oljsdnfr  Oljsdnfrajnl ajnl quf Bdrdab nfplsdta nfplsdta uj bljtl nf ndjfrl ndjfrl ’B‒ quf sf nfplsdta fj uj maj majol ol plr uj pfrdlnl nf tdfbpl nf ’t‒ añls y a uja tasa nf djtfräs ajuai nf ’d‒ ¼Ouái sfrá fi bljtl nf ndjfrl quf nfmf nf rftdrar nfi majol ai `djaidzar fi añl nanl< _liuodÿj; Nfpfjndfjnl nf ia oapdtaidzaodÿj, tfjnrfbls olbl sliuodÿj ils sdhudfjtfs oasls;  

Oapdtaidzaodÿj ajuai



 (j 2 1) 1

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

 

 

Oapdtaidzaodÿj sfbfstrai

 

Oapdtaidzaodÿj trdbfstrai

 

Oapdtaidzaodÿj ouatrdbfstrai

Oasl D; Oapdtaidzaodÿj ajuai

 (j 2 =)  (j 2 >)  (j 2 ?)

 (j 2 1)

         j

Bljtl `djai

 

 

 

 

 

.

.

.

.

.

.

 

      

Oasl DD; Oapdtaidzaodÿj sfbfstrai

j

 

 (j 2 =)

Bljtl `djai

 



 

                 

.

.

.

.

.

.

 

                 

=

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

Oasl DDD; Oapdtaidzaodÿj trdbfstrai



 (j 2 >)

                       j

Bljtl `djai

 

 

 

.

.

.

.

.

.

 

              

Oasl DP; Oapdtaidzaodÿj ouatrdbfstrai

 (j 2 ?)

                      j

 

Bljtl `djai

 

 

 

.

 

.

.

.

.

.

                 

?

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

Oasl DP; Oapdtaidzaodÿj

 (t 2 j)

        j

Bljtl `djai

 

 

Ouanrl rfsubfj. Jubfrl nf oapdtaidzaodljfs  

   

 

 

 

@lrbuia hfjfrai

              

Bljtl `djai

  

 

 

 

 

 

.

. . . . .

        

 

 Bdrdab nfmf rftdrar nfi majol uj bljtl ’_‒ olj ’j‒ oapdtaidzaodljfs;



>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   

 

=. _d ndfhl nfplsdta 13 333 slifs fj uj majol, nurajtf 6 añls a uja tasa nf djtfräs ajuai nf 13% anfbás fi majol oapdtaidza djtfrfsf oana trdbfstrf ¼Ouái sfrá fi bljtl quf rftdrara ndfhl ai tfrbdjar fi qudjtl pfrdlnl<

Natls;

         

 

 

 

 

_liuodÿj;

  

 

]ffbpiazajnl;

                   

 

 

 

bljtl `djai nf 16 333 fj fi pfrdlnl 8 y samdfjnl samdfjnl quf sf tdfjf uja tasa nf djtfräs ?. _d sf tdfjf uj bljtl

nf 7% oapdtaidzamif trdbfstraibfjtf. Oaiouiar fi bljtl djdodai. Natls;

              

 

 

 

_liuodÿj;

 

]ffbpiazajnl;

6

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                   

 

 

1.1.1 @aotlr nf oapdtaidzaodÿj ndsorftl. _d oljlofbls quf;

              

Nljnf5

 

Anfbás.

Bljtl `djai

                          Bljtl djdodai

  ^asa nf djtfräs djtfräs

  J³ nf oapdtaidzaodljfs   ^dfbpl

Sara ajaidzar ia oapdtaidzaodÿj ndsorfta sf nfmf tlbar fj oufjta ia fxprfsdÿj `aotlr nf oapdtaidzaodÿj ndsorfta fstará fj `ujodÿj a;



, plr il tajtl fi

 

 

 

 

a) Oaraotfrâstdoas nfi `aotlr nf oapdtaidzaodÿj ndsorftl.  



Fi `aotlr nf oapdtaidzaodÿj ndsorfta l 

 fs uj jubfrl purl, nanl quf fs uj jûbfrl quf

oarfof nf ujdnan nf bfndna olbl ils âjndofs l `aotlr.   

’[‒ nfpfjnf nf trfs arhubfjtls, ar hubfjtls, tasa nf djtfräs, pfrdlnl nf oapdtaidzaodÿj y tdfbpl. y tdfbpl. 

 

’[‒ fs uj jubfrl purl ouyl vailr fstá f stá olbprfjndnl fjtrf ils sdhudfjtfs djtfrvails.  0

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

           

 

_d

 

_d

 

 

’[‒ pufnf l pfrbdtf fxpajndr vailrfs prfsfjtfs fj vailrfs `uturls5 fs nfodr pfrbdtdrá oljlofr fi bljtl `djai.

1.1.= @aotlr nf nfsoufjtl ndsorftl. Fs ia djvfrsa nf ia oapdtaidzaodÿj ndsorfta.

                        

 

 

m) Oaraotfrâstdoas nfi `aotlr nf nfsoufjtl ndsorftl.  

 fs uj jubfrl purl oarfjtf oarf jtf nf uja ujdnan nf bfndna (fs uj âjndof) 

 

 nfpfjnf djvfrsabfjtf nf ia tasa nf nfsoufjtl l tasa nf djtfräs, nfi jûbfrl nf

oapdtaidzaodljfs y nfi tdfbpl. 

 

 fjtljofs sf pufnf dj`frdr il sdhudfjtf; 

_d

_d

 

_d

 



  Fstará olbpr olbprfjndnl fjndnl fjtrf fjtrf    pfrbdtf rfnuodr vailrfs `uturls fj f j vailrfs prfsfjtfs.

 

Fkfbpil.

1. Ils panrfs nf ^ljy if ltlrharlj uj prfbdl nf 7333 slifs ai tfrbdjar sus fstundls nf 6 añls. Aotuaibfjtf ia tasa nf djtfräs djtfräs fs nfi 6% oljsdnfrajnl ia oapdtaidzaodÿj bfjsuai ¼Ouái sfrá fi

bljtl aotuai l fi vailr aotuai nfi prfbdl, sd ^ljy aotuaibfjtf fstá oursajnl fi tfrofr añl nf fstundl< Natls;

        

 

 

 

 

8

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  _liuodÿj;

      

 

]ffbpiazajnl;

           

 

 

 

 

1.1.? @aotlr nf oapdtaidzaodÿj o apdtaidzaodÿj oljtdjûa. _f oljsdnfra partdr nf il sdhudfjtf;

  

 

               ¼Quä lourrf olj

sd fi jûbfrl nf oapdtaidzaodljfs tdfjnf ai dj`djdtl<  

 

Slr il tajtl

tdfjnf a

 Ouajnl

 

fs dhuai a



quf fs uj oasl fxtrfbl.



¼Oÿbl bfklrar fi oáiouil nf <

Sara bfklrar ndogl `aotlr fs jfofsardl apidoar ilhardtbl aia `aotlr nf oapdtaidzaodÿj ndsorfta.

            

 

 

Asubdfjnl quf. 

 

 

Slr il tajtl;

7

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

            

_d

 

 

 Jl nftfrbdjanl.

Fj oljoiusdÿj _d nf tdfbpl.

, fjtljofs fstl sdhjd`doa quf ias oapdtaidzaodljfs lourrfj fj oana djstajtf

Ai `djai nf aoufrnl a ia rfhia rf hia nf I—glspdtai. I—glspdtai.  

                             

_d;

 

 

]ffbpiazajnl;

 

 

                               

Apidoajnl ajtdilhardtbls.  

 

Slr il tajtl fj `lrba hfjfrai sf tdfjf.  

Fkfbpil. 4

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Vj bljtl nf ndjfrl nf 17 333 slifs fs nfplsdtanl fj uj majol quf l`rfof pahar uja tasa nf djtfräs nfi 6% ¼Ouái sfrá fi f i bljtl a rftdrar nfspuäs nf 4 añls, sd sf oljsdnfra 1= ooapdtaidzaodljfs< apdtaidzaodljfs< Natls;  

        

 

 

_liuodÿj;

                       

 

 

_d ia oapdtaidzaodÿj `ufra oljstajtf

               

  

 a ouájtl asofjnfrá fi vailr `djai.

 

 

1.1.> @aotlr nf nfsoufjtl oljtdjûl _d fi `aotlr nf oapdtaidzaodÿj oljtdjua fs dhuai a;

        

Fi `aotlr nf oapdtaidzaodÿj nf nfsoufjtl oljtdjul fs ia djvfrsa nfi `aotlr nf oapdtaidzaodÿj oljtdjua.  

 

_upljdfjnl quf sf tdfjf uj jdvfi nf utdidnan fj oana djstajtf nf tdfbpl, pfrtfjfodfjtf ai glrdzljtf tfbplrai quf va nfsnf

 _d  _d  fs ia tasa nf nfsoufjtl y ia utdidnan fsta fj `ujodÿj ai

oljsubl fj fi pfrdlnl ’^‒ ¼Ouái sfrá fi vailr prfsfjtf nfi `iukl `iuk l nf utdidnan nfsoljtana fj fi glrdzljtf tfbplrai< _liuodÿj.

13

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Vsabls `aotlr nf nfsoufjtl oljtdjul.

                 

 

 

Iufhl;

_d

 



fjtljofs sf nfblstrarâa quf fi `utrl tdfjf fi bdsbl vailr quf fi prfsfjtf l sd plr fi

oljtrardl

  fjtljofs sf vailra fi vailr prfsfjtf, fs nfodr ouajtl baylr sfa fi vailr nf

fjtljofs bfjlr sfrá fi vailr `uturl.

 

=. Oáiouil nf vardaodljfs  =.1 @ujodljai lmkftdvl; Oaiouil nf vardaodljfs fs uja apidoaodÿj nljnf su nlbdjdl fs uj oljkujtl nf ’P‒ `ujodljfs y fi rajhl fs uj oljkujtl nf jûbfrls rfaifs5 anfbás quf ias `ujodljfs sf aslodaodÿj a uj olstl y uj mfjf`dodl l uja vfjtaka l nfsvfjtaka.

A

                    

   

 

Iufhl fi `ujodljai lmkftdvl sf rfprfsfjta nf ia sdhudfjtf bajfra  

               

Oljsdnfrajnl ia sdhudfjtf `ujodÿj ndjábdoa  

  

, anfbás jls naj nls pujtls

 

 

¼Ouái sfrá fi bfklr rfolrrdnl nf



 fjtrf fi pujtl djdodai y fi f i pujtl `djai<

11

   y

 nljnf;

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

^rayfotlrdas  

Olstl - Mfjf`dodl  

@ujodljai  

 

     

 

   

   

.

.

.

.

.

.

.

.

.



  

 

            



 

   

 

 

 

Asâ fi `ujodljai fs uja apidoaodÿj fj ia quf fi nlbdjdl fs uj oljkujtl nf `ujodljfs y fi rajhl uj oljkujtl nf jûbfrls rfaifs. Slr fkfbpil, sd fxdstfj vardas rutas quf ujfj ias odunanfs ’a‒ y ’m‒, fjtljofs oana ruta dbpidoa uj olstl y uj mfjf`dodl. _d aslodabls l djolrplrabls uj lmkftdvl ya sfa nf baxdbdzaodÿj l bdjdbdzaodÿj, sf tfjnrá fi `ujodljai lmkftdvl.

     

Baxdbdzar

 

Bdjdbdzar

 

Ai `djai sf tfjnrá; Lptdbdzar

 

Fj fsf sfjtdnl nf`djdbls fi oáiouil nf vardaodljfs quf jl fs bás quf  uja bftlnlilhâa quf sf utdidza para rfslivfr prlmifbas prlmifbas nf lptdbdzaodÿj ndjábdoa fj tdfbpl oljtdjul. Fsta bftlnlilhâa sf utdidza l sf fbpifa para fjoljtrar ia sfjna nf uja lptdbdzaodÿj n ndjábdoa. djábdoa. Fs jfofsardl rfsaitar quf slil ajaidza fi olbplrtabdfjtl nf ia vardamif nf fstanl. Musoa gaiiar ia `ujodÿj ndjábdoa para ia vardamif nf fstanl. 1=

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Fj `lrba hfjfrai fi oáiouil nf vardaodljfs sf piajtfa nf ia sdhudfjtf `lrba;

 ∥           

Lptdbdzar

 

 

Nljnf;          

 @ujodljai

 Oljndodÿj djdodai  Oljndodÿj `djai

 Glrdzljtf tfbplrai nf ajáidsds

 Pardamif nf fstanl

Fkfrododl;

Lptdbdzar fi `ujodljai nf ia djtfhrai nf `djai. _d tfjfbls ils pujtls sdhudfjtfs.

        

 nf ia `ujodÿj djtfrbfnda sukftl a ia oljndodÿj djdodai y



 

¼Ouái sfrá ia ndstajoda bâjdba fjtrf ndogls pujtls< _liuodÿj;

Slr Sdtáhlras;

               

 

 

1?

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Iufhl;

                           ̈   ⁎  ̈   ⁎       ̈   ⁎          

 

 

 

 

 

Slr tajtl;

 

 

 

=.= Fi prlmifba nf oáiouil nf vardaodljfs; Oljsdstf fj fjoljtrar ia trayfotlrda ÿptdba nf ia

vardamif nf fstanl fj fi glrdzljtf tfbplrai nf`djdnl nf `lrba tai quf fi `ujodljai baxdbdof l bdjdbdof. Fjtljofs para fi piajtfabdfjtl piajtfabdfjtl nfi prlmifba nf oáiouil nf vardaodljfs sf nfmf djolrplrar fi `ujodljai lmkftdvl. Lptdbdzar

Fkfbpil;

 ∥  

 

Vja fbprfsa bljlpÿidoa prfsfjta ia sdhudfjtf `ujodÿj nf olstls.

   

 



Anfbás ia prlnuoodÿj nf fsta fbprfsa jl sf aibaofja, plr il tajtl ia oajtdnan prlnuodna sdfbprf sfrá dhuai a ia oajtdnan nfbajnana quf nfpfjnf nfi prfodl vardaodÿj nfi prfodl fs dhuai  y ouya `ujodÿj nf nfbajna fs ia sdhudfjtf;



1>

  y ia tasa nf

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

 ̈

 

Siajtfar fi prlmifba nf oáiouil nf vardaodljfs oljsdnfrajnl fi djtfrvail nf uj prfodl djdodai nf ? y uj prfodl prf odl `djai nf 0. _liuodÿj; Fjoljtrajnl ia `ujodÿj mfjf`dodl.

   ̈    ̈           ̈  ̈     ̈          ̈   ̈      ̈       ̈    ̈   ̈     ̈    ̈   ̈      ̈  ̈  ̈    ̈    ̈       ̈  

@ujodÿj djhrfsl.  

 

 

@ujodÿj olstls.

 

 

 

]ffbpiazajnl (=) y (?) fj (1)  

 

 

Fj `lrba hfjfrai.  

 

 

]ffbpiazajnl.

         ̈   ̈   ̈ 16

 

 

, anfbás nf



 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

        

 

 

=.=.1 Ia `ujodÿj djtfrbfnda; Fs aqufiia `ujodÿj quf sf nfmf nf lptdbdzar fj fi glrdzljtf tfbplrai nf ajáidsds.  Fkfbpil; Ia `ujodÿj a lptdbdzar fs.

  ̈   ̈   ̈ 

 

=.=.= Pardamif nf fstanl; Fs uja `ujodÿj quf nfpfjnf nfi tdfbpl.  

Ndoga vardamif sf oaraotfrdza plr quf oabmda fj oana djstajtf nf tdfbpl, anfbás quf jl fs plsdmif bajdpuiaria nf bajfra ndrfota pfrl sd nf bajfra djndrfota.

=.=.? Bftlnlilhâa nf sliuodÿj; Oljsdstf fj fjoljtrar ia bfklr trayfotlrda ndjábdoa l sfjna ÿptdba l fxtrfbai nf ia vardamif nf fstanl, ya sfa olj ia `djaidnan nf baxdbdzar l bdjdbdzar.

Sasl 1; sf dnfjtd`doa ia `ujodÿj djtfrbfnda.

   ∥          ̈   Lptdbdzar

 

 

Sasl =; Apidoar ia oljndodÿj nf prdbfr lrnfj l oljlodnl olbl ia fouaodÿj nf Fuifr, iufhl sf nfmf

rfslivfr ia fouaodÿj nf Fuifr para fjoljtrar f joljtrar ia `ujodÿj ndjábdoa lrdhdjai.

 

    ̈      ̈    U  ̈  ̈ R      Sasl ?; Apidoar ia oljndodÿj djdodai.

Sasl >; Apidoar ia oljndodÿj `djai.

Sasl 6; Apidoar ia oljndodÿj nf trajsvfrsaidnan. t rajsvfrsaidnan.  

Nljnf;  

 Pailr tfrbdjai nf fstanl. 10

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA     

 

 Djstajtf `djai fj fi glrdzljtf tfbplrai.

 Lpfranlr nf oabmdl.

Anfbás sf nfmf tfjfr fj oufjta ils sdhudfjtfs oasls para su rfsliuodÿj.

a) Oasl 1; Pailr tfrbdjai `dkl y glrdzljtf tfbplrai `dkl.

 ̈  U  ̈  ̈ R                           ̈    U  ̈  ̈ R     ..

_d

 fs `dkl

_d  fs `dkl

 

 

 fs oljlodnl

 

   fs oljlodnl

 

]ffbpiazajnl (=) y (?) fj (1)

 

 

_d rfsuita ofrl qudfrf nfodr quf ia oljndodÿj nf trajsvfrsaidnan fsta dbpiâodtabfjtf sf satds`aof autlbátdoabfjtf, plr il tajtl para nftfrbdjar ia `ujodÿj ndjábdoa nf fstanl mastara utdidzar ia

oljndodÿj djdodai y `djai. Hrá`doabfjtf;

m) Oasl =; Pailr tfrbdjai `dkl y glrdzljtf tfbplrai idmrf.

 ̈    U  ̈  ̈ R                           

_d

 fs `dkl

_d  fs idmrf

 

 fs oljlodnl

 

   fs nfsoljlodnl

 

]ffbpiazajnl (>) y (6) fj (1)

18

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

 ̈    U  ̈  ̈ R         U  ̈  ̈ R     

 

Fjtljofs para gaiiar ia trayfotlrda ndjábdoa sf nfmf utdidzar ia fouaodÿj (0) y ia oljndodÿj djdodai y `djai.

Hrá`doabfjtf;

o) Oasl ?; Pailr tfrbdjai idmrf y glrdzljtf tfbplrai `dkl

 ̈    U  ̈  ̈ R                             ̈ ̈    U  ̈  ̈ R   

 

_d

 fs idmrf

_d  fs `dkl

 

 fs nfsoljlodnl

 

   fs oljlodnl

 

]ffbpiazajnl (8) y (7) fj (1)

 

 

Hrá`doabfjtf;

17

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

n) Oasl >; Pailr tfrbdjai y glrdzljtf tfbplrai idmrf.

    ̈    U  ̈  ̈ R                ̈      U  ̈  ̈R    n.1. Ouajnl jl fxdstf nfpfjnfjoda fjtrf

y  

 

_d

 fs idmrf

 

_d  fs idmrf

 fs nfsoljlodnl

 

   fs nfsoljlodnl

 

]ffbpiazajnl (13) y (11) fj (1)  

 

Hrá`doabfjtf;

14

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

n.=. Ouajnl fxdstf nfpfjnfjoda fjtrf

  

y  

Fj fstf oasl sf nfmf nf gamiar slmrf ia nftfrbdjaodÿj nf ia ourva tfrbdjai quf fs uja `ujodÿj quf nftfrbdja tlnls ils vailrfs quf pufnf tlar ia vardamif nf fstanl fj ils nd`frfjtfs glrdzljtfs tfbplraifs, fj ia ouai sf djnuof quf ia vardamif nf fstanl fj fi djstajtf uitdbl nfi glrdzljtf tfbplrai fs uja `ujodÿj nf tdfbpl.

Hrá`doabfjtf;

Fj fstf oasl sf asubf quf

fs uja `ujodÿj nf tdfbpl.

           ̈    U  ̈  ̈ R      

 

 

 

]ffbpiazajnl (1?) fj (1)

   ̈        ̈     ̈      ̈   * ++  ̈ ̈     _d  fs idmrf

   fs nfsoljlodnl

 

 

 

=3

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

     ̈   ̈      

 

Sasl 0; Apidoaodÿj nf ia oljndodÿj djdodai y tfrbdjai  =.=.> Oljndodÿj nf prdbfr lrnfj (fouaodÿj nf Fuifr) Ia fouaodÿj nf Fuifr fs uja fouaodÿj nd`frfjodai idjfai nf sfhujnl lrnfj tabmdäj oljlodnl olbl ia oljndodÿj nf lptdbdzaodÿj u lptdbanas y pfrbdtf sfifoodljar nf uj oljkujtl nf trayfotlrda anbdsdmif, ia trayfotlrda ÿptdba. Nana ia `ujodÿj djtfrbfnda;

( ̈)     ̈    ̈   ̈   ̈  ̈    ̈  ̈     ̈    U ̈  ̈R ̈   

Nljnf;

  Z

 

Nfsarrliiajnl ia fouaodÿj nf Fuifr;  

Nfsarrliiajnl ia fouaodÿj nf Fuifr;

 

 

Nfrdvajnl tltaibfjtf, olj rfspfotÿ ai tdfbpl.

  ̈  ̈  ̈   ̈      ̈ ̈  ̈   ̈  ̈̈ ̈  ̈      ̇    ̈̈ ̈  ̈    ̈ *

 +

Ndvdndfjnl fjtrf

*

 +

*  

 

 ^fjnrfbls.  ^fjnrfbls.  

̇  ̈    

 

Oljoiusdÿj;  ia fouaodÿj nf Fuifr nf sfhujnl lrnfj idjfai tabmdäj oljlodnl olbl oljndodÿj nf lptdbaidnan nanl quf ia vardamif nf Fstanl prfsfjta gasta =na nfrdvana olj rfspfotl ai tdfbpl.

Fkfbpils;

=1

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Nana ils sdhudfjtfs prlmifbas nf vardaodljfs, lptdbdzar fi `ujodljai y fjoljtrar ia trayfotlrda ndjábdoa quf lptdbdof fi `ujodljai. 1. ]fslivfr.

        ̈  ̈    

 

 

      ̈̈             ̈  ̇       ̈ ̈  ̈ ̇ ̈   ̈  ̇       

Sasl 1; _d tfjfbls fi `ujodljai

 

Nf (1)

 

 

 

Iufhl;

 

 

Srlofnfbls olj ia sdhudfjtf fouaodÿj nd`frfjodai. Gaiiajnl ia sliuodÿj partdouiar

            ̇  ̈   ̇  ̈     

 

Gaiiajnl ia sliuodÿj olbpifbfjtarda  

Glblhfjdzajnl  

Siajtfajnl ia fouaodÿj oaraotfrâstdoa  

Lmtfjdfjnl ia raâz oaraotfrâstdoa.

==

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  ∛                                        

 

 

Fjtljofs ia sliuodÿj olbpifbfjtarda sfrá dhuai a;  

 

Ia sliuodÿj hfjfrai sfrá;

      

 

Apidoajnl oljndodljfs;

                     

 

 

 

  ̈   ⁎    =. ]fslivfr.

 

 

 

_liuodÿj;

 

   ̈   ⁎

=?

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

      ̈   ̈   ⁎̈  

 

 

  ̈ ̈ ̈ ̈  ̇   ̈          Iufhl;

 

 

 

 

Apidoajnl oljndodljfs;  

            ⁎     ⁎   

 

 

   

]ffbpiazajnl (=) y (?) fj (1)

      ̈                     

 

 

 

 

?. ]fslivfr =>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  ̈         

 

      ̈            ̈   ̈  ̇   ̈ 

 

 

_liuodÿj;

 

 

 

 

Iufhl;

 

̇̈                 

 

Apidoajnl oljndodljfs. 2 =3

23

]ffbpiazajnl = y ? fj 1

           ̈               

 

 

Pailr lptdbl

 

 

>. ]fslivfr

=6

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   ̈  ̈ 

 

_ukftl a;

 

     ̈ ̈  ̈  ̈  ̇   ̇̇   ̈                  ̈        ̈  ̈           

_liuodÿj;

 +

*

*

 

Gaiiajnl;  

 

 

 

 

 

Vsajnl oljndodljfs; ……..(=)   ……..(=)

 13 ……….(?)  ……….(?) 

]ffbpiazajnl = y ? fj 1 2x

 

Pailr lptdbl;

 

        

 

 

 

=0

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

]fslivfr;

    ̈    

 

_ukfta a ;

           

 

_liuodÿj;

  ̈ ̈  ̈  ̇  ̇ 21

2=  

2=    

̇    ̇ ̈̈                                                    

 

 

182

 

 

 

 

 

Pailr lptdbl

   ̈    

 

=8

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                           

 

 

          ̈ 



 

]fslivfr;

 

_ukftl a;

           ̈    ̈ ̈  ̈ ̇ ̇ ̇    ̇̇     ̈̈                                       

_liuodÿj;

 

@2

21 2

 

2

 

Apidoajnl Fuifr;

12

 

 

 

 

 

Apidoajnl oljndodljfs;

   

 

 

=7

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Iufhl;

         

 

Pailr lptdbl

     ̈                         

         ̈ 

 

 

]fslivfr;

 

_ukftl a;

 

    

a) gaiiar ia sfjna lptdba m) gaiia fi vailr ÿptdba nfi `ujodljai o) hra`doar _liuodÿj;

   ̈  

 

2 -1=

 ̈ ̈ ̈ ̇ 20   2

 

Apidoajnl Fuifr;

̇  ̇   ̇̇     ̈̈      

 

 

  =4

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                       U  ̈R    ̈                         ̈          ̈                    

Apidoajnl oljndodljfs;

 

 

 

 

 

 

 

]ffbpiazajnl

 

 

 

 

 

 

=.=.6 oljndodÿj nf sfhujnl lrnfj 

Fj ils prlmifbas nf oáiouil nf vardaodljfs oljsdnfrajnl ia oljndodÿj nf prdbfr lrnfj fs jfofsardl olj tai olj uja uja oljndodÿj nf su` su`dodfjoda dodfjoda quf pfrbdta nftfrbdjar fi vailr vailr bâjdbl l báxdbl nfi `ujodljai lmkftdvl. Slr il quf fs jfofsardl fvaiuar ia oljoavdnan y ia oljvfxdnan nf ia `ujodÿj djtfrbfnda. Fj fstf fjtfjnfr para nf`djdr sd ia sfjna lptdba gaiiana rfsufivf uj prlmifba nf baxdbdzaodÿj l bdjdbdzaodÿj sf nfmf apidoar ia oljndodÿj nf sfhujnl lrnfj.

¼Fj uj prlmifba nf oáiouil nf vardaodljfs olbl sf pufnf fstamifofr quf fi `ujodljai nfmf baxdbdzar l bdjdbdzar< _f nfmf ajaidzar ia oljoavdnan y ia oljvfxdnan nf ia `ujodÿj djtfrbfnda olj rfspfotl a ia vardamif f fstanl  y a ia vardaodÿj nf ia vardamif nf fstanl ( )



̈

Anfbás sf nfmf nf gaiiar ia sfhujna nd`frfjodai nd`frf jodai nf ia `ujodÿj djtfrbfnda sfa plsdtdva l jfhatdva. ?3

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  a. _d ia sfhujna nd`frfjodai nf ia `ujodÿj djtfrbfnda fs bfjlr a ofrl, fjtljofs ia `ujodÿj djtfrbfnda sfrá fstrdotabfjtf oÿjoava. Il quf djndoa quf fi `ujodljai fs nf baxdbdzaodÿj;

                    

   fs fstrdotabfjtf oÿjoava, fjtljofs

     

 Fs uj báxdbl.

m. _d ia sfhujna nd`frfjodai nf ias `ujodljfs djtfrbfnda fs baylr a ofrl, fjtljofs ia `ujodÿj djtfrbfnda sfr fstrdotabfjtf oljvfxa, il quf djndoa quf fi `ujodljai fs nf bdjdbdzaodÿj    fs fstrdotabfjtf oÿjoava, fjtljofs

 Fs uj báxdbl.

Slr il tajtl para rfaidzar ia fvaiuaodÿj sf nfmf tfjfr fj oufjta slil ia vardamif nf fstanl y su vardaodÿj.



 

Ia prdbfra y sfhujna nfrdvana dbpidoa il sdhudfjtf; Srdbfra nd`frfjodai;

                                     

_fhujna nd`frfjodai;

 

Nf nljnf;

 

Olbpiftajnl ouanranls tfjfbls;

 

_d;

 

:3   ia `ujodÿj djtfrbfnda fs fstrdotabfjtf oÿjoava   bdjdbdzaodÿj   Fi `ujodljai lmkftdvl P(T) fs nf bdjdbdzaodÿj  y

          

Anfbás ouajnl fs uj oasl nf bdjdbdzaodÿj ia batrdz quf il oljstdtuyf fs uja batrdz Gfssdaja. _d;

 

             _d

 y 3   ; ia `ujodÿj djtfrbfnda fs fstrdotabfjtf oljvfxa   Fi `ujodljai lmkftdvl P(T) fs nf baxdbdzaodÿj

Ouajnl fs uj oasl nf baxdbdzaodÿj ia batrdz quf il oljstdtuyf fs uja batrdz Gfssdaja jfhatdva nf`djdna. ?1

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

Aitfrjatdvabfjtf sd ajaidzabls ia fxprfsdÿj, nfsahrfhajnl plnfbls fvdnfjodar quf fs nf ia `lrba ouanrátdoa plr il quf fs susofptdmif a fxprfsarsf batrdodaibfjtf.

   ⌅         ⌋ 

 

 

Aglra il prdjodpai fs;

 | ||   |                    

 

Fkfrododl; Nanl fi sdhudfjtf `ujodljai lmkftdvl sukftl a ia rfstrdoodÿj tfbplrai

_.A

 

a)  m)  o)  n) 

Gaiiar ia fxtrfbai Gaiiar fi vailr lptdbl nfi `ujodljai Hra`doar Nftfrbdjar sd KUWR fs báxdbl l bâjdbl

_liuodÿj;

_d sf tdfjf fi sdhudfjtf `ujodljai

    

 

Gaiiabls il sdhudfjtf;

 ̈  ̈  ̇  ̈  2 -1= 2 20 0   2

 

?=

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Apidoajnl Fuifr;

̇  ̇   ̈̇̈̇                               U  ̈R̈                                  ̈      ̈              

 

 

 

 

Apidoajnl oljndodljfs;

 

 

 

 

 

 

 

]ffbpiazajnl

 

 

 

 

 

Iufhl;

??

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

         * +

 

 

          

 

Slnfbls jltar quf G1 fs baylr a 3 y G= fs dhuai a 1

 

  

OLJOIVODLJ; Fi vailr nftfrbdjanl plr ia batrdz gfssdaja fs dhuai a 0 y baylr a 3, a ia vfz quf G= fs dhuai a 35 y tlbajnl fj oufjta quf 2 0:3, sf oljoiuyf quf; il quf nfbufstra quf ia `ujodÿj djtfrbfnda fs nämdibfjtf oljvfxa, plr il quf sf nftfrbdja quf fi `ujodljai lmkftdvl fs nf bdjdbdzaodÿj. ]fpiajtfajnl; Bdjdbdzar

          

=.=.0 Oljndodÿj nf ifhfjnrf; Ia oljndodÿj nf ifhfjnrf pfrbdtf nftfrbdjar fi báxdbl amsliutl l báxdbl rfiatdvl nf uj prlmifba nf oáiouil nf vardaodljfs. v ardaodljfs.

=.=.0.1 Báxdbl amsliutl; _f nf`djf olbl fi pujtl báxdbl para tlnls ils nlbdjdls. =.=.0.= Báxdbl rfiatdvl;  _f nf`djf olbl fi pujtl báxdbl para uj djtfrvail nf nlbdjdl, fs fi pujtl báxdbl para fi fxtfrjl nfi nlbdjdl para ils ¾pujtls nf nfrfoga f dzqudfrna. Ia oljndodÿj nf ifhfjnrf fs uja oljndodÿj quf fxprfsa ia oljoavdnan l oljvfxdnan l ia oljvfxdnan nf ia `ujodÿj djtfrbfnda nf bajfra idjfai l fxtrfbl idjfai, il ouai fs nfjlbdjana fxtrfbl iloai y slil sf loupa loupa nf fvaiuar, ia fxprfsdÿj fxprfsdÿj sdhudfjtf; _f td tdfjf fjf ia sdhudfjtf sdhudfjtf `ujodÿj , fs plsdmif gaiiar  nfi ouai  djtfrbfnda JL^A;

                 

 

_d  fs baylr a 3 fjtljofs ia ia trayfotlrda ÿptdba nf ia vardamif nf nf fstanl fjoljtrana pfrbdtdrá bdjdbdzar fi `ujodljai.     Bdjdbdzaodÿj

_d  fs bfjlr a 3, fjtljofs ia trayfotlrda ÿptdba nf ia vardamif nf fstanl fjoljtrana pfrbdtdrá baxdbdzar fi `ujodljai.    Baxdbdzar

?>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

]fslivfr ils sdhudfjtfs prlmifbas; Lptdbdzar;

   ∥     ̈  

 

 

     ̈ ̈̈    ̇    

Gaiiajnl ia sfjna lptdba;  

 

Djtfhrajnl



 

 ̈   ̈         

 

 

 

]ffbpiazabls ias oljndodljfs;

     ⁎           

 

 

=. uja fbprfsa tdfjf uj pfndnl J ujdnanfs, nfmf surtdr fj ^21, _d   nf jlta fi jûbfrl nf ujdnanfs prlnuodnas fj   nljnf sf pufnf djtfrprftar olbl fi djvfjtardl aoubuianl fj t, fi  nljnf olstl fj t fstá nanl plr

̈   ̈

 

^lbajnl fj oufjta ias oljndodljfs djdodaifs nf a)  Gaiiar ia fxtrfbai;

  ∥   ( ̈ )             

  

 

 

 

?6



 y ia oljndodÿj tfrbdjai

    

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  _liuodÿj;

  ̈     ̈

Ia `ujodÿj djtfrbfnda;

 

 

Ia fouaodÿj nf Fuifr;

  ̈  ̈  ̈  ̇ ̇   ̈                                   ̈̈                                     U  ̈ ̈R     

 

 

Dhuaiajnl  

Djtfhrajnl = vfofs;

 

]ffbpiazajnl ias oljndodljfs;

 

 

 

 

m. gaiiar vailr ÿptdbl nfi `ujodljai  

o. nftfrbdjar sd fs báxdbl l bâjdbl b âjdbl

n. hra`doar

?0

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Vjdnan DD 1. OLJ^]LI ßS^DBL Fs uja bftlnli bftlnlilhâa lhâa nf ajáidsds ndjábdol quf pfrbdtf pfrbdtf rfslivfr prlmifbas nf lptdbdzaodÿj, anfbás quf fstunda fi olbplrtabdfjtl nf ia vardamif nf fstanl y ia vardamif nf oljtrli ouya `djaidnan sfrá nf baxdbdzar l bdjdbdzar.

1.1 Pardamif nf fstanl;   Fs uja vardamif ndjábdoa ouyl olbplrtabdfjtl fstá fstamifodna nf bajfra djndrfota plr ia vardamif nf oljtrli, fs nfodr uja vardamif nf fstanl fs aqufiia quf rf`ifka fi rfsuitanl nf ias nfodsdljfs tlbanas slmrf ia vardamif nf oljtrli. Ia oaraotfrâstdoa bás dbplrtajtf nf uja vardamif nf fstanl fs quf jl pufnf sfr oljtrliana nf bajfra ndrfota plr fi ahfjtf foljÿbdol quf tlba ias nfodsdljfs

1.= Pardamif nf oljtrli; _f fjtdfjnf olbl ia vardamif quf fs lmkftl nf uja nfodsdÿj ndsorfodljai armdtrarda plr partf nfi djvfstdhanlr l ahfjtf foljÿbdol quf tlba ia nfodsdÿj. Ia oaraotfrâstdoa prdjodpai nf uja vardamif nf oljtrli fs plr sfr tâpdoabfjtf uj djstrubfjtl foljÿbdol nf pliâtdoa, nanl quf utdidza sus partdouiardnanfs para dj`iudr fj ia vardamif nf fstanl.

Fkfbpil; _upljhabls fi oasl nf fxtraoodÿj lptdba nf rfoursls jaturaifs, nljnf uj paâs fj fi quf

fxdstf uj rfoursl jaturai fxtraâmif rfprfsfjtanl plr ](pftrÿifl) ouya tasa nf fxtraoodÿj fs nf F(^),nf ia ouai dnfjtd`doar ia vardamif nf oljtrli y ia vardamif nf fstanl , anfbás piajtfar fi olbplrtabdfjtl nfi rfoursl fj djstajtf nf tdfbpl5 a su vfz piajtfar ia `ujodÿj nf utdidnan oljsdnfrajnl fi pfrdlnl nf fxpiltaodÿj nfi rfoursl quf fs nf  



_liuodÿj;

   

 

_d ia tasa nf fxtraoodÿj tdfbpl.

 djorfbfjta, fjtljofs fi rfoursl fxtraâmif ndsbdjudrá plr ujdnan nf

 

       

Nfpfjndfjnl nf ia tasa nf fxtraoodÿj jaturai fxtraâmif

 

 

 



  sf tfjnrá fi olbplrtabdfjtl nf`djdnl nfi rfoursl

 vardamif nf fstanl   vardamif nf oljtrli   

Slr il tajtl ia `ujodÿj nf utdidnan para fi rfoursl jaturai fxtraâmif sfrá dhuai a;

?8

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

          ∥                 

 

 Fouaodÿj nf blvdbdfjtl  Fouaodÿj

Oljoiusdÿj;  Il quf musoa ia utdidnan (u) fs fjoljtrar ia sfjna lptdba nfi rfoursl fxtraâmif (]^)

quf pfrbdta baxdbdzar fi mdfjfstar aoubuianl (P^) fj fi glrdzljtf tfbplrai ^Ў*3,^+  ^Ў*3,^+ 

1.? Fi prlmifba nf oljtrli ÿptdbl;  Oljsdstf fj nftfrbdjar ias trayfotlrdas ÿptdbas nf ia vardamif nf fstanl y ia vardamif nf oljtrli quf pfrbdta baxdbdzar l bdjdbdzar fi `ujodljai fj fi glrdzljtf tfbplrai U3.^R y quf oubpia ia rfstrdoodÿj nf`djdna.

 ∥           

 

 

 

Nljnf;

       

 

  Pardamif nf fstanl P. nf oljtrli `ujodÿj djtfrbfda fouaodÿj nf blvdbdfjtl nf fstanl `ujodljai lptdbl

      

1.> Bftlnlilhâa nf sliuodÿj; _f nfmf oljstrudr ia `ujodÿj gabditljdaja quf fs dhuai a il sdhudfjtf

          

 

Nljnf;

?7

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA   

 

 

  

P. nf fstanl P. nf oljtrli P. nf olfstanl

Srdjodpdl nfi báxdbl pljtryfhfj; Fstf prdjodpdl pfrbdtf dnfjtd`doar ias trayfotlrdas ndjábdoas nf

ia vardamif nf fstanl y nf oljtrli quf baxdbdza l bdjdbdza fi `ujodljai.Fstf prdjodpdl fs ia oljndodÿj nf prdbfr lrnfj fs nfodr fs f s ia oljndodÿj jfofsarda para rfslivfr fi prlmifba nf oljtrli ÿptdbl. A oljtdjuaodÿj quf nfmf oubpidr ia sdhudfjtf oljndodÿj;

 

  Baxdbdzar G



 



  olj rfspfotl a ia vardamif nf fstanl fj ^Ў*3,^+ a ia vfz ia vardamif nf oljtrli y (u) pfrtfjfofj a ℠.  ℠.  I a fouaodÿj nf blvdbdfjtl nf fstanl nfmf sfr dahuai a ia vardaodÿj vardao dÿj nf G rfspfotl a ε nfmf sfr dhuai a ia vardaodÿj nf ia vardamif nf fstanl

   ̈

 

Andodljaibfjtf sf nfmf apidoar uja oljndodÿj nf trajsvfrsaidnan.

 

UGRt2^ ^-ε(^) ^-ε(^)

^23

Fjtljofs nfpfjndfjnl nf ia oljndodÿj tfrbdjai T(^)2T^ sf tfjnrá ndvfrsls oasls para apidoar olbl nftfrbdjana oljndodÿj nf trajsvfrsaidnan 5anfbás sf dbpljf a ia sliuodÿj hfjfrai ias oljndodljfs djdodaifs y `djaifs.

Ajáidsds nf ia oljndodÿj; Baxdbdzar G olj rfspfotl a u5 Fsta oljndodÿj fstamifof uj prlmifba nf lptdbdzaodljfs tatdoa il quf sdhjd`doa quf sf nfmf baxdbdzar fi vailr nf G slil olj rfspfotl a ia vardamif nf oljtrli, oljsdnfrajnl a ia vardamif nf fstanl, olfstanl y tdfbpl olbl sd `ufraj oljstajtfs. Fkfbpil;

        

 ……….. Olj rfspfotl a W

Iufhl nf rfslivfril;

     

  Fj   Fj





fxdstf uj báxdbl para T  fxdstf uj bâjdbl para T

Ai baxdbdzar fi gabditljdajl olj rfspfotl a ia vardamif nf oljtrli Bax G↝u,

      

 

?4

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  _dfjnl (℠) uj oljkujtl nf vailrfs anbdsdmifs nf ia vardamif nf oljtrli5 fs nfodr nf odr fs uj oljkujtl nf vailrfs quf pufnf tlbar ia vardamif nf oljtrli. _dj fbmarhl ai baxdbdzar G fsta pufnf sfr nf `lrba idjfai y jl idjfai olj rfspfotl a ia vardamif nf oljtrli nfi ouai surhfj nls oasls; OA_L 1; Ia `ujodÿj G nfpfjnf idjfaibfjtf nf ia vardamif nf oljtrli (u) Fj fstf oasl sf tfjnrá nls sliuodljfs nf oljtlrjl l nf fsqudja, quf fxdhf il sdhudfjtf;

  Fxdstf uja rfiaodÿj plsdtdva fjtrf G y u



G

Gbax

Gbdj

Vbdj

Vbax

V

℠2 (u1, u=)

    

 

Fxdstf uja rfiaodÿj djvfrsa l jfhatdva fjtrf G y u  

JL^A; Fj abmls oasls sf fxdhf ia oljndodlj hfjfrai.  

OA_L =; I a `ujodÿj G nfpfjnf l jl fs idjfai rfspfotl a u ._d fs jl idjfai rfspfotl a ia vardamif nf oljtrli, su sliuodÿj sfrá nf djtfrdlr, il quf fxdhf il sdhudfjtf.

>3

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

Gbax

A

V1 u*

u1,u=)↝

M

V*

V=

 

     ∥

]fslivfr fi sdhudfjtf prlmifba nf oljtrli ÿptdbl BAW v2

         

 

 

a)  Gaiiar ia trayfotlrda lptdba nf fstanl, oljtrli y olfstanl

 

Hra`doar m) o)  Gaiiar fi vailr lptdbl nfi `ujodljai

_liuodÿj; Oljstruyfjnl fi Gabditljdajl;

          

 

Apidoaodÿj nfi prdjodpdl nfi báxdbl, fj fstf oasl fi báxdbl nf G olj rfspfotl a ’u‒, nanl quf G fs jl idjfai olj rfspfotl a u. Fxdhf quf;

  

 

>1

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                           ̈       

 

 

Siajtfar ia fouaodÿj nf blvdbdfjtl nf fstanl  

Nftfrbdjar ia fouaodÿj nf blvdbdfjtl nf olfstanl  

 

Djtfhrajnl tfjfbls;

 

Apidoar oljndodÿj nf trajsvfrsaidnan; UGR^2t2

Tt23

T(^)2T ^ 5 T(=)2 idmrf

^ fs `dkl y ia vardaodÿj sfrda juia

                T^23

 

 

Apidoajnl (8) fj (6)

 

]ffbpiazajnl (4) fj (=)

 

      

 

]ffbpiazajnl (13) fj (?)

>=

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                                     

 

Djtfhrajnl (11)

 

Apidoajnl oljndodÿj djdodai

 

 

 

@djaibfjtf ias trayfotlrdas ÿptdbas slj;

             

 

   

Pailr lptdbl

                          

 

Djtfhrajnl -

 

Iufhl if nabls sus rfspfotdvls vailrfs

              

 

>?

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  FKF]ODODL_;

  ̈            

 

 

 

Ga bditljdajl;

 

---------- (1)

Apidoaodÿj nf prdjodpdl nfi báxdbl; Baxdbdzar G olj rfspfotl a ia vardamif v ardamif nf oljtrli nanl quf G fs jl fs idjfai olj rfspfotl a ia u. Fxdhf quf;

                           ̈  ̈   

 

 

 

 

Fouaodÿj nf blvdbdfjtl nf fstanl

 

 ----------- (?)

Fouaodÿj nf blvdbdfjtl nf olfstanl

>>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

    ̈  ̈                                   

 -------- (>)

Djtfhrajnl lmtfjnrfbls;  ----- (6)

Apidoajnl oljndodÿj nf trajsvfrsaidnan;  

 

 ----------- (0)  -------- (8)

Apidoajnl 8 fj 6, tfjnrfbls;  

 

 ---------- (7)

]ffbpiazajnl 7 fj 6  ---------------- trayfotlrda lptdba nf olfstanl

            ̈ 

]ffbpiazajnl 4 fj = tfjnrfbls;

 

  -------- vardamif lptdba nf oljtrli

]ffbpiazajnl 13 fj ? tfjnrfbls;  

Djtfhrajnl 11

>6

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

                          

 

 

 - ------------------------- trayfotlrda lptdba nf fstanl @djaibfjtf ias trayfotlrdas ÿptdbas slj

        

    

 

>0

 

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  

 

Pailr lptdbl

                             

  

 

 

P2 =8

   

 

 ̈       ⌇⌄      

 

 

Ga bditljdajl;

 

---------- (1)

Apidoaodÿj nf prdjodpdl nfi báxdbl; Bax G olj rfspfotl a ia vardamif nf oljtrli nanl quf G fs jl fs idjfai olj rfspfotl a ia u. Fxdhuf quf;

   

 

   

 

 

  

Fouaodÿj nf blvdbdfjtl nf fstanl

>8

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   ̈  ̈         ̈  ̈         

----------- (>)

Fouaodÿj nf blvdbdfjtl nf olfstanl  

-------- (6)  -------- (0)

Apidoajnl oljndodÿj nf trajsvfrsaidnan;





 

        

                                    -------- (8)

 23

A2 - 6

 

 ---------- (7)

Ajaidzajnl fi vailr

 y nftfrbdjar sd fs plsdtdvl l jfhatdvl sf nfmf tfjfr fj oufjta il

sdhudfjtf.  

Sara t(>) 2

 

Slr il tajtl jl sf oljsdnfra oljsdnfra t2>  ---------- (4)

]ffbpiazajnl 4 fj > tfjnrfbls;  

 ̈     

>7

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

    

 

Apidoajnl oljnddlj;  

         

 

A27

  -------------- vardamif nf fstanl

>4

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 



 ---------vardamif nf oljtrli

 ---------- vardamif nf olfstanl

              ∥            Pailr lptdbl;

 

)

 

   ∥       ̈  ̈    ̈  ̈   

 

 

 

 

 2 3

    

63

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 



 2 ?

_d sf tdfjf; (u)

(

+

                  ̈   ̈     ̈  ̈   Gaiiajnl nfrdvanas;

 

V+

 

 

2

 

 

 

 

]23

 

 

 

       ̈     ̈     ̈  ̈    

2

 

 

 

 

Djtfhrajnl lmtfjnrfbls;

61

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

 

 

Apidoajnl oljndodÿj djdodai5 2?

                                     

 

 

 

Pardamif nf oljtrli;

 

 

 

 

     ̈            

 

 

   

6=

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Ga bditljdajl;

    

 

---------- (1)

Apidoaodÿj nf prdjodpdl nfi báxdbl; Bax G olj rfspfotl a ia vardamif nf oljtrli nanl quf G fs jl fs idjfai olj rfspfotl a ia u. Fxdhf quf;

                      ̈  

 

 

------- (=)

 

Fouaodÿj nf blvdbdfjtl nf fstanl

 

 ̈      ̈  ̈  

 ----------- (?)

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

-------- (>)

Djtfhrajnl lmtfjnrfbls;  lmtfjnrfbls; 

    

 

6?

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

    

 2 3

A23 ----- (6) vardamif nf fstanl

    

Apidoajnl 6 fj =, tfjnrfbls;



V2   V (t) 2

  

 ----- (0) vardamif nf oljtrli

]ffbpiazajnl 0 fj ?;

 ̈   ̈              

 

r21

 

 

M21

----------- (8) vardamif nf olfstanl

@djaibfjtf ias trayfotlrdas ÿptdbas slj

          

----- vardamif nf fstanl

V (t) 2

 ----- vardamif nf oljtrli

----------- vardamif nf olfstanl

6>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

        

 

 

  ̈              ̈     

 

Ga bditljdajl;

 

 

u (t) 2 3 ------- (vardamif nf oljtrli)

Fouaodÿj nf blvdbdfjtl nf fstanl;

   ̈

 

]ffbpiazajnl 1 fj =  ---- (=)

 ̈ 

66

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

 ̈ 

 

] 2 -1  

           ̈

 

A21

 ---------- (vardamif nf fstanl)

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

2y

 ̈  ̈                         

Djtfhrajnl lmtfjnrfbls; 2

 

 

Apidoajnl oljndodÿj nf trajsvfrsaidnan  

 

 

 

 

 ------- (vardamif nf olfstanl)

      

 

60

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  ̈                   

 

 

Gabditljdajl;

 

---------- (1)

Apidoaodÿj nf prdjodpdl nfi báxdbl; Bax G olj rfspfotl a ia vardamif nf oljtrli nanl quf G fs jl fs idjfai olj rfspfotl a ia u. Fxdhf quf;

 

               

 

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

 ̈  ̈                  

]2 ->

 

 

 

 

68

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

        

 

Fouaodÿj nf blvdbdfjtl nf fstanl

   ̈  ̈     ̈     ̈    ∥     ∥                    

 

 

 

 

 

 

                A

 

 

 

 

67

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

          

 

        

 

64

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

       

 

  ̈                           

 

 

---- (1)

 

 ---- (=)

Baxdbl

Fouaodÿj nf blvdbdfjtl nf fstanl

   ̈

 

03

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  ̈  

 --- (?)

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

 ̈   ̈               ̈     ̈                              

---- (>) vardamif nf olfstanl

]ffbpiazajnl > fj =;  

---- vardamif nf oljtrli

Apidoajnl fj ?  

 

Djtfhrajnl lmtfjnrfbls;  

 

 

 ---- vardamif nf fstanl

@djaibfjtf tfjfbls ias trayfotlrdas;  

Pardamif nf olfstanl

 

Pardamif nf oljtrli

 

Pardamif nf fstanl

01

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

Pailr lptdbl;

                 

 

 

   

 

     

  ̈             

 

 

 

 

--------- (1)

0=

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

             ̈   ̈       ̈

 

------ (=) ------

Fouaodÿj nf blvdbdfjtl nf fstanl  

 --- (?)

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

 ̈                                    ---- (>)

Djtfhrajnl lmtfjnrfbls; ---- (6)

Apidoajnl trajsvfrsaidnan  

 

-

 

 

 

]ffbpiazajnl 0 fj =

----- (8) vardamif nf oljtrli -----

Apidoajnl 8 fj ?

  ̈  

 

0?

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

  ̈    

 ---(7)

Djtfhrajnl lmtfjnrfbls;

 

       

                   

 

 

@djaibfjtf tfjfbls ias trayfotlrdas;

         

 

               

 

0>

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

    

----- vardamif nf oljtrli ----oljtrli

  

 

    ̈ 

 

 

   

 

06

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA  Ga bditljdajl;

         

 

---------- (1)

Apidoaodÿj nf prdjodpdl nfi báxdbl; Bax G olj rfspfotl a ia vardamif nf oljtrli nanl quf G fs jl fs idjfai olj rfspfotl a ia u. Fxdhf quf;

                        ̈  

 

 

------- (=)

 

Fouaodÿj nf blvdbdfjtl nf fstanl

 

 ̈      ̈  ̈  

 ----------- (?)

Fouaodÿj nf blvdbdfjtl nf olfstanl

  -------- (>)

Djtfhrajnl lmtfjnrfbls;  lmtfjnrfbls; 

    

 

00

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

    

 2 3

A23 ----- (6) vardamif nf fstanl

              ̈    ̈                     

Apidoajnl 6 fj =, tfjnrfbls; u2

 

u (t) 2-

 ----- (0) vardamif nf oljtrli

]ffbpiazajnl 0 fj ?;  

 

r21

 

 

M21

----------- (8) vardamif nf olfstanl

@djaibfjtf ias trayfotlrdas ÿptdbas slj ----- vardamif nf fstanl

V (t) 2

 ----- vardamif nf oljtrli

----------- vardamif nf olfstanl

08

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   

 

  ̈            (  ̈)            ̈   ̈    

 

 

 

---------- (1)

 

------- (=)

 

 

 

]2 -1

        

  07

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

             ̈  ̈     ̈           

------ (?) vardamif nf fstanl

]ffbpiazajnl ? fj = -

----- vardamif nf oljtrli

Fouaodÿj nf blvdbdfjtl nf olfstanl

 

 

 

Djtfhrajnl lmtfjnrfbls; +M

 

 

------ vardamif nf olfstanl

@djaibfjtf ias trayfotlrdas



 

 

04

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   -

 

  

Pailr lptdbl

  ∥   ∥         nt

nt

 

83

 

VJDPF]_DNAN JAODLJAINFI AI^DSIAJL @AOVI^AN NF DJHFJDF]DA FOLJLBDOA F_OVFIA S]L@F_DLJAI NF DJHFJDF]DA FOLJLBDOA 

   

 

P2 ->4.444

81

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