Notes Chapter 3 FAR

AJT % Khpm| Lfjrpmt < fppr?((yyy+lrj%laj+hti

 Ejtnmpjdgm \ml}tcpcm| \ml}tcpcm| |fh}g` dm lgj||cacm` ckph hkm ha pftmm ljpmihtcm| :+ Ptj`cki Ptj`cki \ml}tcpcm| \ml}tcpcm| “ |ml}tcpcm| |ml}tcpcm| &dhpf &dhpf `mdp jk` mz}cps# mz}cps# dh}ifp dh}ifp jk` jk` fmg` aht pfm pfm r}trh|m r}trh|m ph |mgg pfme pfme |hhk 4+ Jqjcgjdgm Jqjcgjdgm aht |jgm “ |ml}tcpcm |ml}tcpcm|| &dhpf `mdp `mdp jk` mz}cps# mz}cps# pfjp `hm| `hm| khp emmp pfm pfm `mackcpchk `mackcpchk ha pfm hpfmt hpfmt pyh % tmrhtpm` j| mcpfmt l}ttmkp ht khk%l}ttmkp j||mp' `mrmk`cki hk pfm ckpmkp ha pfm lhtrhtjpchk <+ Fmg` ph Ejp}tcps \ml}tcpcm| “ `mdp |ml}tcpcm| pfjp pfm lhtr ckpmk`| ph fhg` }kpcg ejp}tcps % tmrhtpm` j| l}ttmkp ca ejp}tm| ycpfck : st> khk%l}ttmkp ca ejp}tm| ck ehtm pfjk j st  % |phln| `hk–p ejp}tm' |h hkgs `mdp |ml}tcpcm| jtm lgj||cacm` j| pfc| Ptj`cki jk` jqjcgjdgm aht |jgm jtm tmrhtpm` jp ajct qjg}m &ejtn ph ejtnmp# ]ktmjgcm` ijck(gh||m| hk ptj`cki |ml}tcpcm| jtm cklg}`m` ck mjtkcki|> C@MJ> hrmtjpcki lj|f aghy ]ktmjgcm` gh|| hk ptj`cki |ml}tcpcm| vv Qjg}jpchk Jllh}kp vv ]ktmjgcm` i(g hk jqjcgjdgm aht |jgm jtm tmrhtpm` ck hpfmt lhertmfmk|cqm cklhem> R ]AM> ckqm|pcki lj|f aghy ]ktmjgcm` gh|| hk jqjcgjdgm aht |jgm |ml}tcpcm| vv Qjg}jpchk Jllh}kp vv Tmlgj||cacljpchk> ptjk|amt ha |ml}tcps athe hkm ith}r ph jkhpfmt  Athe Ph  J`o}|pemkp  Ptj`cki Jks hpfmt kh j`o}|pemkp kmlm||jts &jgtmj`s tmlhikcm` ck cklhem# Jks hpfmt Ptj`cki Tmlhikcm ck cklhem ceem`cjpmgs Jqjcg aht \jgm &`mdp# Fmg` ph Ejp }ktmjgcm` i(g c| jehtpcm` hqmt pfm tmejckcki gcam ha `mdp Fmg` ph Ejp &`mdp# Jqjcg aht \jgm }ktmjgcm` i(g jp ptjk|amt `jpm |fjgg dm tmrhtpm` ck R]AM Ca pfmtm c| j rmtejkmkp `mlgckm ck ajct qjg}m' ytcpm `hyk j| cerjctemkp ha j||mp jk` tmlht` j| tmjgcm` gh|| ck l}ttmkp mjtkcki| C@MJ J |jgm ha |ml}tcps athe jks ljpmihts tm|}gp| ck j tmjgcm` ijck(gh|| jk` c| tmrhtpm` ck l}ttmkp cklhem Lj|f vv Ptj`cki |ml}tcps vv Tmjgcm` ijck vv &C@MJ# Lj|f vv ]ktm ]ktmjg jgc cm` m` ijck jck hk hk Jqj Jqjcg cg aht aht |jg |jgmm vv &R &R]AM# Jqjcg aht |jgm |ml}tcps vv Tmjgcm` ijck hk Jqjcg aht |jgm vv &C@MJ# ]ktmjgcm` ijck(gh||m| ljtm khp pjv `m`}lpcdgm jk` pfmtmahtm lj}|m j pmerhtjts `caamtmklm

 D}|ckm|| Lhedckjpchk|(Lhk|hgc`jpchk| ․ ․ ․

Lhk|hgc`jpm` A(\ cikhtm cerhtpjkp gmijg tmgjpchk|fcr| jk` merfj|cm mlhkhecl |}d|pjklm hqmt ahte Lhk|hgc`jpm jgg ejohtcps hykm` |}d|c`cjtcm| &hqmt & hqmt =2- qhpcki# @h khp lhk|hgc`jpm yfmk lherjks c| }k`mt gmijg tmhtijkcjpchk &djknt}rpls# ht lhkpthg ha |}d c| ycpf j pt}|pmm

Lh|p empfh` &2%:3- hykmt|fcr# “ `h khp lhk|hgc`jpm' kh |cikcacljkp ckag}mklm  Mz}cps Empfh` &42-%=2-# “ `h khp lhk|hgc`jpm' |cikcacljkp ckag}mklm Lhk|hgc`jpm &=2-;# “ lhkpthg :

AJT % Khpm| Lfjrpmt < fppr?((yyy+lrj%laj+hti

Lh|p Empfh` &mvpmtkjg tmrhtpcki# “ &jg|h ljggm` ajct qjg}m empfh` ht jqjcg aht |jgm# @h khp lhk|hgc`jpm D(\ Tmlht` jp lh|p &AEQ . gmijg amm|# Ckqm|pemkp ck ckqm|pmm Lj|f J`o}|p ph AEQ jp smjt mk` ]ktmjgc jgcm` fhg`cki gh||m| Ejtnmpjdgm |ml}tcps

vv vv

vv

@cqc`mk` `c|ptcd}pchk ht tmp}tk ha ljrcpjg Lj|f vv Ckqm|pemkp ck ckqm|pmm

vv

vv

C(\ @cqc`mk`| ph pfm rjtmkp jtm tmrhtpm` j| cklhem Lj|f vv @cq cklhem vv @c|ptcd}pchk| pfjp mvlmm` rjtmkp| |fjtm ha pfm ckqm|pmm–| tmpjckm` mjtkcki| Lj|f vv Ckqm|pemkp ck ckqm|pmm vv Eh|p pm|pm` lhklmrp| hk lh|p empfh` Pfm ‗ckqm|pemkp ck ckqm|pmm― c| khp j`o}|pm` aht ckqm|pmm mjtkcki| ․ Pfm ‗ckqm|pemkp ck ckqm|pmm― c| j`o}|pm` ph AEQ &AJ\D ::=# ․ Lj|f `cqc`mk`| athe pfm ckqm|pmm jtm tmrhtpm` j| cklhem ds pfm rjtmkp ․

 Mz}cps Empfh` &mvpmtkjg tmrhtpcki# “ `h khp lhk|hgc`jpm Mvmtlc|m| |cikcacljkp ckag}mklm “ hyk| 42-%=2- qhpcki |phln' gjtim|p |fjtmfhg`mt ht fhg`| ejohtcps ha   dhjt` ha `ctmlpht |mjp| \h ljk hyk dmghy 42- qhpcki |phln jk` |pcgg mvmtp |cikcacljkp ckag}mklm jk` pfmtmahtm }|m mz}cps empfh` ․ D(\ Tmlht` jp lh|p &AEQ . gmijg amm|# Ckqm|pemkp ck ckqm|pmm vv Lj|f vv ․

Yfmk |}d mjtk| ehkms(tmrhtp| KC' ckltmj|m ds rjtmkp| hykmt|fcr - ha ckqm|pmm–| mjtkcki| Ckqm|pemkp ck ckqm|pmm vv Mz}cps ck mjtkcki|(ckqm|pmm cklhem vv @cqc`mk` `c|ptcd}pchk ht tmp}tk ha ljrcpjg' `mltmj|m ds rjtmkp| hykmt|fcr - ha `cqc`mk`| athe ckqm|pmm Lj|f vv Ckqm|pemkp ck ckqm|pmm vv C(\ Rjtmkp| hykmt|fcr - ha ckqm|pmm–| mjtkcki| c| tmlht`m` j| cklhem Ckqm|pemkp ck ckqm|pmm vv Mz}cps ck mjtkcki|(ckqm|pmm cklhem vv 4

AJT % Khpm| Lfjrpmt < fppr?((yyy+lrj%laj+hti

Ckqm|pmm lj|f `cqc`mk`| tm`}lm rjtmkp| ckqm|pemkp Lj|f vv Ckqm|pemkp ck ckqm|pmm vv \h mj|s yjs ph tmemedmt c| pfm IJJR jllh}kpcki t}gm| aht pfm mz}cps empfh` c| ph pfckn ha cp gcnm j djkn  jllh}kp Dmickkcki Djg . ckqm|pmm mjtkcki| % ckqm|pmm `cqc`mk`| 5 mk`cki djgjklm

\pmr ds |pmr jlz}c|cpchk &C yj| }|cki lh|p empfh`' d}p C dh}ifp ehtm |phln jk` khy fjqm ph }|m mz}cps empfh`# Pfm ckqm|pemkp jllh}kp jk` tmpjckm` mjtkcki| jllh}kp jtm j`o}|pm` tmpthjlpcqmgs aht pfm `caamtmklm dmpymmk ․ lh|p empfh`(jqjcgjdgm aht |jgm empfh` ph mz}cps empfh` Lhk|c`mtm` j lfjkim ck jllh}kpcki rtcklcrjg &athe lh|p ph mz}cps empfh`# ․ Jrrgs pfm kmy mz}cps empfh` ph pfm rtcht rmtch`| hg` hykmt|fcr - &:%42-#' `hk–p jrrgs pfm kmy ․  rmtlmkpjim hykmt|fcr yfmk ejncki pfm tmpthjlpcqm j`o}|pemkp' sh} `c` khp hyk pfjp e}lf ha pfm lherjks  djln pfmk

Lhk|hgc`jpm` ackjklcjg |pjpmemkp| “ lhkpthg? }|m r}tlfj|m empfh`' rhhgcki ha ckpmtm|p| c| kh ghkimt rmtecppm` 

 R}tlfj|m Empfh`  Rjtmkp lherjks ckpmtkjg OM R}tlfj|m aht lj|f &jp AEQ yfclf c| pfm lh|p hk r}tlfj|m `jpm# Ckqm|pemkp ck |}d|c`cjts vv Lj|f vv ht  R}tlfj|m ycpf rjtmkp lheehk |phln  Ckqm|pemkp ck |}d|c`cjts vv Lheehk |phln vv &rjtmkp jp rjt# J R CL vv &Rjtmkp AEQ%rjt# Rjc` ehtm pfjk kmp dhhn qjg}m &KDQ# aht |}d|c`cjts &rtmec}e# “ |fh}g` dm tmlht`m` j| ihh`ycgg Rjc` gm|| pfjk KDQ aht |}d|c`cjts &`c|lh}kp# “ tmlht` j| mvptjht`ckjts ijck Mgceckjpm \}d–| hg` mz}cps Lhk|hgc`jpcki yhtnrjrmt mgceckjpcki oh}tkjg mkpts vv L Lheehk |phln “ |}d vv J J R CL T T (M “ |}d vv vv C Ckqm|pemkp ck \}d E Eckhtcps ckpmtm|p vv `o}|pp “ D(\ D(\ ha ha |}d |}d ph AEQ AEQ &rj &rjc` c`## vv J J`o}| vv I Ihh`ycgg Yfmk LJT  `hm| khp mz}jg C pfmk C tmlhklcgm }|cki

EJI

Yfmk pfm z}m|pchk| |js| sh} r}tlfj|m` pfm |}d hk :(:(2: d}p pfms icqm sh} pfm |}d–| ackjklcjg hk :4(<:(2: pfmk sh} kmm` ph ack` dmi tmpjckcki mjtkcki &:(:(2:# |h pjnm pfm mk`cki tmpjckcki mjtkcki . `cqc`mk`| “ cklhem <

AJT % Khpm| Lfjrpmt < fppr?((yyy+lrj%laj+hti

Ckqm|pemkp ck |}d|c`cjts Htcickjg ljttscki jeh}kp ha pfm ckqm|pemkp ck |}d|c`cjts jllh}kp hk rjtmkp| dhhn| 5 htcickjg lh|p “ AEQ ․ @ctmlp h}p ha rhlnmp lh|p| &ack`mt| amm' gmijg amm|# jtm cklg}`cki ck ckqm|pemkp ck |}d jllh}kp &ljrcpjgcm`# ․ @mdcp? ckqm|pemkp ck |}d Ck`ctmlp lh|p| jtm mvrmk|m` j| ckl}ttm` ․ @mdcp? mvrmk|m \phln tmic|ptjpchk amm| jk` c||}jklm lh|p| &\ML acgcki amm|# jtm j `ctmlp tm`}lpchk ha qjg}m ha |phln c||}m` ․ @mdcp? JRCL Dhk` c||}m lh|p| jtm ljrcpjgcm` ph ‗dhk` c||}m lh|p― jk` jehtpcm` ․

Eckhtcps ckpmtm|p ycgg dm jpptcd}pm` yfmk pfm rjtmkp `hm| khp hyk :22- ha |}d Pfm lhk|hgc`jpm` C(\ ycgg cklg}`m :22- ha |}d–| kmp cklhem+ Pfm eckhtcps ckpmtm|p rhtpchk ha pfm |}d| kmp cklhem ycgg dm cklg}`m` j| j gckm cpme `m`}lpchk Pfm lhk|hgc`jpm` D(\ ycgg cklg}`m :22- ha |}d–| j||mp| jk` gcjdcgcpcm| &khp |}d–| mz}cps ( LJT#+ Pfm eckhtcps ckpmtm|p |fjtm ha pfm |}d–| kmp j||mp| |fh}g` dm rtm|mkpm` hk pfm D(\ dmpymmk GP `mdp jk` mz}cps j| ‗eckhtcps ckpmtm|p ck kmp j||mp|― 5 |}d| |phln fhg`mt| mz}cps / eckhtcps ckpmtm|p

@mpmteckcki r}tlfj|m` ihh`ycgg ht mvptjht`ckjts ijck Ckqm|pemkp ck \}d . gcjdcgcpcm| j||}em` 5 r}tlfj|m rtclm % &L}ttmkp j||mp| . GP ejtnmpjdgm |ml}tcpcm|# % Ghymt ha lh|p ht AEQ ha khk%l}ttmkp j||mp| 5 . cp| Ihh`ycgg> % cp–| j mvptjht`ckjts ijck

 A<%<2 mvjergm> A<%<: jtm pfm OM 

 Ckpmtlherjks Ptjk|jlpchk| “ mgceckjpm :22- aht mvpmtkjg tmrhtpcki  Pfms jtm mgceckjpm` dmlj}|m pfms gjln pfm ltcpmtcj ha dmcki| ‗jte| gmkipf― @h kh mgceckjpm ckpmtlherjks jllh}kp| jl lh}kp| ca sh} `h khp lhk|hgc`jpm Yfmk ckqmkphts fj| dmmk |hg` ckpmtlherjks tmqmt|m pfm htcickjg ckpmtlherjks ptjk|jlpchk &|jgm jk` LHI\# jk` % ca ckqmkphts c| |hg` ph h}p|c`mt|  lhttmlp LHI\ % ca ckqmkphts c| |pcgg hk fjk`  lhttmlp Mk`cki Ckqmkphts

Ca hkm emedmt ha pfm lhk|hgc`jpm` ith}r jlz}ctm` jk jaacgcjpm–| `mdp athe jk h}p|c`mt' pfm `mdp c| lhk|c`mtm` ph  dm tmpctm` &dmlj}|m hykm` ckpmtkjggs# jk` j i(g c| tmlhikcm`+ Hkgs mvptjht`ckjts c| }k}|}jg jk` ckatmz}mkp

Lhedckm` A(\ ( R}|f @hyk Jllh}kpcki  Lhedckm` A(\ jtm aht j ith}r ha tmgjpm` lherjkcm|' khp lhk|hgc`jpm` dmlj}|m pfmtm c| kh rjtmkp lherjks % Lherjkcm| }k`mt lheehk lhkpthg &ck`cqc`}jg hyk| ejks lherjkcm|# % Lherjkcm| }k`mt lheehk eiep % ]klhk|hgc`jpm` |}d|c`cjtcm| &ejks ahtmcik |}d|#

 R}|f `hyk jllh}kpcki  tmrhtp| j||mp| jk` gcjdcgcpcm| jp ajct qjg}m ck |mrjtjpm A(\ ha pfm |}d|c`cjts 0