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Chapter 4

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140 views33 pages

Chapter 4

eijfdefef

Uploaded by

Anu Goyal
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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KB ERR AL, Het momenter @ Bre dihned dn kos oh Ate Ad corctinetin, Ad remote, gral ems only. PLasakere, in gentoal, Qs Qu (ty dat) ) Pe FL typnny ty Mynny bat) ae tA MR tte caeeaspandirs, nist Hransfermakions Gus Au (Gpans $m 8), Fee bu (8 --, 80,0) Pd, * Le aloo agent fak, urdex ths keonshormetion, (6s ‘byes ek: Mea Lapoorgels apn BOM Go permet Wyant Page Keane fatwakins abe duktrd over Lhe em Riyaretion er Space + Howell's (yerersting bancktns » 8 Tha yarcahin hcl coeediretin (4,04) Ord fe nate Ress taecdavakty (8), -., Bu) eriein begotten th € vanish ab Ate Sed painter of dee pth + hee can ums tine a Fonction FSR (4, oy, Ji,-1Ba,t), Neh, sakes lien 6 af Ab acs SLAC, Bian 4m 69 20. Then ua an gerry Me eps Repannrett on frmacbeamale, beans Farwntios oF tr ¥ FH (CRD ft), lak ah 4 ‘ = PTE RA KORA, Lat.) +48] HF = + ple thea hiya ann generally rhakel 6, ofr Pd. (Bade) = LRG MHP) + » Recechs Ona enn glen tak, Fav afte caromest bransfarmeton, yeh, Tarkon, Te HBG) > T Rd RBG # SFG RK © = z RAH KS Ot 4 a t E 3B 4 a4 4,) # Raciting a ohare ayantn td doflennkil fan % 7 a Tey Head) > Fuge (2, gt) + ot ak i wT CR ty * 4 43,) aoe Noe Kuokey BOE ay wndeprrdsne Varohdes, We gob o-/(2 Ras -(% Gist GB, BA fat ayers? e294) 2 HCE 8 + 28 Tl he bento 6 (4,84) 6 collet fe _serarntory Fonetom 6 fa cararteal boars fycmekton * Hens, be can see Mak OF Rb net an expgital Candin & boty & (48), Mx vodms ch Kb Ue sewn on Het of H, te Ahan @ pas peck pens ylase. — * Buk, cngernt, tthe walinn We lango Heo Le Horns dependant caretel farnstormetions changer den OT awe © Hime he dotekm ft. rypsed CT than ke gerarwbing Fanckro, bs gh % Oi) tmshonet Meo weep rstioos ke be ld morak eaisg wt . ; 7 we (4ainr? (2), Fron tana getshins one bas Ae ndbet Gee th'S by algehose rartyotohim, so Atak gts ana res exprised Go Sie GAG. ThA K pisaila pecrune bem: becouse UU AM vamubles AR pen vanctelher Lyensformattons aan trweakible,, ee ee Bes of Me da exec diretny fd wes oid Bye. han tesa, Lah oh As aor negrinsd equations fx fix OT 2 08 ens bonrkid. (2) toa ene Ler Ge Ailue fla seumd goomp af MN intiperdint egpoticors ke te wee seam le. afi Re - (Se, sx ™ (48+), Ard substi fee UL B= Gi (4, bt) Aor are fatetnee Geom (\) te adh ot Meme @, aqatins tn oven Ay oblite Ri RlEbAD. Sq ok delim, Ah meri waeelR an fe Fane, Lions te tte LA earidrohio, Ad women, ond fiw &. CH) Le tevenre Keamscarrebons MU git Rk (894) Ona 4,2 4.(9, 7,4) (ec) now Gere! e(Q,8, 4) crm PEER H(G BIT ER by Sob stitwtag old pls oma t's 0 fonctions FO, Pt, Excrye! Uk » z Hecrrete, GUE ane H = be ie rk ary fankin | ad timg 6G Geo, bp: Bs Ie stg * jeden e 2 ae Te aKn§ > ee Orn = yim Pome 72 Sa Breen Et) I” r coree (fee! x) 2 SE a cone hts! (SEA4)} 2 Jie z ~% Ue & a apf Ay] dake Fe pt > [Luneeg tow (SEAN = ee Pe re Memes , © = Filres ob Ji knet tht dew SB (Bue) = EE ae) From 2)! a v )e née 5 7 — leg AF 8 9 teeny , ecacching he PG), ma Las Bre tute 4) tn toms £EQ) Foe Ha Kast enysessiony © bre Mie Leet, -~ pe ~t a JE Ele ¥) OA feom Cre peed any aSRon oe bet Ju 4 2 Amd. ee ce e (+ aat§) a pts TRE 2 JG? eda wd 2M Ce)entg sec"G alee Qa 2% ong we Pye, = Be kan = j= IEe eg Ang, “eae Fond ee ke dn tein resi erty Gee " sat &,9)- . Thans| Hes, F han rit exyticttly ba dependant fens, B itBeta} K(9,0) = H (609,90, 269,21) > KL, 8) = [en it 88)" | Rent resngy : Les Qeeastg + & PE 0158 > JR@e) og + 4 Jk ee) sg ea] K(Qe)> J&P Det com nde [Ek (He ostginad Han Ueto. Wd Gere iand © gpadotie te bah god he Tuk AB bres formed tars lincen Be Lyear te Bad Pedugerdort of G. tat lone 4 opis C5056 dave Ke: > q: Sia (ey sts (Ja** x) er A ter (tut+ f) . hea eet bet tae AER ined endstion tte fe otetn te gewely flnctin Fp when te CT agin: fh) Tack Oe frosfimiins 6.2 G. (4,8) of BalG bY bs dha Be (88+) ot Le (6, 60) (2) Elirirekt alk b's Fron me above Aarons forre Done eand alin rearranging gob gbtie =F (4, 4,4). Semi lend, Apa fplne Ha Kronsfoimetioms ard elim wake ahh O,'5 $0 Fak rows akiten npeoe racvargonek, ana obteins P.= halt, Gt). (3) nests tone wanly obGonds anysersems fe Reh (440 ak CeO 4G) bn Be PDEs PCO) > FE ond BCL Bt 2 “8 he respectively, fletasteme ond inttgicke both a PDF. Te Lersgt one WAAL gle Sad seluton 5G (4, 8,4) BE ONL om thagse- Fron umsbonk trem ward ® be o function st Gis ant &. Seem Loovy dx second md AM abor gh gle Fi. (4, 84) auth o emstent functin ot gh Gls. Teas temtegtabins er panleble with Sool Suctlte Cambtretions ok 22a bier Gre eelutins mud give fe R(4,8,4)- (49,4) & dbbarsd, K can le doteten four Hl empties (BBA) > (ho t+ a (4) Ores F Examnds, le Ps 2 sen G> dn (SSP), P= TeeY, ard HE Eat he’, FOB) re (ge) 22 _ ~ g =m(¥) a pe swi(weUr S FaB)= Seilee§) ap ? , (sectxde = xsucle adie + C ELD Sek ne aed aw des eo dy aAp eed Flaps gS (oet« ole eee -e4 [xsstx ae) e428 + ,(Q) 2 AGG) ce 9 L128 sot (428) +Ji-¢ ‘at let 2 gov! (229) rend Spates +409) fle offen seletim P= quky > - 28) ably floskeae, Pe ek [51/ 425)] = ~2, Leseysed) ee $ Soot + 9(4)] avicte e ge Le Aine - Se ge grer8 ey ~~ =e ee es » <8 re 2 - $&a qreh _ Ah 7 ee ey a o(8) = ors zo - [A 4,9) = goe(4e9) * eo nre ? wie 28) rene 28, Beer =? (ee§) qs e7h Roe et Soars ane 2 5) = se tect 4 (er8- —e) © Okan Cot &: gensekery fanebaons | 5 Soins, te Cosme Fe 4 PRA) y mare teh Gay, Bug SS Ova can emsbinl © fron F by me beans fermabting (4,84) = £4, 90) a+ P@ Eh Fon T vada Wats £6.48, Kak + dF, > TR dB Kae + : -a(& 4) afi a& 2LaeG edk + E nf 40,7 Mie, -Z3 We - Zz at, the Zz Qdt, — Kalk + = 2h i ag CR, Ree be ebor, “ get Qo =e 2h us keh. Fe a * A? ae u 0% 46/2 Hed) Ah > Strchenky, Le Lae RG@hU= ean -F ay 3 bey a f.(B 84) = Ce, 94) - Teh rE Ry , 3 GGG + T ede ee a = F(4,80 - Tak > We Tis yah: a 25 ee he G4 2B a Beene? h. By 3 2 Far Ge ist sek & ~~ a= 8 a = Bi aie, we gtk m 27h 2 2 (R)2- 2% BB. Gd OO a [aay = - 7% au Oa j eb Strilely, Grom Be ot eck & polees : oF Cron te te set ot oaleters Me Aika eA, OK : sad form fe i sok ch 3 2s) use 38. oe an dem reed rates, Whi Similan pulebins cov one F,, Fi, Herd ghee 28 pest Le fear Harmanbyrtod privicle UAE edt, ant (4,208) —> (nib, + Pees 2 Phare hast @Finn epattons cor ler on Mancalls nobobin in Eagradeprarns > Flare fon eqpetios aon spmrsio te ark ann Setally (ndleper dark & Hantlteten and Els (kel Zsa. A finthen teresting poet & thak fae oh Ala Farwn C002, fe Frersfetvad Hortttrtan Koy suhebd & the valine & fhe Ad forarlinds Ho by « sintlan bslion, ee, Bee H+ Be , bel, 2,3,4- © Condes brs warrenty > Meaning: d edt, sora Bot tain Me plese epeess (4 b).e4 (9,7). Us (a, (42) 128,108 09) a @ ter, Was) a! (g, te, RLY) 2 msde Be be fsb ntetom! Zhden - Bi he ts ee = Z Oa, (6 9, tek +46 (4,80) ) @ dy, sd ARLS ore vortekatin A 4, oad By bn nn dA ide akyed +, AraD, Man da, 84, ort 44> 654, Ls thes gob T (Pe Stu — BEG) = AF (4,00) = palek Ader kech of exock difherertrak, Fea, ge olga ee > tenets Fors wach mulatem Fk > -& = ges Me eg dttien & er Ate cha® anctt dofhewertial , becarar tye bres attek of art 5 2 Sy 7%, a BA Hae dy oom gene oo & perfec Ai fhmtal SS Silent, He te hep Btw pancelt’s aghokions ge Bae vores pes fed dattesetitn ey Sint Wh Ehe 4gSre.t PES ashing O05 ° Properties of conmicch trans Feerratins | (1) Aha debirtinat of Ae Te Tacub icon of be canonical thomstee eke 4 wraby, Q> Q(t BX) od Me wlth t); k=l,2,-— Tawyaige = ven Bet Buca pt, oo Ba) mea % oy, ac) Be. a n TT amag, da = aN 4g oe > DEL bee it kei beams Fas rekicen - Fovn3)> 6.82) = gtsee +) 2 we noial (2) MUL carenteol diansformetons pes & Np. Thana foce, am ee tie she ta lrg edt ti cts seheshy bbe btlansy. (6) Tha Rarity trensbeoration (4, b)9(8)P) 4 CT an (8 a) "( “ye! wm OP ot 4 Op Fee tht teentGrnetion, 12 Lace Ay lnne fi (4,2) = mh - 8:6) @: 2h - Poe a > oe ch (b) Teo eanorresl Loans Crmnatins parbosmad wn & SHtymtnes carvespod KS a sing ct (lov) Lee §= §(8,74), BrP(a, Pt) os gc hU4btl, prP(t bt) 1G WA 04 Rand Ber Kies $e, He cam 0S AFOEA)= FRI 4. 34.) (4, 8,6) = E St — 7.54.) Adelony thse bie, we get Aa(P+r) = Ths, — %.39,) g (ce) Dh Te trove sj or a rtm CT exists and ts 2, aeten, & GGptrot Ui bo Bh CT, fin MG more ch fas tnshoometion gag (B,BtIOd P=FGEH) ents by and te careetent: (A) The CTs penromad in epdin (Er) Cz mrA Cy (Kreg) aR 5 Jateak (085 orale) . © Som exomrplar & CTs - 36 24, ; (0) FC4,G,%) = Ets, Th gles AT er) Hy, @: 8 2 - waa TR quin & an tebinesting enangic. Ma tHe, meme ane canes walin Vane gi suited Hain roby angler, affin Ate fears Farm Eun. 6) Eylecdad pointe Keensfeemibns oe te garonl na Cts, - Gye tal, 1804) | Qra-nr : ontinded P Lake op tension FB ZL, f (tyes tub P. Then % We a = Oh, tee 8) Tem & onky satistgtey = pated egpsarmende of PT Buk Me dtr exprassion 9 . wet > [he ah ‘ “Ft wee C- 2tP 4 a at wi eat dere tier DA one a) Peow, tte Frans Frvrmetion mee on extunded PT. Q) Gravege byes Cor medeon ok Ate eluckroregratie potatos Z NE petintech + RUA) Sokon 9 5 Bt) Ris) + PE(SAD Rive) > REA) 2 at(RA) pk er a A) bans eh oobitraml cenen seston d ast) tase (RY Curb. yt ee sobs (FR eaprok ons Sr Chee 0 gereebg froin RB — 2f(R) y e = abacdawm uarye ee) od (Fee) gehts fy Ate sare Magu 5 (88 = ps oF 2B =F B- eo THR a® =P +e Thy a aud js eR a get el oF Ta aH Hens rete ? af = jo (BG) = Ht? eH -e 5 Ne know tak Me carerceak werentinn, a = wt cmv teh TE de gouge, translarwelans @ careesped fi Ae carenteat Ko ansforwetions fer dhe nen canonteah yromavtan Boh agp Bre Th wee rash caceacpad fo mG +eH hak d bs jong agptentenk rae shee thn bon FlorAry troy | Pa Rr etheons wep +e 7h ane ee if arG + ek" ek 1 For AER Ba tdtintan ee Stee or woe a = = peo Leh - eit str “se(a- of sing tee 2 dnV ree! a Fn The nae cartetcad peter tna od 27YR ann fhe Jonge hearshoers hk A At eararnesl yrtrentinn aval O97, pespeckeal- lin shews dtak fe EM gouge banskatwstion can be weed as a CT. (4) fla LagSergien ganpe Aeansforretion + £'(4,9,¢) 214,40 4 ALLE) ae sidan « germokeg furor! F (4,2) = car if (E543 re % x ye A Hae om Bid § 0 Ke ned. o 4-2 ® oC 2e Hew, We ae figs ye bet AS kee flue beak fe pele womanly Paral He brent Ketan dokeirad vn CT ant Gh Ame cone as those expecked fogn Br (Ea nurs Lag targten fe yee aa. cy 28, Now, i & Be > e bo %, ( (4 + dt) t Bt4 5,(& \ Eire Bu ( oda # 2a > Ete ¥ 4) Rafter rst2, = Gy he T 4% aL Ee (n +H) samfl -¥ ae (Behe 1) 8 2 he of ok Lageattats ister, @) “AY pase skate ok asys tin w nepresentad up cundya peek ike ye Syne, wh ard stab pont Webel image dts ete shake wk hte systion ah any shen Aine deiDicacleeen dtts she ok ar Atm baw, Se acl Jakes in le plest span vtyealz dafimined by ath inshiel spat tm’ a Tle path tered by Ae (eo pesca tye poo ne Me phar Rnspisa an te soe Inacessdance wh fhe bea eedkym ob the oystin how cated bea} ectiey. Ms pa wed hy em ene beshertiry quer Heregh each yor pre fesacoyess oo Hnmnilin's: eqyectimn oh wits (ex Ae heen gnsalcanks otqpely. TF Supe de gee Bet ty, He 9 york Bak Me 6rd degre etter Bas (Ete) oc sent Ee pate gmege pend My. a Poe pos Pe ork we aint each dhe vacyvely. Than fore, be cas 509 Hak, Anodny [te Boxe UKont (ead teat tothe Ma gink Wo get? 0 he Ae. P Derg fe sare tinh, meiry Aton pot oe tie _pla, goo t I oe & ow deh eH paver + Tn dhe ered, He etic gers 8 Mpceny Abor Lamplartretinn 4 om be o? beemne Me pasttio Hen pike $ ino dafiwtees Cbs pen ees ak ke. e LE tee beep te eed ard ory + axbittartly Man Ge sob Ff oll po We chages of 2b dusing tate bite gir gsm 4 ayes 8 trans fremed ents held. 2h % tak anon inknil © epeere an om inh TA (tnkirnans) seyvente ct he CTs elt plese span ob vereldy smelr bhak each beans fatten tn We bee segpenes eee em tnkinttasteet drome” bn hone fle caer aboct duseibed wihin bite pase space in sel se eathad chs Seatsnel wetter. @® A imbrttestmel teams formations wotloty a shaft oy 420 Wales 2 eT feat conrecha ke exdlnttin pectin at to ites we AK ernneots dS onlie ck hs, eee divalin ard qraminka te Done he frthestmel ET (ze): Consider a ST gaverekea by FC 4,0) 2) = EP + 2U(G,?32), dle ghia can Finenernn pore rekn . fla Rest br nugsererks Ha rdw kgoms fromebion ion ed peer ae xh 4> x =4 tues fle Boenehrened capenteah coms divekin * an 2 ahs cy Be, bE 2 = Pat oF Qa) = B ¢~ 2 Ze aap Bers Deke (6,7) ¢ Ae H(t, BD — e9 44 (9,7) Trans frerset cancel teat diveh opts 0): gce) = ates 5 P(e) aps o dQ. 4? - 2h ae oe (depordones. oh 4,7 » 4) nat deatcet emdation glo) 2d ord Plo) = Pe Th vee sek fe a emtinnar Poranshin o> € (tie) 23) ben t& bat He em dbet Qe 2 od B= 2H fan fn / we (9,2) = W(G,P). TL cwggeste Hex Hoey Hama taeda [+ ane (german! A Berlin ae tht ‘Ces dnbenstintv srk Kop ee bee Sep ie (acaa), (4,2) = 4h + DELP) 4+ qi, ; 90) = 3 * et Fe = Ot ge arate & g(k+bt) Tn & ae encee pt O(DE). Semclanly, Ke aged > 2h ’ eh plat) > 2B = wr as BB = play — pat a par) = pias) + Pak & b(4+ 44) aad chee 12 (gle), 70) = bs (ater an), plete) The above ayotins shew Stak om tnfinitasinel dranye & bre by Bt dando pp fix ortetin we tin emsortie 9750 Keen = barat), od qe) fe git) > get Oh), cua pls) Be) = PATE, H (gto) b ve (geet) eH ( £terey), p(etay)). Since CTS ge essoeip tint a Alex pandas of tnftrttasimed Son eh oe ad canie aplied rnin ® te bs bon bee (mat), wre ARO fry pearak sh” G2 OF( fyb) and Pe P(Serbyt) from dx craton seman (Hey be) can be tegarded an & CT betveten fhe trotted aud Gera ehean dan, sey. from bee Co) fo (bh 8 Lek He darstes a sek oh ports ry plase- spect ee Vo) FO ak Lemme FH Doms the weterel ction oh plane spot [Pr sek gous wat AS Basak Me in a ben seinteorel f Mth vobne Vik). Laewseulls's beaeverm Ahan assets Hak vie) = vA Pec The keansrimetion Goren Me he Meh & CT wiht os ae anak seyrerer oh a LOT. ump ttitr coon [pe leserts [pak every Ct eveseteen valine. Cn plsssnopae (403 =1) pun coe quiks de goesk: Proea tonsegtion peorey ce Haretlbrtan Clets + Lak (4%) davde Some emmeearnerk exoedirekin tn Ate pee pe « Cangidan a chesed cunct (ere) 6 te fe er pret Pe “han Ata ade spin te esed herp C4 detoed pan se A= 2 A Pa 1 My 2 Eftine fErmed sear ThA suggests Bek fee aman AL te baeke gum oh oth Ge pecjetnd gevernd ontas on fia Camedivete flan dabred boy He cenjuget guise oh Ga, hd). & » Bary yeti on @ — ay | fom, aecetdomee Lh ie Mon! s Y seas ayo G, ha) yor a Se ie ul Single walmed : Useng Banclinl baton -§ ci ayr + Lares} =etert 6) Deters yoo | Ques nh = toete (00 hid Gasuys (uop r oh Ne} ) Rlysy > OR bs She Tages Charly « Hees co (eepp + Oy feed] +(e tod] =e (G) Lek Ae Hath) ot ECM ne ad be o debfee- eke Loot of My tn, —--) Ae Tan fF (s,- Ha) Y = © 2 Cush ey Sqmt chenenkery PBs: oe Pha dey = Le et 295 Lim b= Th wy Se > Gu tey =- 2p > {Ped = ae Tec Coniston comedivekin ft ted) {a= eu 96) (Be) = Apa ewe = ha So (Brsplrety why HW) i bee WY ae Fe Contagion eeegieth Ke cxey 5 Oe UR) => waht) od qe) Vie & (v4) ~ feeye z me ae 3) W os ER ab ny rs Ressem's Toren eee ee Ap weulv,44), oe _@k Ts we eee (od Reach lon fie au: “ak se ro ow ee 774 te wv 1s) % aA PH yp DA DR) 4 2+ TRB ROR) TR 75 (Be a 2 a 7 LCG 7 Gn, Fe) Fe = (MHD OTE ww a emsherk, ta BS co, ttm Be Cy pe B TE wens), om e — oe - ee ne te ah y ah. 2 TE us osany He camshntn ch ardtim of ary glen WAmrarmte systim, btm am B® Lu vy alee aemsbre of mikier. nek Cnanton A hws = Rew + Lota) Fem « eeronaly mantionad tdandaty B fasts LEE Od* 1 BE, fete ck Dacsot!? SAotily, bee. aro 4 funy = £4B wy + LRRD - Ed - Ks, uJ, 97 2 PBT turd, vy + foo olor) 2° o . {4°} (a 20 © Thin Manan Las podownd ayy rafieanen, oes dabiamindng, nae tanaka A wdtion, 8 Te shark oath, «of oe lemme hat ony Bee vrdagerlank const A watt, Aber og BR ind one com be eangtinetad From He 8 ot fane free © eth wee owe erdank & te te, TE a omen & HOt art ed frehy wtlio, euin vite ems fark ee Saom, (ralpe keeweelly alin of Je Fost am bre, pe ny wee eee po es OR, porerate out, ano Ten easton f * Ln fee thn Wiz, we mage geraroks oll He Lidolen ‘nitty ED wditon, 4 CLR dy rawtook shan est a @ncl) (dagen dank umsteys Efady ene Gunabrons wedi yout Awedrt Kine exglaty, AON DR can bert HR st chor, he cK (4) tly, rd ome emstare sh Aw isdttepte 2D hemes silchss + H dea bey) (beth tt b(xre7d yy const ch ee 5 Seen ben torn hee trl OM, pe angehen prone pergerdionten fe Ba xg pe Ly 2 #H — Tbe h alis emsesrtl ebxawys | ae, > Hey, He es titel ma tet teak Me HeredA rman LL eam be deempord whe eas dnd Ke hanreetc ascthetes lbs HW = & a thyh, Kem Tle ivdivtanel #M>Y Hy= By at H,- ant aloy cestank energy Fre tole fx, Otividienl aselbleter, Heres Uo Hy = tel be - bt) +H ke (xt~z) = Cor) A cy te thd emgfank of robe > lek pe emg ides a me cag tnt of meaty @ fm Lok wrtey Taetot. 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