s11_mthsc853_lecturenotes_07

s11_mthsc853_lecturenotes_07 - 7 Euckihfin sgmshgg', ’...

Info iconThis preview shows pages 1–18. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 18
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7 Euckihfin sgmshgg', ’ 634‘ Ash; A may 6F Edam axe—meg. (1)") "fix/raw LAM; Punish“ s+mdcw¢ m X LL a ml “Mm-M Ema“. 3pm, m 0 1m 2m mt“: Tu (“J-ea or xex, mm 11x”) (, m aw“ Rom Y O Oren/‘0‘ R3 "I’Li cram ‘H'xewem Hxll‘fiijh-dkfi‘ TIN (10+ [amid d: yd“ \‘3 (n9: >331. J'\ 1 am“), MIR-(H8- Sm. +Lq. 10+ peode r; gym-rm Lzlmew.’ (M) “55 t (’8 @409 0+ (w) T? “X’juz=UXHI~Z(x\3) + ’13“? Non fw flu; \‘sl («Wald wt chm a? mama raw,“ Pick ><I $0 ‘HNJ— )(2CIXI “gr 50M C}d‘ Pick XL so “H441 \jé Spa/\(XUXL) >< (M, 0,...,0) Q ‘ ‘ New W‘er +‘u Ellen/.3 firm/Uh: Wt dusk almw flu [Aw a; cosms: anazflgzl Za‘: Cos 0 ‘ TIM, " C5 NM in} 'H'u] (Lo'from, df yum—b) (Le) (LAJ'HL; amJ GAJLQX‘ We can Ags‘tnu} 1Lth. 0:99 A' Eucliw/x 3+‘rmc*w~e (A. A 11.190 viébr SP4“; C: 2M '33 tux CAMI: termini) w‘v‘c‘w U: « {yuan-(v.2 5:11AM QM wa+k +Le Must-WA WM? 141‘} (H320 WrH" "R: Xi‘O (l(posl‘+('./i+ .7 ' WE‘“ SL4»; M AK ac Eudihnh Rum kin/DU An l‘nMr {mach}. ABM/N. X U An {\‘Jl‘MA-Sibn—J NJ MNr seqm‘ thhu +‘« m a? HX L_j flxH='-()<,x)yl) RAJ 'H'w Al‘shAu L4+w~¢m 1,3 ex L3, HK-ju. Ttwmpem 7_ \ '. (Caugkj~g((l\waf?:)‘ gr" A“ y,“j(* XI, me é {lxu'fljW ’ Dag: mgu A Mm 6:fi2-~NZ, wk “X*£3”‘2>01. -—\ we Cm Nah. 3H) 1* Hx\]2+ Zt()<,fj)* Asmm 3?:0, P“). t ? ‘U‘wfi “9H1 . W: uxu‘: “ME MY =leui M; 7, o w MP MP W ' No’u ‘H’mi +Lq requ (s +mvcd hr 370‘ ' '1 Twaren' 9.7.1 HXH = WW { (yd): Mel} E xuaiu (NRA. Tharem 9,11 (TAW‘JL— bev‘A‘ol'f‘j). Fur a” $154 9W5“ é Pap Not. “H'Kd “)“juir “5432* 2(th)*u‘jul é w) + 2 (NH; nu T H j): 2" (6mg scam) ' : (MU MW- Q ng~ Two; “Cf”; )8ng am Orfkogorvj .«P (7c(j)_—'O. We, wriJu #6 as XLj. Qcflfil K i 'j, 41"“!!! “\LT SUE: (pjfl‘jgrnn fitmfm) E) M: A ‘onny fix) 3:" ~p0r. X [j ar+AOAdrM~0 A [3"‘7‘ Emlmchflhrx fffvxg'i'udr) ,‘f X03) : r 0 ' .--7~‘J ) J l I‘J ( [\(OI‘CM 1‘ (Gram\§c[v\m;¢( GM“ “A “PUHAU Lav“; .5! g . J "'l I A 7Lth {.5 a acfixononmfi Lari; SEN"? ifi- gr “(qua w. w mm m. mw.,.,.,m Wm M« +1», CLWLVV of Law main}! is (22E:~f(‘io\n~jml¢\f" [E] («C X), ’32“ \5 An a<+kmormo L5,“, 11% 19» av AevX/ «5% Wm 051x, 3;,» MoreMr H7 3:; 5J1 ) flw (my; 635m}, 9;} 61ka {A Wham .? 32x 7%“ (1,42:qu M it“ New ><-WZZ ><«-—~a(«u-..,«o, a;="(><,‘>§-) (5. 4“ ‘kfiomrpa‘gM M CRVNU m mm {new} 09 X m sad“ 40+ Freaks: 01?! (2'2 TLw-rem 313'; ENS “Mar Q‘MTTM 16X, CM L4 wri'f’él/x A} 900:0”) 1} gm 30S {EQLC‘ i i“ Lt Arx Or'f'k-oaormuo L413, «ml hi {of 955;). P“; 5 2 2 Lk 32k ‘ kt! ‘3'“, Ctm‘m‘ TLC” blurb. (E153 "69¢ *5 (j C(jrouér ‘_ '. Xha x: 3 M-ch! 0 cm (So Mvr‘p ‘4 if M . QM: is an Adojflwg I’M? LX1X"""? X.) X‘fl¥()‘/“B. [63 DE: (VF Y a SoJISP‘iUL A: 71¢ «Head/xi COQBQMIQL 01:- Y x3 kw {XGX1(X,5):0/Jv‘3e~§’}‘, ; flew/molt: 'A Sus'fmn 2‘) Iwc YL=§£FXH (1’3):0 ydcvg“ (Ada W Ad».er :‘Mtfmth X -l~——[:—’5¥-—>(xi-) ) - “ML It” WE art Sfihl/ M5 pvt ago L OCWJM 0F Y Y ‘ Til/tare“ par «(L3 SVJU’PALQ v or X, X = YQD y)me We [N‘s—e sh,» M 4% m3 XeX, We CM “M345 wah hwy, at"! 36V, gLFYi\ My gbwoh X,j+j1=3*ai) fligéy) vl)zlg\/.LI Tm 3-2:ji_chYnY‘L 2—.) 344$; ":> 0—13—23 3%): “3"?”L “:3 3‘5 Emma: (a 5? 32L kg ‘irx or’r‘womd’ 9456: of 5’. [J N.) J EKW 4m an 0r+LerflJ 194:0“ am “'1 x“ 0'? n k . N( y)" thJg. t ElaiXQ+ J I‘ Z Ojiitfl‘ffl‘L‘ D i=5.“ DC£; MAP Y } th‘f‘ji MD US A W "Hi. arf'ka’oA-‘fi 269%} (ITEM 04: x ,‘Afd TLloreM PY h “M”, 30111:!°fi_.dfl ("’5 Pi}: (32$.- EXQFCSSL. TNOIQM (J; a «VJ/age. TLQA > PVOQ : 1, NLt’fi 1 MIA g ‘X~j” '. ~ ' M wow ><~1=us—2\+a*) My» R3 ‘HxL pj‘H‘KJGFCfin Wren, “will: 5~£II1+34HL '1': minim/k1 wbe 2=\0_ (3 Now M“ X AM UK EA. Emhhm :pam} m1 A3X”—’M a / Lam MAP‘ WI; On TAM—“£3 4451 M wfflw X! AM “‘1 fiAJ WHLJ' ’H’V’S (M‘V‘CVUAI‘M, TIM. WWW/ulna 04: A my); (A -->X, We (VU +mfljpo£g a“: A adiow‘ a; A) Aeu‘QJ .Aéé. “"I\IN+I'QA‘. (A) (34 A (imLar Pic-q) Eudtl‘fifi SPQQTI F0? “’3 Kiel/{l > £(¥)=(AX, Uk> U A ("Mr RAN“ R3 Maren Em EON :jéx/ = (X, a) : (AX, (A). r WCtur AVA], 0“ “(M-3 fig, gr S‘OV‘WL RAC*!'W- A¥t HF") X7 ‘3 =Ay'u, Tkms/ M km. (x, Am) : (AN-u) Solar pmauJ m X ) Q Kai» {mid m U. E] w ' (i) (f A.rs=><~—vx m (z‘wr, “FM (A*3\)¥=A**K¥~ (m u: A:X—au’ azuflv mm, flu (CA\*:A‘(,*. (m MA:an H, w (A“Y‘=(A*)" (M W)": 4. PM... w xéX, Mu, VGV; (i) ((A+t3\x,u)-(Ax,u3+(um) a (x, Amwmm): (xlgflmuy / m (CAx,v)r(Ax,C*v):(xlA*C*\/), / (m 133 m w flu 2433 (3d 1%! TH: I =0¥VLY= AYA’T / (iv) (Anna, Ax)=(A¥u)x)r(u,/1“y>= (wam). / D )6 SJde Jru (may NM§CA-E~+im§ or A gm M erspm of «CL out“. Manama-,(“Lhfi WW" mama Fm «Mn-.4 “Jung In MIMI} Si'Em‘h‘mri wt +~° Sat-Mr aA. anh‘tcrmml Mafia/n 0 1r fibula—hm}! (we) A x z b) WLWQ A {S A“ m m Md?” M > A ) Y' (a 6 “2A- In , 'H—JJQ. if} M SOL-“+604 ‘ {EM‘NS Ceeitf +0 “96+ 'tpriM‘xJn‘oa“ £3 MM‘W‘EWU “AX‘SU Quark Sublq a rotu‘hm (‘5 u/waf oil-‘3 1“? T) 3:0 L w / LXCIw/u {f Y D a £053th RAJ A370] flvn ‘Ax =A(x+Lj> / Car 6M»: (LC («u Ian“ R j a NWUWC+ar 0‘F LE Therem (OI 6A I’UA “Mter I M 7 A] 0&8) “wwctdr [.3 (MA-VON} chw x M M,~Mm('t€S “ AX~ "S +(‘\L S‘OLA‘éiOA +0 A*A2 :A¥ 14qu (391$: S-‘LE l: Slwu “Hui AVA? =A¥$ Lu: 6\ unf‘bg, sd/ufi‘cm. mud} (${(+(dn S) TU 'H’h‘x LHUJ “HM. homey/1‘94; byuafiWA [309A '2 : 0 Lu“ a (AN‘IDL‘L Sd('/\ (he, DAL) {VA/"J Sara) . - _ w - 1 ' If A*A.j~0, +‘w 0~(AA3.®=(A19A3)*HA31/ =0 Tth {mph}? :0 =3 3 70‘ / N fLQA '2: miv‘iMin Rib-J.- Picg ken? Hamel jrx~2' Show ((Axvgli \‘5 Minimi'gazA “Lu 83:03. . S4221: cw; Mun? m «La pmperlcj flux A225 .1. RA, AX~B= A,(%+Z)~L :(A?-L)+ ) fikJ A24» masw WW :3 Hamil": 1m-.ul7‘+ (MW ' ,ertj) flu: is min/mgch {(3 1-0 ‘5) 5:0 ‘6 x *2, / 83d; SLW, +114)! (“a a WAG” 9: ga-Hsee; A¥A-%=A¥5. We 514M.” ‘H/uJ' (Ag-k, A33:0 5r «(I 36X- ?) (A"(,/.\2.~g)/33:0 Star a)! 35X. (3.3 aSSuAflL‘m; rmk A = A >5 Pan‘k qun . t) A¥M2~E):O 1) AA’A‘LTIPIL, f ‘ U [a TNOreM PY [5 +L\L OF‘HIOJOILJ Pnej*{(+(.dn OA+0 ‘szA pr : pf. priap: Exerciiz. mi; V Fun (+(‘0A M ; X fl X ‘3‘ 0d] (SON‘(‘F;‘ I I": C"— xlrje- X, Mom-MM)” : ‘ (“Bishnu * (mun/i3. 9) ELKG‘CQQI Ans +mqykfi+ifln M(7<}'=X+0\ (5 6m (SoM‘H‘J, Remark: G-iV‘EA «A3 (semifinal 0M Can Compose (4 Wi‘H'} a +mnsla4ion +0 an isomfrj “PM O‘ Can/{Hui} via/3 (So/MAT) an Si Maw mfio 0M “5% Fixes 0) guovwd. 5:3 in +FM5L4‘HOA‘ TIA-{OWN S& “A {So/Kl"??? Ci)”; 71M; M {s *iwr 0i) M*‘M=I (AMA (“whim m with M q «A {SGML/j) ((z‘v) ‘M {.3 inwr+,‘5le) and ("V! \S an (Kowq'f‘rJ. (iv) M M t :1. ' Damp: PmL Y, 3,? (E X a/LJ 5.3 (“I”): x') [Vufijdl’ ia‘ N-oJu. TL“! MFA“ : (+44 3:0). m we. km \[wihfiqh MHz—.113“) M.) t\><‘~3'li- ,...~.‘ (K—jfl. my 11%? ‘3(_x’,3')+\|jt1}‘:“xtj‘u‘”: ux—jlt‘zuxu~1(x,flAmi}? . . IE Tkis V sl'Hw; (ng) : (x1, 3'), 3,2 M (Myra-Cc (“Mr PFDOLMLG. Mm, sway hm. we‘u gm 2‘=><‘+a“ . I uguxuj'u“: uzluh ([5117;ugllll—z(2jx')— 203 9+ w; 3‘) (l2-x—jt(i Mn N 31/3 «xi/3w» WM) + 2m a) 3M M mum—e) new c; Mr pmplnc‘fi/ 1'?“X"3'-[1="241”:O => Z'—x‘r3‘=0. ‘ / (n) (M) = (m, M t (X, Wm) Tum, (y, M¥M3'j\) =0 Aous 1C” «H w Y/ am So MAP/“131:0” V (Note: QM» «La we; 7Q; ~H~¢ mam.) (m («Silvana—.0 1m“ ((xuco :) M u (\Avcr't'Q-(e ./ (1%“ a 414.43 M (jam—(73') (iv) gm, (W‘M‘vI/ (wwwm’q: 1‘. (qu 1%.; M~(W:MM1 «q 50 M‘Mz’il‘ / 5 Tu WNW NAME 04”» Tam“ 411 g, itkd «3 mp HMJ pruuwy Afghan» is limp ((\) axan FNMA/(J Lo?le “Alfie; Fma‘r d‘r fi/LJ VGLIAM, (}V\ . [1:73 mp; A. New +w WI 112“ 4:0 r9941! rsmmmuj c, ML” W1 ‘ » m armed m+~m (am. A) 13m a 4sz .mp MHMLLA—hm, C'o-JLJ «(km—MFAJ groth Judd WINK) Th MW “e m—nm ma Agawwfi 1' a, c4124 +u sag-J ar+ho§gw flow) 04mm soc“) Alp: A Mdny M is #1111130va NI: (Jr; Cab/ma; Nam ‘g/rm M 0r+wamJ 9/0” Piaf: Exam-LL (2(a)! M 1%. Mammal 1'; cm; m3 4:0 MLAS‘MN’ #4 “SQ-e“ (ff a ((‘MAr Mfl‘p from A Jpau X Mia film—Jr; Rod" I’W‘vv 44; Mr”? WAMM 5’74: 0F a Map 5:10; i; A W Euc,(1‘c1.on SP’Uflf/ 1%“ ohm w m J A +0 Lc ilAH=§w§quuzuyuu§ (Recall Sup (3 w, 0“ 14011,“ Bourke” a‘f a There/q 1 Ear“ AAJ HM." MJKP '- X """" W I E3] (3931: O) 33 ahcmrl'ion 01: NA”) "AEHéI‘AH‘HZ'H Cr a.“ W‘H’ mt“; éex‘ in fwd/w"? 24¢, Hem-l. NW “A?” 4W1“ : M Ac” -. Mime” < lk|~uMl~Hefl = UMHIZU/ (if) 3; m0f¢W7-2 (“5A”), "AXH‘WWfl/MV)=KVV‘(3 r3J MM», NAH=SMO{HA><I(= Mm} = yawn/xx, V3: u «41 =!, IM= 13} —~ WWW]: uvtl=rtxrt=l}./ 13 Thom/1 SM’pfoSl “WC M.) 'A,@3X"-rU, CSU‘HV. m M" =lt<l W a0 HA+8H£UAU+UBV (M "mu e “cu-w a» «Afll=HAH. P593: a) '1th SN? {Hg/Ml ziuxu—rl 2W WWW {Mr/3% M “@le = MAMA! g Mel! + UM, "W" ‘ Wuwuw (W '34 w {mm [a A! - (t vi! = ’ } 4 “PEN/1rth (“1143+ sea M! Ma} : «AN1-Val. «' ' (iii) B3 mm mm, HCAer((c((~[(Ast HclLHAlHlxIL mm W 9* wmmfl sofimlt» Va“. m mm / av) MN = 5m (w) = M r, AW) =~ w (W x)? NW, 0‘ X,ve\<_ / NW {Ade fume/Anny at ("a A Mr a“ WH \rCCfc Tho/{m 311;: Afxfix L24 ‘mV-gr‘HUq. gt/Lppak QIK'fi-X. M w WWW we "My TAM '1 c, MAM. pg“ch (if C‘A“E. rs = A -c A(I- NC): Mrs), Mm §= AZ If vafi‘nmj "(:0 314.9“, ‘H’MJ" IFS (‘3 t‘AVCV'fi'SQ‘ NI»$~ New, (l‘5)x?0 :9 Sx= x. =2 “Ella! KM [(SII=MA“C(/<((Ai'((-uc[/<1 ( a “MIC—TM: Pro-of 45mm) elm X< MI QM} 1+ also (MU) gr JAM X’OQ Sumo“ Inf): m1. pick O-¢X€ (fiACL K¢0>\ L J “mm/fig”) é 50 N émS I C .' Di A 5e0qu VF nmnkr) {at} Qflv-Lray ‘(Co (P \Mk~0\\-”O. W “3 131.2, “a “*- A “J “A”? SE”{§"“’"‘~~{ C" MARCIA lakvo‘flao (E "(AL “MAW; n-L 59531412, PAM/j WENAQ Murat; to a (mi "W M WW M “'50 mi u, emj [30W KbvchL—e Cof“£ah3‘ A Subwamaq ‘ GE; M pfo'urfie; Fran IMAM/(KI) {:9 waffles in 6x CFM‘JQV (AM/{A} MAJ gmclrha A‘ {/(Q, Dig—(L A WWM‘ or we“; I?“ R EucL(‘~*L¢.‘/g Sine WWr-gts +0 4 K Le? Xh : K) (E fl 0 / keno as ‘(Hoq A Sc?)qu {mg (5 o‘ CAME” £5 2“ h‘ H m— XJ-ll—r O a; Jy-a m- ' I+ (s Lamp.) ,( 1} MM (320, (lxkttsri Canal! k. We» 31,“; i X (4 &~ meée \(JcWASIUAJ Euch‘alun Effie: . ) CrAMJ/aj Ebouvtku “kitty; (he! (‘j ) WAC e a ca (5.4,, Ff ('3 Egéw/x'h‘é% Mai") Doc-oar: Nah gr Anj X:(Qw"’an)/ (g) (13 m ohcmflfmj [(bexflzé (“I‘d-“ailpa 0’ é) .xk—ax./.n{: M {x8 ea Lamw, wH‘L‘t lk-Xk‘flsk‘ TL“ {Owls- XkNS (Z, ‘9'“ a” 19 a? in; Q.» wL‘fl‘LL‘ {at TN; SALSC‘u-(Atl Cm‘bm, é :wbgLDu-enq {p k/krcln {0193641, 0”" 50 0Q \ 7‘4wa We CM CM+MIAL ta J} a Mubmi. for wkrcL CALL {make—say "M x :>(fia\J...,aA)_ 'L A z. » a. ' “XQJH : §«’Q“,J’QJ):0 "~”~“>' VXk’Q’V " ID flat/“Arc: we : Xfl 3 I'x'IZI} Lu4g,W\g‘H\[3 OWL, (+8 w mflwu: nxuw}: w a WWW m: (.uxhuq) firkw‘wh "Axkllfl “ML r23 Theorem-91¢», ‘+‘~s mm M 0L SALSIZ-(IWAM {X1933 +M-amvacyfi 750 San; x=(a“,...,an\\ Now! “Aefl f “gr aU uni—1‘ vtcéafz ee‘X‘ / Tfixe emery of More” QUL, U416 T rem 0x Ebmhdfioq» Sfau. X {(‘S $£BNA+iaLfij MAJ" +L\l/\ OQC‘AX<M. ’ Pcva£4 Samoa 01M th/ owl (5“ 35gb.” Ilse, am MEM'Q g9} a; -lIN&P5 imo‘l-epenobd' mafia“ Far QRCL!‘ L) M CA“ 0x ELDHAQ XLV‘VXn ‘6 OPonrMJ V‘CC'{‘0(3\ WL Ugf’v‘fl an (A l"\"'t( '90UV‘QAQ‘. 19, 43v We“ Ham-UL:ux.-Iliz(x,~,>s)+fl>s//"‘:2. Tkm {X13} nyb‘m sdsévwm, D Peg \F akin ><<oo, fl“ Axe/A .fl Aacan 43(— «U MK. Paar: Exact“ ‘ QCMAFQ" 72m) 014;; {tiff Llatrj [( X :50 ‘ ( Eu‘choléa 5+M‘Eufg; (4)“ X ox C'M‘b ~011‘WAVSI'IV‘,J Spflbcj Mr mam 7% mm- (MAMA M “(3):: X}-.- (Ax,u\>:()<l AK!) ,2“). 2+ ‘3 M (waif “hm/{wax ms, 2 am a (Any g aw, . I‘—" 30 A” {a Mdnxflgrm C; #1 @3214»: Caniut’qj‘? +F‘fl/IS&)€ 0“: A Oomph Eat/[50Lqu §+mc+yr¢ M (A WfLW \fed'or Spud. v; (Maw g3 A a; Sexifiremo’wj'j wa 629) 5(1ka Thai"? (L3) 1': alimen- anci'm day (:7 (Am!) .0") (Ta) = (w) , {Cot/"MW ’JMM‘W) (X! X) EM mu x¢_0 {flax-hvichs‘ VQQMKPk; 5Q~Qfif is LJWlQP’ " QHLV/ qt L‘; (A fl‘cu"l¢Nn-P Wanna-hum 01,: ()9 igr- «H y[J()<’ ...
View Full Document

Page1 / 18

s11_mthsc853_lecturenotes_07 - 7 Euckihfin sgmshgg', ’...

This preview shows document pages 1 - 18. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online