252_lec15 - 5F UL k») Note Title 2.45 151'- Croollm’c,...

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Unformatted text preview: 5F UL k») Note Title 2.45 151'- Croollm’c, Bluvsmco. and CUM. Tul— H [2/03, Luhure \S 59MB zoo? {LAN noktS] bQJ o?QJ‘o’D\' V1: T3— +" a. 4—?5 A. 3X 33 ‘32. — a umbr owl-{on (7qu Assume. .Q kw‘xce, dlccwxléokfio. Scab:- Qua ‘\‘= 3cm dafiumwm umbr (we $434; fist in Cma'm worm: 9E A 3i” 1; “ Crwm’c: %¢OA.§ = V? = 3x\+ Bub-*aeh —3 a 3?. EFL \B‘squamcti dim F "-' VLF -' 15¢ "' '33 “' 3% Curl (Lust E, = V" g T: a? 3’8 ‘2' ’éx ’33 é532: F. F7, F3 3% 93 9E Lofim A? ‘- V14: = 3;" * 33'“? be 6‘? c Lv‘mh (v‘ma + (6‘ F333; q Tudor No‘cohon and \)Q.cbr WVqu ”——————_'——_’———_—_— \AL Cam mes-2.85 fifgd,d)u) owl and ‘dfifl. Laflao‘uoa (“I-flex ) mko’a'on. ’“Aroufikout W‘s Smack, QSSuMn; Q (W‘mz) dL-“WKQIO\L qu Quads buSor W) in C‘ .-' Cu 5;- , 45 , .. dflzgzflnfia’ok, Scalar S-wds m .a com o S 76‘, ‘5," Consbm'c. umbrs ( A: g; ) a, \o, .. can.is scalars asswvxld .3 A E as (fir— Fo, QC»); = $6.; , Luv—.3.) 2.4L; Cpmuaflns '- ' Cgor-dino’oes (293,?) “A Lx”x-L)X3) i "wont v cu. a. 5) 3H“ ComPOfxm‘o a? dd cfvabr'. ‘-'- “ax.- \IW CW cart—Q 3 . ‘ W'We— 3L 4‘» /8x;, Cfibrwofion) i, = '91, 4" Ru“ cow’c cc dd vmbr Spanker (5‘ sOW‘L .lk Ks (97*wa £0 03;“ C.-fi_ 9"“ gr qumflika J; Nana Mack wuokm fifiififl?fifim =- 1:3 ' UNA: boss umkrs (T ‘ ’8 ) A (4%, I 22,) 3.33 3 ' Summob'on mmom‘cionfi sun cov- rtqcshzd induces 2‘» as F ‘ F: 6c, A 225 v : e’L 63‘; = e’v'éi; [KchaM Egg; '-'-‘ via; = VQC‘G "" Sq F‘C‘d LFXC)\. 7’ emu ch‘k. 1 Tensor mka’c'xom germ 9Q wax/kc? O?Qro.bbl'8 : 3i A) ‘33:; Cradlznk= Lax-0d = (v9\; = 3;} -= Q’L Burzrflmco.‘ d)“: a '2 9-? ’= 9;, FL 1' FM CucQ.‘- (Curt = (QXF>L '= 2%»; 36 Fk '= sukaA L-Qflaolmt A; = V11} : DLDLQ = £Ju 7_.L\§ \iubor Owomr Tdm’éfims: EC chum.) dLQQu—adfidéo. W {kids (5“;; “Ssh og an“ vs.“ £8 Chum.) dug-Moan. scakor gnu; be. Md on a £2344; swig o.,\o (gnaw SW; '3‘ (“wow “uh, Linwa‘. ® V(a§+b3) =aV§*\°V3 C23 V-(a? +b-a) = a0? n3va, Q) Vx (of: *5?) ‘= ane oovxt Product ru\0.8'- (Cnuokfing o. Scale-3‘ Qud (L9 V = + 3-9.4“:ng +3 3nd? © 7' 4' 6340323) ‘= C dzu'5.«'c’:..3rod$ ) © Vi 1 Qan-kvf—x-C: mrQCGEA=chrQa*3‘-od§xa Chain ruh. 1 dq, ® 91(4) coTév£—'—q}C4)V¥ ® ~q (4/3) = (gm-— {Neg/31 Eda/GEde Cnudoinj Smmd du‘NoXNLS ~. G) V" LV¥3 = 3 "er. 3,04 =3“ 0' (Vx 3‘) = O “ (in: euro. = 0“ (D V . (v.9 x V33 : 0 @ WLW?) - VCv-e) - v12 “mm mm 3,64 om More. PrOdAA-Ck. weaker 'xdm§-\:ie.s -. —\.q\o.c‘»on“ @ v. (6‘23 = Z. (we)- E-(vx‘c) @ Vx (E x?) =La-V)E -r (VI—'5.) ‘3 — (V535. @ <7 (-5 .2) = C6. ma + (6v) 7‘: +EXLVxZ)-rax(v><$) v. («CV3—3VQ = £v‘3—3 ‘71:“ @ VLMS} = £ V13 + 3V1: ZVPVS IdeH'z—S CnUO\O.V\3 the. -. 3 ® v ( \l—M“) = n mm” (Vi-ix) (Vaacvfiflk Pym) V- (i id = 3 @ w Gl— 7x) = 6 ® '\5- v (i— 713 = <3 @ vUi-i) = 71 2.45 Bum 05sz __o$} Voi~khlx_\$£_d®r: A __ J A A A A A A R. X = XCeI‘; (1'- x‘e\+x1e1ax3o3ax\*tfi+2h) =3 -.-_ XL 4’ @MPMthS a? figs'flfion. v0.9”. Note. -. “no, fidu— Coordfmahe. cams X, ,xmxs on. qudohk- =§ 3mg = 9:5 = 3L \ x, =6 3x; o c =\= Q a if = (xkxkjh' x; = >2 -—- (a; K K =\ VK= K ’— 1W3,MU\OQQJCOD K (5“- HQ Q’Momng- 1.20:) ) ' dm i = V i- ‘-= 3; 3 at)“ ‘= $1; =3 ’3 vi = 3 ' (Curl 1);: (VXR‘); 3' Zfik iv; Xk : £“y, = O 2. LP!- i 22:3! “225°; Emir _T_év;’i~’cig$ {m ALA-41 \. WEE: Grow a w + 533 = ms; ms WW 4.” SK“ " © '9' (OLE moi) '-‘- aV-e +bV-Z W‘H‘N Curl ‘- @ Vx (of: 4002) 7- on$ *va5 (Sec. 2. ?<'t>cQ~Lc,b KUAQS (wowaxs Scalar 569mg) "3-: :dwma a Cxod: @ VC£33 = H73 “iv; staccahgamajakswc b'“; '. © 49'6 t ELVQ- d‘w =4 d'uIZ-k ewe -. (9 fix (4%,) =§v><EJe vcxé “mm-Ame. , -\- firod£ x O “Na kw... cmmdoxdzj {an "(Lu crouan 9.9a.“ ck mus (3o: wens DC on». m}\0b\o_, as W ‘03 wfi‘oms M mtme out mmpnmwse (an. Aug. owned cumb) {3r YncPs) Usma ’omor m’cobon © . '3 -.-. . A = . 9-3 Q ’31 )\ DI Us“: ?r°d’w°k “At d (:3) — (—a;c; + 6:9;{1 *Kcor 3m?sz \l a a 'u '01. var. ' \'- '= Q Q-C. 4 C-V-Q Wihofifiwg 8% Moi—2.: m 6.4.5an (or va xnsfl. (perm £0:- dos-“>3 ) .5 4. 4% A 99 JAE at. '3 a; C-(VQ) ——- C-(|'ax+0‘-U+\vat)= (Sugx-vC‘Z 5E3+C3§1 I (2.3;; 3 9 1 _, = (Cu—334 + C1515 +Caae3¥ = (CuVH: =3 uz can hkvprzt as 0. SW dicewfiol operokur Q-v= C“; acct? +c. 9 = 5:3 =C.;9; 3* 3:; 9% Ex; 1.4% gCnco. =CE-V3(— ’ flat. zag‘rmss'uon CS W‘o\8uous \.q,. aw; ?oro.n'“A¢—S¢LS are. me. D C 115‘". 9% an,» , I 1.. '_‘ 6‘34“ 8:3 to.“ “33:35) (we «on. cram. (c. v)(—¢ch,)(-) .3 L39. bx’cvah as “GM. (Scalar) (>wa C-V 0.5% on QM Compme 5Q ’dno. Umbr $0M $1 (E'V e )I 1' ( "" c; = g; 3. Ku\0. '. o. abQQu-uh'obh. QMALROA oc- onq. ’— 5? SVOdJ-bm ® mam —— a; w = cum v; d? V -— ‘0 V ( = 3 ——‘:8—1& 3 (qluok‘mb rule.) (tn VC’K) 3 —VKE. = “)9?!- rs? - "' {(3 ) (Vt-045: w. Hal-e addik'omal 1,7.(93’8'3) [m “4.3 Idm‘olk'xbs {Ix\t0\\):n.3 Second Baluofiues (@Mbhmns of; 3.04) —— —‘ Aw and ova-9.) Curl and GD Vx (<7?) = E 040. (am; 43:3 B‘w WQ V- (Vxe) ‘-‘- O a.“ (curt-e3: 0 ® V- (XHL “733 = O Curl om ® Vx(vx$) = <7 (0-?) - <11? Cur‘LLwQ T5): and (AN 3) — LaQ\QdM(-‘E) r OW Second dnfiuakuej that m $062.: w and v- <7(— = <11; and (gmd&\=\—°9\ac$m Ch 0:06 am 9 — camp‘s be. ismpfiud Marisa, ® —\ .5 91¢. «aw-ms sxv-m Seam = 3:3,“ - _l 2m ’“AtsL \amfliu cu-o. Baud am ‘dno. J, Wad Smokdvodnr Posed dauoflues “or hbza. Con’chuousqj dsfluufickho. finch“) e12, Eras—9 ‘- DQVS , 466'” (TM, first Wm \dug’v'ms ®I®J ® “emu dame. ho d“. sum-33.53 under U‘kQS'O‘AOASQ- or: OyU‘a—br-S,md ’dan. afismz’cg as m cuss we“); x _ ) in M31 Eloimfi 21:1? 2.9% Ewfi‘fi‘ifi) “239-: = _ EM 339k; (éw’3moathi) = — eM may; (qwn 4 ww‘ Pom) I = _ aw“ 353v}; (wows; W3 j = —— [vxCVFflv 39’ c) [Vx (VD-3; = 0 J ‘u°\.7—~3 a V. (vx : o -k_(,\¢ wqgrsmcg 0Q ONJ OUQ IS 3130 '. C393. 253193265 $21382 welds?) (rwmber: "dzv Curo. =0“ , swabamm " [twain-.0“ _ Scalar bar\o. Produwcb “M937; [3,311.63—50) ? '- A _\ e92? V-Lva) 7— '3; (VX$): = 3; 6;“. ‘33 PM = 6;“, 3(339“ ‘- '- 65m. Pk c ‘— 63‘“, ck 3“ ‘ c " 36 (Qwafm) '— ’3; (Vx$)5 '- ’V‘&7X$) => vivwfl = o. a ‘2_.S'O @ vxklx '53 = vcvrri) —v°-$ (“wen Curt -— grad am a W\a.c}o:~“> “('0‘- Pmfi.’ 5“, H»: S Vagina: 0C 6&5 Rdom‘ékdg chsous‘lq. fl“, LoQ\c.cLon 0? o. vqibr £1945 was 0.4).: (kw Kn 3mm: 4; «mg mass 4 a“ vecbr an Cathef‘m wrathes. ms nub: ‘\d.u\’€\b\3 sues V1 ought“! £0 a uzcbor {:1on ".\;.o. to. Pflical (Vang; geodeid and urge“: can m be. “ma ho cit—9N2. “M- L99\0~€5-OA o“: 0- vLokY (lad in ‘5qu Coordinokz, Sai‘czmst .3 CpordImokLJ ‘Q’u dag$fi$m 0? “no. \,_oQ\O.:$-o'\ of; a x)er Raid F -. ‘l.-; a V F V(<7- ‘=> -' Vx = -mrqcmrfi) ll) —_ 5- Wow. §rodwab \)o..o\nr Tde’ckS (,M L‘Ffl ® V- ('5 xi) —-- Z-(Vxé) « icwa) @ vXcEx‘av = came 41am: + (9.5.)? -Lv.e)a © vCE-fi) = L‘é-m'c’. + ("a-v)? +EchxZ)+Exevx's‘) ® VUGQg’ 3V“ = 4-st —— 3V??? ® = ‘g V13 —\v SV-L-S— + ZV-G-‘VS Ida/$36.05 ® and ® Con‘oc- 415N126 'QQM *9» x)er \dm‘é’c‘xzs (Sun and PW: rum, and v”¥~<7-ch> 3, II ‘\ \ovk fine. cskku’ mu. CW2. no.) . ’“Aq, about ‘xdec‘xLS ®-® man quake. usui k0 Moniprohc More. chPYLn’ud 40.0%»- ogwgssbn; '2..S\ a5 0% ® " ’ [Vx (ax-2.)]; ‘- 66k 33 (“33k = 6:3; kékLM FLGM) cad/mo? et- 6‘5 t 6.6“- ele 3Q£F1 6Q Lace mm c (Scng'mgm Sm) ( F1359“ “ “"34?” = LQ.Z)C;—LF-V)Cc. flit-v»? aLv-vma = [ (Var: _ GENE +(Z-VVF— (Vail; c5 at 6) -. —'\\6 Rs M": c.\m.r Wé ‘co Foam—d .-. 1‘); Rs Qas‘xuk kc basin Om 4cm, das- oC— ® and sGw‘NCn: (flag .b = Gav) a; + (2;.v39; -\— [5x (fix—551; +£3><Cv><$fl§ ‘t €1ng (ekQM'BQI$M3 = 9966‘: +659“- :; + efiketmh (Fémcwarcéazcm) \\ 6T) 0.) 9 + .0 9(2) I!" + (g; 1 $0.." gins 'Q) 31 Grad—(:69! F...) n ‘P :5: ,0 A. j} in 4- g“ S” 60 l -n 0 (52.2. \w 5 sec “.4 4g;) ...
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252_lec15 - 5F UL k») Note Title 2.45 151'- Croollm’c,...

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