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ma100_note26 - /é-3 6 TOK ES 77124 Fem/é-E>r Rafifle...

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Unformatted text preview: /é-3 6 TOK ES 77124] Fem /é-E>r Rafifle Grimm (if mea: mg! 3m lags in _ -I. H The nrien'ted surface cr is = The Esjtlua direct-inn crf :1? Tha negatlue directinn of C baundefl by HE SJMDTE closed i relative in the urieniatiun of a". relaLI-u-E tn the silentaiien of a. curw: C. _Sfio keg WW 1:] Section 15.1 we defined flag curl of a memo: field FIX. 3n 2} = fix. 1!. zili + gix. in 2H + MI. 3', 2}]: 3.5- i j k 3i: 33. 33‘ Hi: 3g Hf) a a 3 IF: ——-_- —.__ - ___ k: _ _ _. 1 can (fly fiz)l+(flz fix jT 3: By 3:: By 32. U f a h but we did not ampt to give. a physical explanafiuu of its meaning at that time. The {allowing result. knnwn as Stakes" firearem {am biography an 1:. 1155]. will provide us With a physical interpretatiun of the curl in the context of fluid flow. I 15.8.1 "Emmi {.mim' Thalia“). later be a piecewixe 5mm oriented surface thin I is bounded by a Hawk, aimed. piscmise Smai'h curve C with pasirfue orientation. 15" - the roman-Bum of the usemrfieid FEI. Jr'. 1!} = fix. in 23” 4— air. )1. zillj +h {If y. 2}}: am'caniinuaus and haw.- caniinuauxfirsrpmiai derivatives on some open re: comminhg a. and if T is the unit tangent vector In C, than .T- . jfi F mi; -——.]}T:{EL-1rl..Fj-15}Iiiél :2: . $3.: -:'. , +. .' -'I _ E'Tais= _FE'PG’) 6% SE L76 72’ is {A m ~ 9 m 35 'fi’éfi. Wark 32:32. 7?? Mag SQ F? J}? 1%; Lime»? (la-ME C - /é* 3’41. f: = fr+jf+0§ En 3"?4LL. "F _" E 73%" 11L .3; = 33 3—05 a} '31 32: 3. ) E J M0 E at 3 a ”V U ‘ Fer“ C in )1 PEARL a'H CounTz/LCLZG fiCéWIE-E Jaflafih-L F“ :13 :9an 075:;a20f 31-, E'Z. =fiix z 57"" flfgfli‘ SMQtycfl-‘la MMMeag 50 (2.4ij ‘ :1} K ffil I?" 35' TIE:- VA 57 15m; sfecxiafi Cages I‘Msmtijfi 184% GT. {#823 COTE fmmjmzffizeeg £74 _%=2Cbfizfjj=2r5imf)»€=§ :35 52?? ~ F43": 35: zzaZx-rsxfl +943 C _ pz—o /,z"=o izmfi +ngjoéf+sy .zx’oéfi _ 2W 31"“ .3 _ ‘J‘ fifigppd‘ =££ 113:: 2&3‘6 r2{&n—L—)fi 2T? 2 xzf 0.05275 mf=gatfr 4,- ?” If E a —7}- —, -? —,r vx/Zzii A =£(5)+jrz)+hfs)=5£+§+3,g 371: a} 3,2, .22, 39:: gr} Lflww- ms = ffCW/EJ-F %?—Ejjf+‘fi)m l fids=—§—§*r£7m)ab4 (z /é—c?r%: C F'DEFE 14/ (mm; C. .33 #41; Aanmflw c; FAL ELM (L. on: m Z=j p/ma. f J '5’" L5" 2274c Fecfiigfit mcfas‘wz 453’ C. Pram v/Le. alduafivBU-L 53f C , 0" {15‘ fifbé-mfiaz aémvwfloz ’23:] _ ms=%?+%§ J $25824 =(\j —E)M .955 «:15 E” 2 03/4 Hi IQ. MW dawnwwtaf E- Figure 15.3.2 FfffVX?)-fj—§)dfl I S‘nzfiat-«L :héjfimi fl: 0&5" I 32:99:92: pfamfifirfl 33rd Jf‘ nil/q _ j? *3“ E s? | .___=, ‘3 'aJ L "r" 2—?" 3-? VXF: 35-2332. :ZZCjL—jdfl'4’jk ' x1 ‘99“; fix L : [affix/V »—f»+}3>‘<0«* “2*” M I gC—f—fiflM = fig—jtfljwdfl Figure 16.3.4 0'; : = mrfiFrP,)-E AWE) ( 7E Cm is afircla, of radiqs £1," . m \ . [ Figur: 16.3; G’Jc 0:5 ‘ | U}: ,9; 1/14; mcfa sax f/fli‘ 9&5 k, of firm 3TH} , ariwmzfzfim. I —.3'-' ' ‘H' _,., .55? “3 ’1’ ~ MrK/Zf/Da)*-Y§ iv___i?:m/: {032) Cad]: (Po) E = Am 66‘9“ Fifi mam 5:4an alwa- Area) ...
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