EE101 Vector Analysis Notes

EE101 Vector - AA'A CO5 aAB Scalmr‘(Ciafim‘hun 5 9A6 AA 9.Q;3‘5:1 Mzmzmm A Commmhd'we Loud\5_J A_s_A> Assoo‘m‘wt Laud,4(5 C f6 A C o

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Unformatted text preview: ) AA'A: CO5 aAB ? Scalmr‘ (Ciafim‘hun) 5 9A6 AA 9.Q:?.?;3‘5:1 Mzmzmm A ) Commmhd'we, Loud \5 _J A __s _/_A > Assoo‘m‘wt Laud ,4 .(5+C).: f6 +A C o Ved'e’r' Pro Aucf ) Ddt‘mef‘Bn ) Anh— Commut6~+we Laud P Dst‘fs‘bt/J'A‘I’WL Low] > UnnL V6057“ I‘n Cour'b/span QxQzfi 9x9 /\ QW=§><Y=§ —Zx? .4 +1 A IMAM fXE= 743M841?) :AAX Cabral? A :X Aa+¢ /\ 9x£=y x? =- o ' (er‘MJ l (L (/62?de U” V + f “N sszfp/r g 3 A Awh‘afl Cenjfl‘ x 3 g d2 : A I all ‘1' 9013 ‘1' 30% \/ e013!" dfy : 9 dXdé 0‘ 59 1 /3\ fix 0‘), Ved’ef ' D‘fiuwfi‘afl Volt/"'4 5 Q 01V: did)! d3 SCAIAI‘“ dv: rdrd¢dz ([5,.2/13r d2 r = r1 cylinder A /\ A r CF 3 r 4’ 3 ' dcfiMMHa/fl [ea/5+5 012: hr + $ MC? +3 0'3 V‘C‘L‘“ (19+ ; filamé VwL‘“S (\ 53—.- Mu— Mom Mesrnadc? veal” o DtfiWi—Dal. dgn: QRLSFnBa‘édCP . V IL“; 06% = §R5«‘n&o\m& QC (3%? : Q; R awe ~ OcHMe/«J’ML Valgtrng dV: R16;m&o\rdGo‘§ 364W ' Fasth‘m q /\ I9: R K 4 Va do r It‘th __\_A__, F : FQR):FC1)3,3) V: VLF): chl g scalar fincjfsn évmo‘t‘emL of {—T‘dd \/:_ VL?>: \/cx)g,3)’ 9 /\ 9 A3 éTraJl‘enT Ofe/rad’trr +535. +3.53- éerohe/n')’ 067005me (Sada; .; Vac-Farr) \/ Agv 3m; v: \7V%3°U=Q-§—%+Q ‘35 +33} L9 Vec‘hsr a AFpACCAhb’M 0+ firuh'wa afflafi‘sn .4 ‘3 4 (JUL: IQz "‘ RIA A : de+g A‘d,+ 9015 .4 01V: WE) ~VCE): Ve:7‘“o'r Vec‘hrr H3 E :_ ELK):— ECl/yl&) A flux clot/6033+ /E\ (Scalar) 42:61? 8‘ : E-QLS :9 /\ é (a? 2 ’1'” . DCVe/‘CIC’MQ. 0+ Vac‘lLo'r {1‘44 (De/ffv'oDh‘én) A? CINE: L AV—PO AV 4 .5 - .. SE + alsz .. V.E_§%+Wz I DeVMOre/nce. Wcofem .__x '.._> /\ jvxfi AU :: . Q5 } Volu me, [41% mg gthQ/Iflb/a ma Cu/FQ of Wm fee/4 5: BLZ):ch/g)5) .__\ '4 ' . Cl‘rwlah‘on : fig .019 1:412ij 5V” (19560! (bum/or ‘3__ I /\ ._..1 "1 CM” ‘ {616 7d“ BMW a 9.3m ma rule, 4 _\ Q Q 3 Carlie): VXB: _<_9__ ii W 3‘3 a; 3% 6)! 35’ Manh‘hes VXLK+T5):V><A+VXB v (vxfijzo VYCVU):O shim flowery) €wrfmcclm4’93mQ [AWL Ink/3% C \x 0M V‘Vr- ~13- 233 fiz + flgl‘n/flfiéf/Mfl .+ [Q / a‘l/ ‘J/LM 0‘ ’— 0 61+” 16 w A' A — Ax + My +5 A; :.-~—\ -‘ \7A =V(V\A)— W (in?) “ 112 GRADIENT, DIVERGENCE, CURL, & LAPLACI VV A8V+A3V+A3V :X——- __ z.— 8x yay Bz BAX 3A 3A V.A: +__y+ Z ax 8y az )2 $7 2 8 8 3 A 3A, 8A A BAX 8A A 8A 3AJr VxA: — — —— :x<——“———y +y — Z) z(——y— ) 8x dy 82 By 82 8z 8x 8x 8y Ax A, A a2v 32v 52v J g} V1/4 4,” + vzvz— — ‘ 5 8x2 + 8322 8Z2 X y / CYLINDRICAL COORDINATES (r,¢,z) VV_fav+(i)1av iav ‘ ar ra¢ az 1a 18A¢ BAZ V-A=—— A, —— r8r(r ) r8¢+8z a a» 2 1 a a a 1aA M A M M 1 a M, V A:— — — — =f — Z——‘E + ’— Z>+i—[—rA — ] X r ar a¢ az (r8¢ 8z> ¢<8z ar r 3r( ” a¢ A, rA¢ AZ 1a av 132v a2v V2V=-— — —— —- r8r(r8r>+r23¢>2+8Z2 SPHEFHCAL COORDINATES (R,0 1(1)) Aav A1av A 1 av VV_.R 9 8R+ R86+¢Rsin6 a¢ V A 1 8(R2A)+ 1 3(A 'na)+ 1 aA‘p . :—___ __ Sl __ RZaR R Rsinaaa " Rsina ad) Ii 6R $Rsina 1 a a a VXA: , -— _ __ R251n6 BR 86 8gb AR RAg (Rsin6)A¢ A 1 a . 8A9 A1 1 BAR a A1[a BAR] :11 ——A a——— 9— ——————RA +——RA ——— Rsin6|:89( $31“) a¢]+ R[sin6 a¢ aR( w] d’12 8R( 9) aa 1 a av 1 3 av 1 azv V2V=——— R2—— # '9_ _ R23R( aR>+R2sinaaa (5m 89)+R2sin263¢2 CATE’S‘IAN (fi‘ECTANGULAm EATORS (x1‘y12) (VX(VV)=O The, M of +Ae,jrml.‘en+ of any scab,» {/Je/¢ L‘S l‘clcmLL‘caQLj 5M0 Com/em». Shh/nod: If a Vedvyrfa‘eld (‘5 Cari—kw)+5eu\ Cf am 192, Ciprcssad as m cjmoléw’raf Sac/M {Mail 4 A Vanta'rtft‘eld E. Cf \7XE:O —9 E:_VV 1AM+I“’:Z H. iYW (VX f):o’ Tim J‘VQX‘F/Nfidf wrkafanf Ve,d1¢-f«‘e(4 1'5 IL&QMJFt(/4Q0j 319/‘0 Com/use SHE/med I! (M/Lckrr foe/[d c‘s defiMQ/(ess/ Hm» 82‘ cm [02/ awn/55w 0.5 HxLC/ML 01f mafia/r Vufiyf @‘6[& A W%fiflfl3cfv®=o—9B:mwf Haj/n $1493 A 70%” 1'5 Adam/Wad fl NI‘fA/‘q an Ad/clt‘wbve, (Earnsth (‘75 5°74) 3,745 dame/Ten“; and. U,an c,qu are sleazy/‘qu Mwm If WW}: and V XTAJa/re, £4a—kjn \7'x4sf,ce) _..L 4 _J chC/Z) J [o‘l’I/U 4550mm, £074; A and ,4; 9414*qu Agave, grAafiW .5 _l __\ ¥ .“1 V'A : V'Al : 7£,L() VX/r: VX/‘rl :— {LC/6) 77%” XX: 7. + AD ,1; Consyl'zlvflL Vic/77’ 7’5.” ...
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This note was uploaded on 12/14/2008 for the course EE 101 taught by Professor Williams during the Fall '07 term at UCLA.

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EE101 Vector - AA'A CO5 aAB Scalmr‘(Ciafim‘hun 5 9A6 AA 9.Q;3‘5:1 Mzmzmm A Commmhd'we Loud\5_J A_s_A> Assoo‘m‘wt Laud,4(5 C f6 A C o

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