Applied Analysis Ch1 - À ¿¾ ¼ §» º —„½Ž„§ 9¹...

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ƒ ¾ ð Ö ` Uf q ‘ tEB j T ‡ y HCBE Qf Bi yB ‡ øBt C B j `B ˜ — š žŸ ¡ Àë Ð Æ Åà GƒÃsÐGSÇsgÏ Õ Ø  XÚ t x yB` rB m `C a` B gfE Õ  y f ft x y C ‚ ’ c€gh#‰•fdrG—Fdhˆes™€Fe€g³ ‡ ° ° ’ ³ … E Q Ÿ ³ q ñ m x y C ’ ³ h ° ’³ ì ¤y’ewfv™Dˆu wì‹ D€Fgu™° ì ¤™ E Q Ÿ³ÿ ñ m yBa n q³h ewf9g™ôv wì‹ 5gci!€gu|° ì s¤™†Fwf™¤g¿v Sì‹ 0€€‰©D—fpshPER!g¤dPfVHewfxFC ° q³ E Q h³ ñ m B y B x B X ‚`t U ‰ t X H Q t m p  ¿ ` Bt E f` y C · B a` Q f ` y B T H q T f i B a` y f m y U` i y ‡Q C B y  B x B X ‚ t x U a` H x U ‹¡¡A€ï gsˆeG•I—PcGyFu•gDgPBcDFgcGDe•4FPfG‰€cwq€€‰©xwegc“PEcGVB©€PxDT Qf HCgf TBE B a`  j m `Bt E f` yC · B a` Qf y U`i ‡E t yfi B a` d U X H f t ˜ — š ž Ÿ ¡ IRIddDghDcGm•––‰GveG•I—pchuIbFPfG‰€Gh”`rF‰™ch9cPyYdPfVHec‰ 9ª—r'uS edeš ¢ B ´ — €F ì ¿ uF w‹ ¹ %£ ô 1 H C E f ‡1ŽiPHI¤ewQ ôä ®ì `C a` ai ‡t drGŽ“€si F wì‹ I— ® F Sì‹ g€g€eusrcsDYWtGpcG#€„¼ B ´ eVghs`Geƒq Qf Bi yB ‡ øBt j ‡t C U BEB a` ‚ ï B U Ut f Qf Bi yB ‡ øBt d Ut CBEiB x  yC E Q ‚ yB a` ‚ Bi yB ‡ øBt j ‡t  ai ‡ C · C t C a F U `C a` B gfE Ig€g€eusDcPyseph‰u©Ž#I¤ewfcpcGcF‰rgc•pG€cGŽ#“€F—T¤F€Y GSì‹ VQdrGxFdhˆÕ z}Vy4g€gc•us~tƒD "wì‹ gVBv€FYF‰e€GmPihGgD'tr™ ¹ m§ ‹ g¦ 9ª—r'uS edeš ¢ § U Bi yB ‡ øBt C B j F ` H x y C ‚ Bi C qt UE`B T C B j ¿ `B “ ˜ — š ž Ÿ ¡  § Q f `Bt j ‡t xBt Hi C U X U H y f x yC U B` H q T fi U ¿ ’eF¤‰G€cGŽus•Vfg{Pt’sQ9PceŽrI|sQqGgVB€{e‰¤Wt— ¹ wX ‹ `C a` B gfE Õ  § ò X x yC ‚BiC qt UE`B T B` H q T fi C B j ¿ `B € ˜ — š ž Ÿ ¡ I€GDedGuÖz–¸‰€I|FgF€GPihGg{ŽGgVBcDe‰tpƒ! ¹ m§ ‹ g¦ Cª—r'uS edeš ¢ ´ « « û ã µ Ÿ³þ¯ â x HCi U H ‡tBE U a d™{‰V­³ ‘#4gleGpPBVHFgYWtYs`cGphYWtcin mì¹ö lì ñ ì % !y¿ w‹l…! S‹o ¹ !¿ w‹ ¹ u S‹  o l¿ ì y U`i y Q B a` EB Ut yf ·  á ß eVfhl€€w‡qcG—gcPxG€FwR‘¤ànÞ  o Ið ì ewf˜ï ˆ Sì‹ Ipi ‹ l EQ ñ  óm EQ ñ  DIð ì ewfx|ˆ Sì‹ rj ‹ ó ô  ô ï  FS— wì‹ U{eC ‹ `Ca º drG` ai ‡t ¾ “€G7„¼ ¾ º ‰eVfhl€cw‡u€ec#Vyhee‰{iPtvGpcG—drGòdc#uD“e’I€Go“€s©eVpFPgG`  y U`i y Q t ‡ f ‡ U` y fi C U BEB a` `C a` Xf a ˆ  l ò m `C a` ai ‡t ‚ HB U „ i B q t B E ¾F Q f t ` B t j ‡ t y B q f x y C x B t H i B E l x y C m ` C a ` B t f q q ‡ i ˜ — š ž Ÿ  ¡ ‰pƒsuGƒ‚ F uIhgs€€smpre4€Ipus•Vfg˜GFC €I¬Rd€hs•r€c#ˆ 9ª—r'uS edeš ¢ `iC q T fi U BiC qt `i C q Tfi C Qf `Bt j ‡t xBt Hi C `C a` B gfE Õ  xB x y ‡f p‰F€De‰YWtvgF€G¤le€DF‰D|IY‰G€cGpGePf‰™¤d€hedGulfpc€cFƒj x y C xBt Hi U Bi C qt UE`B T C Qf `Bt j ‡t `i C q T fi EB gB `C a` B gfE W ˜ — š ž Ÿ ¡ €F~pGePf‰{PtŽ‰e€sŽPihGgDmI{‰G€cG{‰F€DFg¢hgeg{d€hDFdhˆÕ Cª—r'uS edeš ¢  y U`i y Q ` yC`t y fi C U  yB a` p FPfG‰€cw‡i•Ihs€e‰D¤Wt4FgchYU° ì T3 ° VHFoFwf'ï m Sì‹ ¨EVQodrGmg€©u|{‰hd“cÅ m€s·dd˜Ih™’chvpPBVHFgŽPtoV`cGph9Wtcin HC E Q ñ ñ  U `C a` Bi ‡ xB š  «­¯¸­ ® ­ û´n µ´­ « B a` x HCi U H ‡tBE U a % ¨©3  p ‹ FÝ ‹ ñ Gˆ©3 ‹   ‰p ‹    ñ  `C a` ai ‡t p ° Ý ° 3 C U BEB a` `C a` BgfE q yB a I€GŽ“€Gx“1T†¤WtqGpcGYI€GxFdhcpg€G` ‚ p¿ U j U`yBEB U x x yC p¿ yf t ‡f ‡ U`yfi U ¼ p¿  0 ˜ — š žŸ ¡ l‰Tr3 ‹ Py{VBHcFPCh•ghgyœQ©¢€F|T!ƒ3 ÿ Fx€ec#Vyhee‰Wt€¾ ˆ!Tƒ3 ÿ º ’…Q‚ Dª—r'uS edeš ¢  ñ ñ  yB a` ` cï u Sì‹ ¨Fg€G©‚ ì IC T U T f T U rC T HCi H C tC a x y `C H j U` yBEB U x U  U `C a` B gfE Õ  c‡VTcPyUDwEe¬c‡˜PT©d™yIg©Pf!—F€o€IC ì dqVBcFPCh•ghgyœQ©iWt2VQ—I€GiedGuvpi ‹  cï7ñ ì dCY€efc#Vyh`•F‰¤FcYWtveVghddPgGp©!cGYcc{7ñ ì IqPBcFPChepGpƒQ ©YWtU ` t ‡ ‡ U yfi `f y U B U`C UEB x B a` ` ‡ j ï `C H j U` yBEB U x % 6ï ñ ì sQU ïdñ ¿cï ‘ì sQU ‡8 ì ™7$VyGt 8 ì eˆ Sì‹  ³Û U Vñ Ü y U`i y Q B a` `C a` Xf a ˆ  eVfhl€cw‡q€GYdrG7d€#4rj ‹  ì dY€‡ec#VyUheye‰iYtW4Fg€Gc‚ ì dVB€IWCG•ghgyœQc¤Ptm'VQ¤drG¤edGuveC ‹ `C t f ‡ ` f U  yB a` `C H j U` yBEB U x U  U `C a` B gfE Õ  Ð ÇÈÏÎ Ã ÅÌ Ë ÊÉÈ Äà s…ÉugY…ÊiƒÍlˆiIl—VǃÆWÅG! Áë `B p‰Gt xBt Hi C U a qCE U qB t U U H yf x yC U t ‡f ‡ U` yf U TBt EB X H U y U`i y Q C `C a` BgfE pGePf‰DYWtocFheVd€gihV`eVQ9PcFo€I|VQwrFc#PyG•FgPiDgGig—dVfiWtpFPfGlrcw‡!¤I€GFdhˆÕ %# ì  l$ w‹ “î p © 4…pi p ¿ S‹ —‡cpB ¾ » § ð ì ! ñ Uq  Qf a qCEd B a` Bgf jC H `C a` t` U f q Qf d U` Ut y fi ¾ § Qf `Bt j ‡t B a` U  Q f U q º 2IŽcI“FqchedrF!VBPUYd€h—h•PyFƒeIDcPyGsWts€e‰”Ž» eI¤gsrcsch—Ptm2F4‡€gB 0 ˜ — š ž Ÿ  ¡ Å ÷ ´¯ ° ÷­ B a n  § ` Bt C y f y U` i y ‡Q x B H C g H C BE C B j ¾ ¼ 6“GIsúy…o€i¦z¤‰G{pFpeVfhl€cw9pcP‡Id…s„Fph{!r”„½§ º 3g¦ 6¨§r'uSedeš ¢  `B t ‡ f ‡ U` y f U TBt EB X H è `C a` BgfE p€ec#Vyhee‰WiDgGipwdPfYWtU ‹I€GFdhˆÕ %  ˜¿ ì ¨x‰ S‹  ‹ Py{7u w‹ ‹ UTñ ì è j ¾ ¼ #7„ק º €jc€‰xlugƒ˜c#y è By B š EB j T‡  ˜— š žŸ ¡ HFph9qWtU ­€F€ec#Vyhee‰WiDgGxg—dPfxWt8¾ ¼ § º XI€G˜s•r€c#ˆ c¨§r'uS edeš ¢ CBE C ˜ x yC t ‡ f ‡ U` y f U TBt EB X H U  `C a` Bt f q q ‡  y U` HBE Bi y HC U ‡ øB yC U h  TBE fB a n Qf Qf fE q B a` U xB y B x tBi yB ‡ øB eVfhdWCghvg€gPBIdPgc•pI¤Wt˜yÑF pGegci¦IeF#Gc€GVyuc€‰cYp‰rgc•pGt  ai ‡C · yBB `B j y U` HBE B a` `C a` Xf a ˆ tBtt Hi Bi y HC U ‡ øB ` U U x Qf y U y ‡ •“rI—‘pg—”X‰ƒ‘5FPfGIPCpG{chvI€G8d€#qppGhFWC‰D‰€pVBFPgc•pq•Vye”fwkWt©wFteVfc€9C fh•Vym2rFPfGV`GGI€v…GIª‚F€•p¦F¦•Vye”fwkWt©ˆg€GV`guhIRpGhFWC‰i‰€pVBFPgc•pv—”XRI€GˆFdhˆÕ ` U ç t y U U`EC q ft HC ‡ øB Ef ` U U x EB a UB BEC tBtt Hi Bi y HC U ‡ øB f ` `C a` BgfE % #p l™”E3 © F‰Ôñ s m ç ð p!  j ç ð 3 a U X xB` Ui ftt m tt Hi Bi y HC U ‡ øB B a` B y B •zF9`GV`Y9uGIPCg#GhFC s •hFWC‰g€gPBIdPgc•pchqc€‰xš Ö 3 t Hq U Ö p xyC p 3  dU0•pPBVU€{PTvU(€Ix%0vpi ‹ ó3 p t Hq U p 3  ƒ”(3uVBPUcDVT%0srj ‹ ó3 3  ƒÀ0veC ‹ B gC a B X ‚ ç ð Ö¿p¿ 3 HC E Q U µ ® û­¯ ­± µ û´ ° ·ü º e€qw©Yxyd!ƒ–VHF¤Fwf€”‚sQmIS¸ª°IV´gGhy‰P­dd¨n©‰“­ yC x HCi U ç Qf t` Uf q yBB `B j y U` HBE ‘ `Bt C B j ç `B § ˜ — š ž Ÿ ¡ F}pPBVHFgoWt¬EF9h•PyFƒ7gpw”Xgr×GeVfhdWCgh½›u‰G’bƒ¬‰g¦ G¨§r'uS edeš ¢ % FÇ Gì æ  5 ¬å¬ Ç 35 yF Ð Ð • • ñ FÇ Gì æ ¥ 5 ¬å¬ ¤F 5 Ç Ð Ð • • 5 ¤F 5 Ç ¬¬ `C a` BgfE I€GFdhˆÕ % ’ ° FÇ ”™«” Gì ” Ð Ð •• `C a` ai ‡t § U Bi yB ‡ øB d€ho“rs„pVyq‰rgc•pGt xB rB x U H j ‡ f x C U F Ç x yC ‚ Bi C qt ai C yC Ú C U § `C a` Bt f q q ‡ — ˜ — š ž Ÿ ¡ u#g©€Py9PccFc{YWt— GSì‹ rIcFgF€GŽ“e€Ii†YWtפdrGvs•r€c#ˆ f¨§r'uS edeš ¢ tBdEBg y fi t UEBt ` yB dEBg yfi HB` Hft jC EBgB U H yf x yC U BiC q guFhgF#e‰YpPBhgG—•geGpF#FgoVpG©P‡FG€F9GpFg¦VQoPcFŽ€I|VQvgF€Gt aiC yC Ú C § `C a` BgfE Õ  ¾ U B HCg B U y  C f` tB dEBg yfi F “FrIir˜PtU !d€hFdhˆ)—~VyDcP‡IdDGV`c€Ž4GpeGpF#Fg{” Gì ” Ï VQxr‰•ªúgGd“± U ® µ­ ¯­n µ¸ ýþgƒ­©ý·dg‰yWtU 4PyU F ì Ï pPBGps€Ye‰FrsFpcPyPUppDGec™˜ƒj g¦ c¨§r'uS edeš ¢ û ® û¸³b´ § t UEBt ‘  Bi C qt E CB H xB TE f y C B § `B — ˜ — š ž Ÿ ¡ ­³´± ° ®³ ã °n­ ² B a` x HCi tB U`B T ft U a qCE ‰g“GŒ¯I…´l!³ yŒûpAFoch9uVBPHIpYpDPTG‰Des¤Wto€I“Fd th…`™€IS¸ª°gƒ©“¤I…¸rdˆ¤chmuVBPHIp!Pt'eVfhl€cw‡vWtÿ ci9€¬ wì‹ P5€IC ¢12ð ì hgegB ‚  µ ®± µ ·¶ ¯ ® µ´ q B a` x HCi U y U`i y Q U a n  ï ñ ñ m x y m p ¾ EBg `I9VB€IWCG•ghgyœQc!PtU jdrGFdhˆ­—¾ w€@cï º 6eVfhl€cw‡vrFc#PyG•Fg9c•Pøc€pmG` C H j U` yBEB U x m `C a` BgfE Õ  ¼ ¿ m y U`i y Q t ‡f ‡ U` yfi B ‡ U y ‡ C f Ð Æ Åà GƒÃsÐGSÇsgÏ Õ ë lë  ¼Št }’ 4ieC ì ¼ F ì `C a` BgfE Õ I€G!FdhˆP U H B T C t B a ` t C a B i y B ‡ ø B t j ‡ t ` y B d E B g y f i  E B g B ` C a ` ` E B q f E q B a ì s`DPTVU{DIh{€GF€‰€pc•pG€cGepFhge•e‰4hgFpxI€G”GgƒFhc€G` a U X B C qt UE`B T `i C q T fi C U Bi yB ‡ øBt C U hs`YŽ‰iFrsŽPihGg{{le€DF‰t2Py9‰€pc•pGt{Pt˜ F wì‹ I€Gos•r€c#ˆ G¨§r'uS edeš ¢ `C a` Bt f q q ‡ € ˜ — š ž Ÿ ¡ B gfE q U x Ef BgfE Õ ì T ‡ T  FedG€sWt©¤FxFdhˆzD€˜€©PyU t U U C `C y U`i y Q ai ‡t EB gB tB f  ¾ ð í HC E Q ï î  í ë `C a` Bt f q q ‡ hV`}VyFh`sI7FfPG‰€cw‡v“€G2hgFp9u•xš —‘€G¿ ì PHIFwf¢×bcs¿ wì‹ Ed€h4s•r€c#ˆ i ˜— š žŸ ¡ ppPBcFPChIdgiIuBG¢w”X`xIòFPfG‰€cw‡—IWCDFc#PFƒ¢pƒ–¾ ¼ 8 ¾ º Xg¦ c¨§r'uS edeš ¢ t H j UEC HC E f Qf y U`i y Q H U Tf y Hf q C B j ë `B  T ‡ T U t U t U C``C x yC X HB j T f Q xB x y ‡ f j U  yB a` ‚ B UiEB f pc˜€cVyY“s`irVyFhsIŽrI8dVfpr–eGwEŽu©€ceriWtmFpcG•FeVgghp#‰i x C t‡f‡ `yf U TB EB X U €yFY€F€•PyUG•e‰iW{pst¤pwdPfHYWt•¾ ¼ ¾ º &VQd€hedGu’”Y wì‹ apPBVUcDPT€Uq” ì ”  U `C a` B gfE Õ  ˜ î  t Hq U ê î `C a ai ‡t I€G`b“€Gpï µ ê5FPtU™hgB€G`Žï µ F ­#I!ewfqd€hv€Iu{'eVfhs`©rF‰WtchFPGV`‰WiPUc©|† yC BE a ˜  yC E Q `C a` t yCB T y U U x yfi U a` ‚ H U H q r é 7é …  F‰'F ‹ %’ñì ÀSˆ S‹  • ¹VTPUH W ˜— š žŸ ¡ sQ˜¨ngGgp“˜Wt7¾ ¼ F ¾ º FFPfG‰€cw‡•‘ G¨§r'uS edeš ¢ U ­ °±¯­¸± U  y U`i y Q Ð ÇÈÏÎ Ã ÅÌ Ë ÊÉÈ Äà s…ÉugY…ÊiƒÍlˆiIl—VǃÆWÅG!  eë ...
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This note was uploaded on 03/23/2012 for the course AMATH 567 taught by Professor A.g during the Fall '11 term at University of Washington.

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