{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ass3sol - (3 CENTRE R DE RECHERCHES M MATHEMATIQUES Mam no...

Info iconThis preview shows pages 1–15. 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 Document Right 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 Document Right 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 Document Right 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 Document Right 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 Document Right 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 Document Right 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 Document Right Arrow Icon
Background image of page 14
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (3 CENTRE R DE RECHERCHES M MATHEMATIQUES Mam no , Ema: Zo\o Assigmwflz 3 Sokwkcwg (A+BT: AT-t-ET O-ALL RAY: CAT G {a «LL «Am-Mu; A oucL 6 (LA «LL Salas c. Nob. 4w: «gaucw A 496 as “it mu shut (CA? = (1* AT 3 Mt CAT . ‘ 10 wt A3002 , AAZU, A3472) wk Army- was :5 (x was 4 m vtdwsm AK m. me. '5 \ "KL “493th umSuJfi/us JN‘MSPos'xJKM is “A Smut. (ATV " A Fe»? Mn Ma‘knc A 464. Makm KFKSMK ‘wawostkm Must 31w -\0 +49. toknfiflkj {MA s£ aims '\ ® SW AFA‘ ) AI=A AI=A1 MAI=AM® O O l 0 -OOO I O O l 0 O O 0 “‘3 www.crm. umontreal.ca c CENTRE R DE RECHERCHES M MATHEMATIQUES m (Msiw 0. 30° Mkdoduuisz rthoSsA 1A R3 MOM "\La 1-0945. ULAAQJ’ +£st fimsRmkm) I 0 (“1(0) {——5 at: Kl) ’ o O o -\ ° asij—s-e‘: o cud. 2.1: o O O l o 4 $.14. MM): MPKSMEoAx'v-c is [2 = \ 0 o o 36 FM ex ‘100 MKdodeisz rota-KM oJcouJ: Xxms, e‘e—ue‘ ‘ (av—72.3 we). a '50 M mk‘m reprcSukkoe Ks R a m" H." a M w. crm.umontrea1.ca C CENTRE R DE RECHERCHES M MATHEMATIQUES 203 1% $050st $L1- ,X , 78 ,‘X‘, S is “Man [AJAPWE EA P \oo—cmse Q°i+ a‘xle «111+ 413L3+'“ = 0 => a°=a\=a,_=q3= = 0. LL W WS 943%in (S me, 0.1L *8 memo‘uh cue mo.® DA 1h 0% M, mufi Fo\jmial Lam be mug as CL “Mo: mkimk‘m c\, h . Basis thunk 0&3 duh/1k H , So Kl: is wéddfl o. sPuw‘Afl at. @ A il’QL‘XIIX'Sj-us 3S a “451$ 4 P. “'3‘; S 0‘”) K3 Loi Pvflfl: n“, so PA {5 Km vx-{k bust; dun/LE, M, +54 \szad Husk-(Mafia P93 \---9 [3‘ (sq has 1:“ \——5 “Pa-\- TLo. PCPI‘CSfl-Akhti Wkly (5 W541 m MFA/(Ca. McJNIX O 0... 0 o 2. O“- D' o o o 3... - o o oo.-; A c\ “M VMSWKM pCfl l—-§ xphd is “mu becama 0) 1(9ng + W” = mm + WM Ma “Mums = a<prdj IE films P“ Jro PMH So \Es KPKSM'Hki Mcdfix (X www.crm.umontreal.ca C CENTRE R DE RECHERCHES M MATHEMATIQUES DM RPKSQA*S Wlkphxnfl ‘03 7L‘ 'RM-A {alt-£43 {LA doxhaVei PCO r——-> jig—C(ufitfl. MD (twinks kalulna “We OLLF‘LUQKM‘ KM WH‘Pkfil'fi k3 9L3 PQA \-~§ 7L. %(P(x\\ , G) 3 Snug Prom “it (Kw-cs us %(XPL~Q\ *- PU.) 4' Ki: PLX at 30; «but BM-MB mat cut as 9&0 l—é PQO. 9:) DM1”M1D WA; mvmsm’: m Huxfifw’m’h‘ea 1mm“: pm E3 ( \AA’; (38‘ PM)» - 7L1 2%: P(3t\ '— 2.7L FHA . Sim, Wk “fluid \‘5 mama/Jack \mj 2M , we @ch 'VwJC DW—M‘D = 2M. Q 00900 0000 0000 $20020 1000.. 00:30 0 7. 'L 1. 0300-" 0\o¢> .. co - M-gé?°° MDM’MD-oo‘ec‘“ “007.0 .. . 0005‘ 0003 vi | . .O ' uh ' I" I 'o '. t = 2M . Q www.crm.umontreal.ca (3 CENTRE R DE RECHERCHES M MATHEMATIQUES (3 (ANN “s SPMMA b3 Hu. (,o‘mns <%)‘(%))(i>s(%)~ MEL Wu art o‘ouiomfifi \{N‘Mki fadLPmoGAh. IA fapt‘ my; w\ms 5PM flu. “MAL weds! 59m. “(cm (”.45. 5% Lemma“ («W D3 = ‘3 mans 1A; \386 = 5(ng {Monk}! awaken} ouoo tuck W; ODE \MA 0. SoKwKM 5‘9: Lu-er5 Pohsmwicl bbd (35¢ :S M M‘RAulxuqu-Qx . \uJ (BX wfléSprLS *0 Fatwa-«axial; Je-r which 34;?(fl1-0. “MM PEG wk \oL Ox msbwt‘ Wu. 0. w\¥\PKL 0’3, Ks—L Rrgk \oos‘xs vedrw [3° (-0 '- 1. WWW G) M rMh-ALXLU‘Ls {Law «39216; M «4me + awmm = 1% “k wKu-wxs “’a D, W D ‘S k Mm’hfix. Rue, J4M(w\(\3)\=°°, 34M(\w(o\\-.\ m +m #a} (Jams 53 D :3 ea. CL oo+\:oo‘ ‘ ox m muck ls \u‘nok rX kn. "‘ \6 www.crm.umontreal.ca (3 CENTRE R DE RECHERCHES M MATHEMATIQUES l .7305 OH. ham?“ «5ch ht (o) aAA (:X M Out “M3 M‘. © ‘03 Two m-wo wmswak «Ants on alums (MML3 {AAAPmoLmt (PIONA~1A LukucQ‘ So 'HLL Mk3 loophh {S {*3 (Art 6M- 03 M be 130‘. Tait-e. (:3 04d (:3« G) c.) In R3 at CM dunk 1 . ‘ ‘ L J L (I.\‘I\X(\,'\,°\=“‘ ‘\=(‘,‘ ”A. \ -\ Sim—L ‘Kq H'KwAMJ (JG-MPW 5% SPMKU.\I‘3,(',",°\X MS dims'lm \ ) it {8 SpamucL k3 Cl \ "fl. 1%. MM»: {3 SPmi(‘.','Z\-g . © M \' 00 Saw. mm :5 gauged 1.0 \kaL we, my: my; xelwm, Ba {ASPLCXM (64‘ Lalwicu‘naa\ ,x=(2,-\’o\ w?“ all). ® ] SiuCAcJMS, LOKAX _.L 104(AT\\ So h‘q Lsé‘UJ(AT\. €st “SPAM (a Manny \3-U‘\l-l) an a. Q) 1\ Quit (HAW 416. “my“ 1me o. Ma’NIx 0.3 mm (MA mw-mcluui Q \ 1|) <\ t \ \v -—-——3 \‘2. '5 w 011.3 ‘ u made JR whawai MFW QM moo 3pm, wkid" (s ‘K-L [WM/k. Note. ma km: ’2. Ru VoJloJoLQS 3L3 cwi 1Q. x3=\ , aL‘fio =5 11} '2’L3’Mq=’1 MA X“‘X1'7‘1'°(‘(= ‘x‘ X's-‘0‘ I“ =\ =) XI: ‘11-7LL( :—3 MA X‘ =’7~1'x-S‘Xq = 2 . “x4. We NWSM USMPW {s SPM§(‘\‘2)‘,O\)(21'3.Q,‘\-§ @ www.crm.umontreal.ca C CENTRE R DE RECHERCHES M MATHEMATIQUES U50. Lewd OJSO Molu. HMS 45¢ (0&1me 6% & mlw‘nc 04¢ ‘9Adx cx has“ $4 J44. LLQE-WML: \ l ( l r3 2n \ \ a l 1- k ‘ . . l 7. (A O | ____5 O l ”JAB \‘e I H tie-H o 3 oo 1b. ‘3th 46*“ row-recmdéw MaAV'cLu is ‘ 1 1 fi \ ‘ t -7. l \ ' l 7‘ l -2‘ 3 ‘r l ‘ ‘ -l I 7. -'s o \ ’ m we. 1;}. Kn. 3w Basis 0.x leek! H QLLOU. flak m row 59w MA. KL (uni are N‘ngw LGMQLWES Slum, UIZ.\\‘(O‘0'S\:3’ we @1me («cw-c WAC- mm m comm: mm A, C7,) “03 “\kuz = fivkw‘v+w3 = (vyb + (Viwfi + (NIV5 + (wlw‘) \M‘ \uxxwu"s 6) = (vlv>+ (may) i? (v‘ws = (N‘v‘) = 0. b3 1% (leV-t-w)‘: 0 MA <v,v>+<v,m-<w,v>—<w,w>= 03 So <v,v>—<w,w3 :0, (new. \lv\\1—.\\w\\1' 0AA l\v\\=\w\l. (“at <\I,w>=<w,v> Low +64 3AM: pmduu’i {36:11.} @ W c) “Hafiz + “ac-3W = (XWQH‘A) + <x’3~x'$> : (1,30 + (/1737 + (247 + (3,3 > + (>917 4%? ~(W+ (it : ’NxUz + N3“? 6) www.crm.umontreal.ca c CENTRE R DE RECHERCHES M MATHEMATIQUES = lbs—“1 + (5L(\35 + (330+ “319' s \M‘ + “um“ + uguuxu + uja‘ = M“ + 2 “mg“ + “3“" = (“Ml + “3“?" ® ‘01 'Ku. Camel/t3— Sduuuz ch‘mUH \<x,\1>\~< “AMEN. S'mu. \lX+~3\\ MA “34““le wt Mupsswlls w-Maeéx'we‘ Luz CM bin. 'KAL 31w: ME ’to ay’t “1+3“ s M +13“, 6) as merit-«5.. Sch 1*} P is a Pfi‘dfim: 1-9 is also a Pmdzédm Rama 6) (EMU 1*—P*-I-P MCL (1-931:I-29+P‘=1-zv+P-—1-P. Bui, W 3L6 lurQPM (I-P\x=x-Pag=x—O=x_. swag, '1? 3e me So \if-Px rot Same. x, : (14333 = 3-Pt3 -: Fag—Pix. = Px—P-x.=0. Thug I-P WMIoA-es w\(P\ cuxcL (Mimic/Es who MICK“. Sum UMM MA \uJQM on amamx Myhnmbs (mKW‘lbwGi ‘Kais aLLScs-Kbcs M ac’n'm $5 I“? em a}; utdfi's. lo, P Pmizd's 54d» \I'= mKP) News 1‘? pm‘sedfs Mk) RIG” =\/'\ www.crm.umontreal.ca C CENTRE R DE RECHERCHES M MATHEMATIQUES b» I? Shimmy-g is M‘Vumuwl w‘cfln WiS?MA~i/\% whagmi Po'buKS-«S PUMP M h Pix = <Vl$1>vi° MM RP. 3L = P‘ <v- 3L) V- = (V- :0 P‘W' \. _\ '~ J‘ 3 5‘ ‘ 5 7 (VS'K><VL‘\’:X» Vi. = O (‘-#J\ BLLMSE. (V'HVjV 7- O. . 2 S-‘mu. «~13 \m\As (9: went) x , P193 = O . q I; P‘ ML PL M amawa. PacSackRms Law Page, PIP‘ : {P593 - (my = 0* - 0 Q Mel. Pfi-PL {s cm why/ml ijadu’m Bo‘ Q (My: PT+Pf = mp,“ (Pfipg‘fi Pf+f4fl+ 4&9: = amt, <L\ I; {V\,...,V“’X {s M Mammal may we EM 3L1<VH>L)\I\+ ...+ (V |X>V = PV +...+ P V k: alL 1. P+m+Pn=1 as requixd. ® a\ "Q E amok 91 M WM‘KA3 afimgmak MSZLHNS‘ ’(kux mm" = a: 9’: = 919‘ = RR MA (3913‘: mm: PEP: = mu® (mm—Pm" = 93914939" .-. 3+9; P\P,_ @oui (WE-PPS = (mm ~(P\+?1\P\PL- PlPIQWePQ + (9‘90” = FT+W+P§-BX-%- Pin-Xi + 3er www.crm.umontreal.ca : P\ 4, P2. .. PIP'L ‘ m 66%- m Pmiukmg ‘ c CENTRE R DE RECHERCHES M MATHEMATIQUES 00 Eo.‘ LEE. qfl'r-V‘AN‘“ = \J\ =< \ [email protected] @ l LLE' $1 = V1: <°\v\\V1»q/1=Ko»_ 0 an ._._ £25 MJ‘ $1.: at: “$1“=(:) m «awn-«we» (MA 6&3: “AMA“ = Q33 .\ (/7, {yfimqflfl is M HWNWA M . ,. . MAC: 6% (R1. wwwmfi QR ‘ Atwpoy \xea \s o o \ D o l i O A -. o \ \ : (o l o)(o l \ o \ \go o ¢>® recall-KM: M R..-. (V‘V‘) ¥m LS3 (McL R" =0 o’ckuwlsc\. Q Lg: l l ( A= Z -\ Md. k= 2 , -z N 1 TM. base-Saws Souk“ {~o Ax1‘6 (S ’fLo. SOMKM 6% ATAR=ATB (W‘kflM-L as HoA MS “MAKES («JLPMJ-Mt Loth}. “*1 .2. fig :1) :C‘i \1)©ATE=(: 1 fiGj-(zj). 3° w (aw-w). @ ‘ '5 i=(%:)<;‘5=(;- ( www. crm.umontrea1.ca C R M CENTRE DE RECHERCHES MATHEMATIQUES MA; = NH ‘ 3 3).. (”‘3 7+3 1/3): _ 5/3) _ _ S/q u. (j S"? 3C. = '6 1/5? 4/51? ‘ ‘ o ‘9 7L: 0 . \ M0“ V1,: 3). Ml -( I; (191+ ME A: .OR m LUtS'Ef $61me SOMKSA {S M 0%. n _ 1 =3 RTQTGR§L= RTQTQ» =3 Rx=QT(‘>‘ \ l (D ® I . n 1.-.;0: SM (2Khi\ dx =S L-———-——-. 008““va 6.x = [39: ——__S‘A(L+EAX\1° : 32—) Item“1 = 3; cos (Zmfl TL:— Wmsurel ) www.crm.umontreal.ca o 'L 7— 8M - (* ”3““! 3 K SMOKING ' t &x S; ——7f—m:&*:[24- Qm~ ] 11‘ <:> émxf—fs Mbflms’coii C CENTRE R DE RECHERCHES M MATHEMATIQUES l b\ (SNHSW3 = Jo SKA brand $~\A(21U\SL3 ASL tog—.3 [‘05 (2“ (M “N 3d" cosh“ (mm 301i; - l [ Sm (2119» «\\ 5Q _ Sm (mum 1L\ 1 o 7- 2w («a-M 7.1: («4+va 0 ® (cmshv = 50 ms Chum) s‘m (Zwmd Ax 1‘ So [an kzmmmad - s‘m (kW-«0&1 (ix _l (.03 (21tkMM‘7L3 _ L08 (2th» «310 1 7mm— 2mm. ”“1 (“M ® \ (CMICA) = 5 0050‘“st cbguwwfl A»; o l = :‘i 30 [MS (2I(M:H\\X3 'l' Log (ZEQM-IOXSI it i sin (21t(wev\\ fl sin (21: («a-«dad ‘ E Ztr(mv\3 + er («m0 1° (“Hf A ’ Mm * o) @ Note. M W M+A=O Fu- (co’to> wMJ/x we, km DJWCOAAfl WAQQRA. Sikédaflsa, if M=(\‘ UK M Muk& <S‘A'SW7 MA (CmC-n>- It WM: (3ng R duck (MUG I l (CMS‘AV = 3 (Amman) $.\A(2RAOL\ d.>L = {S SKA (Quad ix 0 ‘ O =-u~°sa::wxo -— 0 ® www.crm.umontreal.ca c CENTRE R DE RECHERCHES M MATHEMATIQUES Ms {#1, (1M MA s).A are Mwémallfl e—rmjwd. pm H‘ffiomum 3d: Is WM 3“ch M {1 , I? $1A(2n3L\,E¢oS(Z-nx\\y’3 mom» ‘ Ewscqm , ’3 Q) (w: WMLL‘ISI 'nw. SA mi C“ wiik nzW . c_\ Lté _ 2w EF O$x£ll . . SBA ~ { 2-21 W . VlS 3L$ (1 . (LAMA’J‘ PU‘OA‘tmufl“ M, ”SWW3 M cur orW-bhwmol $0.}: is an Nfiww‘ual {443‘}: I ll-L . \ <C°,§) = S 1' §(*\ 6a. ' S 27L 43!. + J (2'213 AX O zll'l. 10' t ”z \ \ ® =[*L*1w-n.,[1=n*1"“‘+n=z, 1. H HOS“ ’57 = 3:3? Sin£21tn7d SEA Ax = EU 7. ( SiA (21m X) 21 JUL 4* 5" SM ('1me ("blah I _ -cos(21mx\ ”1- "9. - (2 A 7' -2Yz‘[ [at 2““ L —S° $4“ -oos(21mu\ I ‘ - cos (Zn-nag) + [W3 TL; 5.,1 2m "“ “I 2 (£3 . "7. . l : 2Y5 _l (9 I Sm VIKING] _|_ LOS 1C _ $M(2nnx\ 1[ 7' 2““ + E leznl o + 1/. 2m [ ("tr-WCL t/ = E'FiT[ sin (M0 + $iA (A101 : O , owi www.crm.umontreal.ca c CENTRE R DE RECHERCHES M MATHEMATIQUES \ a“; > = FPS «mum 5am on U7. \ =2E{ jg x. wSQmwAlfi S” tU-uA cos (zwfl 4x2 ‘1 1 = Sin(2mx\ 1'_ '11 smhnmfi Zfié [3L Ztm 10 So T A L AUX-U 3a Smf’th-Mdlo 1 + L: SMZQVVMO (”.3 \l m « L M _ _ -Los(Zme\ 2 -u>S fluid] 3 -2fii [ Quint 10 +1: Lnt‘aL ML =Zfii wstfl — \ - Los(21m\ + cos (Md-g Quint Ié Mu: {oflows W §= (c°,§>co + :[(Si‘5 §>fis +<rc 9pc M u §(7L\ = 1-7. + Z E<§TCM§7 wsutnad “H u = t‘ Z; 3—? 103(21th ‘ Catlin“ 1: ® .0le . : -;—_ - Z, -—l+—§{-T 605(211 (ZNAML) . «:0 (DH It Hog‘lufi, 'Kuls Mix a& calculu awoL Kw 01321957: {5 mum/‘3. Wt PM: Sow “pu’n‘ol Sum” - ZC—T— stZdZMOLjH (2M \T Vt www. crm. umontreal.ca ASSIGNMENT 3 MATH 270, WINTER 2010. PLOTS FOR THE SOLUTION OF QUESTION 7. Here we compare the function 2x forogxgl, f(x)= 1 2 2—2x forjgxgl, extended l-periodically to all R, with the partial sums of its Fourier decomposition fN(x)= ——nzo—— (2n+41)27r 2cos(27r(2n+l)x). l llllblllllkilllil lit.‘ 1. —O.2 0.2 0.4 0.6 0.8 1.0 1.2 -0.2 0.2 0.4 06 0.8 1.0 12 FIGURE 1. Plots off and fN for N = 0, l, 2 and 5. Hopefully, the convergence is convincing (and rapid!). ...
View Full Document

{[ snackBarMessage ]}