Fourier Series

Fourier Series - Lecture Ncfi'cs , (OLD-:51? _, Nov. 9....

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Unformatted text preview: Lecture Ncfi'cs , (OLD-:51? _, Nov. 9. 4.. Fourier series. sum -—n———-' b Consiw LILQJVA :2. 61-. [0:51) [mngI3Aoc (co-g. The Set fignafions cm th) Advice! ([3,, 1011 an E: 3;: 4' ws(%xm sm(.%x).1””-I “5(fix) sm(b—a is an orfhoaomfl basis cg PM). Aug funchm f in Labia can. be PM H's Eurier' series w'I‘Hn resend +0 bands: co ' I but . 2|n."- (x') :3. Clo + ; Claws +bn5|ncfix> b ‘ I “W do = 4— Shficlx) b—a. a \3 1L an '-'- figagij Cos(2£-:a:\c10¢—J a? , amt b bu = flia S ¥(1)33n(?%x)¢m J {1.7/1 Q‘- We. Ca.“ 6*) fLa. ordawwj Fourier setting at? f on [11.5]. Rama“! fl (*3 i5 “tango-“Mafia we, aw in elm gor- a: —Q.ob:.£,3 {Win for L'QBJ. ' E [23(3) (“—3 Com be regoJLJ-zi as o- ;JM-h's“ gov” 0-9-2 at) -ao4¥-¢4>. I'l: has Patient (Jo-o) and» is Hm. Fourier'SErieS of) ‘hu. ukmidfl {E f a am.» women: m‘fl m‘od b-a, G342 1517 Nov. Lec’t’ut‘e, Nojres : i. A worked etamPlg Fourier set-{es caIcuLx’rim, Lei g(x) be Manchhn defined m [0610 0.5 SW33) '-‘ “‘95 . We. mi“ mlwhi‘g: A] The arched?- Fearier set-{es 05" g . This is Hm, Fourier serics “1th rupee): +0 HIE Cowpld'e whoa..an basis {1, one. (29:), 5mm) , whirls": (4:3 , ..._, astznx\,5sn(znx) o‘f‘ L1 [3.1!] = {a an [offl]; ifls‘lxmoc <¢n§_ ‘ TH: Fout‘icr' series J when reamcbcl as :1 ohm. deg-ma gar-4.051 x) -—n4xcao, ha; Paioi'flaamdi‘hus ism Fact-tar series OS: +luz Pen‘ocl 1T exhfiim an; RV. Th. Mi -Couirul. so.ch gar“ ?; 51 TM Ml}.- Sim mates for :3 DJ The Gender "Gosivu. series for g 3 a TM Ova/01M, —S.;m Stu-{es firg, (34w) = Ir-x 1-0 Rum Hue Add: a? PM derim‘ions H' is «£qu -‘-o reer gauow-ma gormulas, derived in’rearahon % PM}: in Snfox) 0:50:13 1 l-'C4‘=*S»(“"-'“3 (13 {my mch = (Tr-2a ..._.‘ a - at = Q2. 0 O 1' hit (2.) {CW—x)5m(aac)clnc :: -(1I-x)°°_§_[£) —- 5w '= '_I_T_ _ Sm (0.1!) a. 0:2. 0 a a3- O For‘ gut—x a». Log!) 3 and; , an=o,n;| anal En = er: 0%. Thu. resufli’am ob’nicucl (a £43 anot- (3'). Ear Wampfll, £104 C2.) wihi a=2n "Ir -5;“[Znn) _ _‘1_ bn .—. é}. K (TI-ac) SmC-mabclz = .3: can)“. ] __ N‘ Thus 4 F5 (3) (cc) =-' 1.7:— + Z 5"; 5342112) “1| m m Hog-Cesium. series) 0-? o. gang-Hon cm IDA-3 is 14M. Radar" Sm on [-LJJ o;- ‘HAQ QUEH extensimn 0? :2 co . wevy P = an 'F 2 an x) J ex+ensm Ina-4 ‘- fln TI L 1 M an: J an: pagan." o In Cased L=1T ‘ Gar—E2) carnal.J Ci) 1 o l d3 n 35% on = (“—23 msCmédac = % 1-finfi)= ‘i _. (I, n ism”, 0 "M1" (10 Hence) Mama); 1;: + Z ‘l mammarth h: 0 Tr (2.“.an g Th-l. Haw-Sin. series 0‘; o Lacks“ 1? on [OJLJ is 'Hu. Fours'ersma cm [*Lfl.) 0F its :3ch ex‘ensimg: CD (x) :: Z bn Stnt‘l-Ex) I adieu-(2min “1:; b 2 "‘ "Tl' . n t I SOS-(szmtflgx)Ax u a. 11' bn = 3% [ow—kacmaax .= as??? Hana. HSSHM'x) -.: Z —- SwaCnac.) you “MM 2] The Oofimcwus semis is M f—Buner mica om. [Ill-12L] oH'm'r-Id lay an cull aloud L Whit M M 606m exknsicm about 0 Gram-,5) = Z an” @51an x] hat) 1 I’. QZRH = "if [0 ’em “51%xjéx' 1 In Our ch azml: %LCl-%ml(h+l{.\x]dxz 1%." (“+1531 and gagging : i “finazmfi[(lz+1®x] =0 E The 000M s'uua. SM 0; f on LOJL) ism Ewrier series an Ell-31!.) of‘ 'HM obblucfl E17 We,wa +0 LL39 we {Lon 0AA axlem'm 1-» [—anle a) cassmcu} : b2“ sin (23$?) 1 i En“: IS fax) 5m 25133012.. In cur can. b: H 2:- L _ s;n(@~*tfi)fi)] m: 11 h . 111 Ch ._ my). __. 1 1‘ '.... C4)“ -« [m m: ...
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Fourier Series - Lecture Ncfi'cs , (OLD-:51? _, Nov. 9....

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