10.1+10.2, fourier series in pdf completed now

7/31/2019 10.1+10.2, Fourier Series in PDF Completed Now

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Jao-nchagem-cidaiccraidnetbcnetags

Jy Nobenneh Wakeiher-kbei-Mohba

[LOSZACZ-WCZACW0 GB-56 AXW EI CIDAICCZAID NEXBCNEXAG GBEVXCZ0


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(CIDAICCZAID NEXBCNEXAGW 8, GB-56, WCG-56.5 & 56.:)

J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc : OL :5

LOSZACZ-WCZACW0

(56.5)

VCZAOHAG-LSIGXAOIW0 Eiy luigtaoi l(x) bevc sonc posatavc io (p) eih ats hclaich lor emm

rcem (x) .

[ > )> 96 ..^

lanamer pcraohag luigtaoi erc saic & gosaic luigtaois.

(l>g>goisteit) >9 ats emso e pcraohag -luigtaoi, jcgeusc ats

setaslach cquetaoi (E) lor emm (p).

DZEVB0

tbosc luigtaoi wbosc erc iot pcraohag erc lommowch

(a-c)

Voait(e)

Voait (j)

Xbcrc as eiyaitcrvem olmcidtb (p) j/wpoait (e) & (j)

l(x)

x-excs


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J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc 7 OL :5

[ .^

XZADOIONCXZAG-WQWXCN0

Our projmcn ai tbc larst lcw scgtaois ol tbas gbeptcr wamm jc tbcrcprcscitetaoi ol veraous luigtaois ol pcraoh ( ) ai tcrns

ol tbc sanpmc luigtaois.

(a-c)


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(56.:) stert bcrc

LOSZACZ-WCZACW0

WXEXCNCIXW;

Xbc louracr scracs eracs lron tbc pertagem-tesk lor rcprcscitaid e

pcraohag luigtaoi [l(x)>l(x+p)^ ai tcrns ol Gosaic eih Waic luigtaoi.

Xbc Louracr-scracs erc oltci emso gemmch es tradoionctrag-

scracs(Cq-[C^ ai scgtaoi 56.5), wbosc gocllagacit erc laih lron l(x) jyusaid gcrteai lornume Cum cr- Lornume (jcmow).

Iow, wc larst hravc tbc Cumcr lornumes wbagb erc nost usc lumm lorlaihaid tbc gocllagacit ol louracr or tradoionctrag scracs.

CSMCZ-LOZNSMEW-LOZ-LOSZACZ-GOCLLAGACIXW0

Mct, l(x) as e pcraohag luigtaoi ol pcraoh (: ), wbagb gei jc

rcprcscitch jy tradoionctrag-scracs(or Louracr-Wcracs).

(a-c)

Tc essunc tbet tbas scracs goivcrdcs & bes l(x) es ats Wun.

Kcy wc weit to laih tbc gocllagacits *e 6, e i & j i ol tbc ejovclouracr-scracs ai cquetaoi (C).

Tbcrc [ i>5,:, 7,8,..,aialaiaty+.

LOZ-e 6 0 (Cumer-lornume lor e 6)0


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Mct , aitcdretch oi jotb sahcs ai cq(C) lron * ^ wc dct,

(ejovc)(Cq-GC ) Ats tbc cquetaoi ol e 6(tbc gocllagacit ol louracr-scracs ai cquetaoi[C^).

LOZ e i>n 0 LOZ e n 0

Tbci (n>i),

[n> eiy laxch +vc Io^


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GOIWAHCZ 0


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Iow pmegaid tbc vemuc ol cq(P a) & cq (P aa) ai cq(D 5)tbci

cq(D 5)jcgoncs;


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J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc 5: OL :5

Tbci (i>n)0

LOZ j i>n OZ j n 0


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*n>i>5,:,7,,+

_____________

Zoudb-work0

Tbci (i>n)0

__________________


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MAWX OL CSMEZ-LOZNSME OL LOSZACZ GOCLLAGACIX0

Tbcrc0

[ .^

Tbcrc (e i ,j i & e 6 ) erc rcem-Aitcdcr-Io,emso tbcsc iunjcr(e i ,j i

& e 6 ) erc gemmch louracr- Gocllagacits ol l(x).

Eih ejovc cq(C) as gemmch es louracr scracs or tradoionctragem-

scracs.

_________________(LAIAWBCH-BCZC)__________________

CRENVMC#5) WUSEZC-TE\C0

Laih tbc louracr gocllagacits ol pcraohag -luigtaoi l(x) ai jcmowluigtaoi wbagb as davci ai cq (E) eih skctgb tbc drepb ol l(x)?

Womutaoi0

ZCUSAZCH0


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J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc 5< OL :5

E). Wkctgb tbc drepb ol l(x) ol cq(E)>?;

J). laih louracr gocllagacit ol l(x) .E). Wkctgb tbc drepb ol l(x) ai cq(E)0

Drepb 0

J). laih louracr gocllagacit ol l(x)

.

5) LOZ e 6 0

Jy usaid Cumer lornume0

:

-:

+k(enpmatuhc)

-k(Enpmatuhc)

x-exas


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GOIWAHCZ ( )0

Ai dcicrem ( )

LOZ LOSZACZ WCZACW-OL-l(x)0

LOZNSME0


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J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc :6 OL :5

LOZ VEZXAEM WSN OL EJO\C LOSZACZ WCZACW EZC0

DZEVBAGEM-ZCVZCWCIXEXAOI-OL-EJO\C-LOSZACZ-WCZACW AICUSEXAOI (\)0


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k

-k

-

x

(: )>V

>(-

Lor

k

-k

-

x

(: )>V>(-

Lor

k

-k

-

x

(: )>V>(-

Lor


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J A O - N C H A G E M - C I D A I C C Z A I D - D S A H C J Q N O B - W A K E I H E Z - M O H B AVedc :: OL :5

Kcy tbcsc ejovc ladurc sbow tbet louracr scracs as goivcrdcit

eih bes sun l(x) wc iotagc tbet pertaem-sun geusc to jcgoivcrdc eih bes tbc sun l(x).

Ai ejovc cxenpmc wc iotch tbet et (x>6) & (x> ) & (x> )

tbc l(x) as hasgoitaiutcs & tbc vemuc ol pertaem sun as zcro, tbas

l(x)

k

l(x)


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nceis tbet tbc scracs ol pertaem-sun as goivcrdcit eih bes tbc

sun as l(x) [es rcprcscitch ai ejovc drepb^.

Mct, l(x) as tbc sun ol scracs tbci Essunc wc sct ( ),


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____________________________________________________


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16

:46

7:pa

5

-5

6

Gos(:x)


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10.1+10.2, fourier series in pdf completed now

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