11
study ii am pied

pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

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Page 1: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

study ii

am pied

Page 2: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

.info#w.xeXgHyhhokb%ddkTn: × → Y sipper

.CH#hTn1Btdqb.%bdFs , > { Tna } Is

11 Tnxll c- HTNH . " x " £M '" × " :@

twin Ak - { x : 117×11 EK . nd }a

X = VA , . ⇒ .

Elie K¥4k=l

B ( xoir ) C- An ⇒ th , #I x. +rxslkkt×£BGi1 )

HTXH £ kt 114×011

HTNH - Sup -

rmillet

£ M

Page 3: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

.ci#&sIxHEK:ITn:ct→ R

Tn¢xmED=m§,.cm#t*vKiacteeo1Tnlx)1sE.lxmlsnHxHa

HTH - n → a

X=(xmte.at#-y.oyTtHt.ixeAsH4X=(x

, ,... ,xµ ,°m " ' " ) ⇒ TNCXKTNK ' n±N

Page 4: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

.

I # E# Footed k¥444 :&a

F e C [0/2+1] f ( × ) ~ a÷ + [ an Cosnxtbn Sinn ×

.

n=1

An = ftf"

fan Cos nx dx

bn= ¥f2"fan Smnxdx

M

T (f) = aoz + [ an→ xeo thaw

mn=i

¥bx - kit It # ⇐ , ,yoK{t.nefpk.tt's Ht KT/

'

m=l

o 1# HIM@ out ibid.EE#noyI.:

Page 5: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

ITMH ) 1 = / a÷ + §,

an / =/ Enfs"fwd× + §,ftp.fcxicosnxdx/=1.EIFcx

) [ It 2¥,

cosin9-

mcx)

C- It , {"

I 9- maydx . 11£11*

⇒ " In 11 s In f"

I 9-man ldx

9-man Sinxg= 8in It ⇐ §in( ntk )x -

&h ( n -

'G) × ]

= Sin xq + 8in ( mtKDX -Sin ×z

⇒ ofm

( x ) - Sh(mtk)×SinIz

Page 6: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

f"

landefeld× > 5.2"

I sina.tn#ldx

eE¥¥I⇒l¥a= 2 f←"

' "

1sing 1 dy

⇒ E.Html # lds >ZM

> §.

⇒nnfY"P;yldd=mE¥* → a

Page 7: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

Mullet, # lqmixildx got # K

TmHI=¥,f* fanqncxidx

F=sgn( Fm) - {t t Fm > °

-1 FmE°

⇒ Tmcf ) - tznfttfqmcxydx→ E # f :#

HE zgecco ,ztD ,llf - gHz=(f#Hcxtga,pdDk< e

!Tm(g) - I #tap"( gotta'D Find

'Ts Hgfllz ' " Fmllz£ Ellfnllz

Page 8: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

Hm(

91/2In f

"

lqmcxsldx - E 11 9mHz

light % Ein:%# g

9

ftp.#VVfH* ⇒H I 112¥,f2" lfdxildx - elite

Page 9: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

t.us#ffixn ) } d. is fex'# # et : xsiwi # s { xn { % : I

.EH #

,> { a I of T

Tn : X'

→ R

Tn ( f )= Fcxn ) ⇒ HTH = Sup HK ' l

o ¥ex 'Ffnx ,

= " " " "x

. Indy.

51 ( Kd ) # x ? xn d. is owinxrxk% ( × ," .

" )¥ # Id¥oI÷x'vk.IM#*a.h*iuF.d%ddfboiFeX'gHgh)xn-x_xnw-

×

fcxn ) → fcx )

Page 10: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

. Xn - x Egin ah xn→xFP

. ( i <p< a)end ° : JI

v. feely 's lot ,fcea ) → °

to

IHmMoftttaf.CYmlm4.FlxmIEEYmYmm-1fcen1-Yn-2o.ento-dsbf@t.fenEF.ds6A.duVfeH1-TyeH.fcxkcx.yp

Sten ) - < en , Ys >A

119£42 - [ 1 < end > j2no ,

⇒ Fcen ) → o

Page 11: pied - 213.233.161.92213.233.161.92/notes/course/FA951/FA-16.pdf · .info#w.xeXgHyhhokb%ddkTn: × → Y sipper.CH#hTn1Btdqb.%bdFs, > {Tna} Is 11 Tnxll c-HTNH. " x " M£ twin Ak-{

s.at#msI?Isaf :&Xn - x

, Xn - Y

VF←X'

,bifcx .

)=f( × ) = fcy ) ⇒ ×tf

(

4dbiIx.6lIx.jsh.Ih4hIsxn-x5.olI@gIbEEIgT.uH.oKxnld.isoETxn-xsT.otFliminfHXnllZkxll.ETxnu.x

I :#n → a

IFCxn ) | { 11£11 . 1174 "

Fix) ) - limlfcxn , ) fllfll .limit " 24 "

⇒ Saplfcx ) )

o # exitsS hhninf Benn