(z.c) ooF x Exo zt . Dai x (u,,unJ R= (t,,tr) Cfiz 4. Ve\\ - - PDF document

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(z.c) ooF x Exo zt . Dai x (u,,unJ R= (t,,tr) Cfiz 4. Ve\\ - - PDF document

( 235 L' r"th ODE Ercct f{cvr r e\-w,2les 1 fefcrrltal l A.i" Rer"/f. t j 6cie,-0. (, to- lioiJ l ?nctor *etloy'. rhf?trc6tl (z.c) ooF x Exo zt . Dai x (u,,unJ R= (t,,tr) Cfiz 4. Ve\\ 'f I er e., iAr.,r-


slide-1
SLIDE 1

(

r"th 235 L'

Ercct ODE

1 fefcrrltal l e\-w,2les

A.i" Rer"/f.

6cie,-0. (, to- lioiJ j

rhf?trc6tl ?nctor *etloy'. f{cvr r

t

l

(z.c)

slide-2
SLIDE 2

x Exo zt

Dai .

  • 4. Ve\\
  • oF

R= (t,,tr)

a',ol couh'wuo"!(y 4t {uu c f,'ot 3

/1, N : Q+ the ebE .'b tt e l: (t,, t.) + tR

x (u,,unJ Cfiz

'f I er e., iAr.,r- bZro

tRt

luft, val

14 (t, yrt)) 'o

l'ny

exo-c t

,'lf

h"hts

13

t, I

ln tlr\ =

LN )t

)_/ /t

),r

\, N tt,u1

slide-3
SLIDE 3

Stio'r,, th{/

2t la>

tLe

lh) +

t l4(tt

  • t)E

2t

tr

\ 'I

exort,l

I

  • )

5o(.

LrryT

N (t,l )

I'

Lt +/r J

  • -"

I

,,

M(t,l)

Nft,Y\

^( t,yt

2ty

zt tlz

Jt (t,y )

\/vt(t,r)

2l

zY

7he

R ?-rct h .

7he

  • 0E
  • 0E

.5

,5

\. O!.- ldgPc- .

r.of Sqaa'-*51..

slide-4
SLIDE 4

Y

Fxurr a{e . 5in (t)

so( .

  • t' :

?ro. a / t

  • Y cctld -2t

,t

f+

th.'

t'2

  • bE

v'

[s;,,(tltltaY-rl

Nh,yt .

S(v, ft I

+ t' eY /4 tt,Yl =

Y .dt ltl

)rA --

t2

aes

cxtcf, ,

1

"'.l

/ . I Yc'lttt + tf etl =.:

  • t

(tt

tel !t) a 2t €Y

  • oE

at

slide-5
SLIDE 5

{

Ep-, p lP ;

5o(r

fr, the obl

L l' . 'e[tl

bCL,. €xcc /

Y + bt .

,J

lttfo-a1Y

  • b/rJ]
  • -e

t-{

Ntt'Y ) . I t^(t,Yl : o"(.lY

  • bl?)

ItN

rrA

,o

= 4lt)

lhc

  • Df .'r

u"t ex" c f

'.lal I o

l"r r.lft t o.

slide-6
SLIDE 6

.t

r R e c{r/

s r 3.9!!- €"9:.

The .olrt.rsouJa),

Jt ((c r eq z'i ". bte tV:R-oP

{.rv'cttorJ

s.,t, r {),

)t tV ft, u)

)n M {t, tt 1

it( trare

con i,.'wu

  • u

t /y

fuuc f, ou

t; R

1a f,r f7r',1

ex,rtt \

  • lr't{ e

rar tvtc e t t* ble

  • > [r

P-.f , (€) s.'pzu..

' )r)u A

_- )")tt

\til

)nM

lg

1..

t-'

l

lo.

),. a rt,uy

\ 7tr,'.t

(=5 ) o,'lfrc.lt ,'

Potv.crr c' , tl

slide-7
SLIDE 7

{

Reco"l/ fho. t thr) 2t/ y' I

{S 2xee f

  • Dt

be ac-\r J e

N' 2tY

/r\ . 2t +yz

br.,r q J e

2/1

l'>'tru=srvt

2/ J, I

)tM

'y4

Tha fqv c f,, ,r v,

at\v)

f,h,S zaJc .S"

.r, t

ry

I

  • /vl

lr! '

Tte fc,rod.ru t

  • !

twpltctt J./trlrors t"

zt 2t

Y2 =o

ce,tc;o.l to k-o/ t tr. DD E.

slide-8
SLIDE 8

{

Thrr'r I

The the

* tb!,

rirq.lf €xrct

/,(t,,r.)-+R

e6E

te

A tt, f/rt)

be

Whera

  • s. t,.r

€y,

  • o [Q

Y'tt t (t, Yct) =o

X tvP Yt

i\',ptft(try ry

at

{,.- < ti ov

^t' (t, ytrt

)

R

t 'r.l

l" a/t

)r "f (t, al

M /t, u1

slide-9
SLIDE 9

.l

P.oo{ .'

l'+M

=O

er,tt!

))1=

)t7 --

\N . tyA

f5g;4 fore r

6vr)

ccch thet

a

A

a [ttt,

,tt

v'

(trt) 7 o yn1)

t

t (t, l,'J)

slide-10
SLIDE 10

r-!yrl? ,

ttfs. f <)

\r/ = tl

trA . zY

l'+

I

I

  • o 1

{

fy*7

lt I

zt + y'

th . el.

ts €t<qt f :

Sl( t

Rp .,^,a fL- f Lty

=>

s> rq: 2t t Yl Ther , f,\r.P ef .'t tt

7

d)

(tl

(t) ')

)r?

2t f

(tr"t\ "ty

2t Y 4f

t-t

2t

s"-6.r

+ Xl{J

v

{

t

x(( t

tft)

dy

t

{,'. o/

"fh,v) =

slide-11
SLIDE 11

.q

l: = "^,' zn' I

T'h ere f"te .

(r)

Thc ("1.. E

  • " !

>tt

f^,

1r /f\

= zt 1/L

X'rt)

zt

ltnt, tl

l'tu,v) ' tt" *t^ l

Y tt\

f,|. c

  • $

E s* a't fii

eclR

('n p !;6;t erpfeSJ.'ov,.

It yY,, . t' = " I

( ^f (t, Yftt) -- c

slide-12
SLIDE 12

itx^-,,te.

I (s.-

t

("J.

Re

  • r. (a

Ft",ol el/ Sol,r ?'

  • r.

: "f

u\ 1t2 eY -r) lt t I cts(t)

P2t

/="

It,.t

  • th. e?.

+ t'e

  • l

t't CXa c t

l/ : (rvr ft)

I >ru

  • ."ttrl + ^t eY

f

A-- | coslt\ +zt€Y

  • )

\rA 3 co!(tt +2t eY

TheFefoFe,

there erts f, s

?

s r/rr f,yt rr1

u/

(2)

(tu4 t

slide-13
SLIDE 13

"|

siv /t) + t2 eY -l

nltt,f\

  • ysrb/r\ rtze'-/

+1tt)

(e) =>

)ra =M

I co| /t\

+zteY +1'tt1

| .os/ 1et €l

.ott ttl = o \(t) =

The"of,..',

the tolr .

Ittt s*tt €y

{

/t) =)

.tf

>/

c.

nf (t, y\ =

S.'t' I f )

iv,plioit

e, Pr A5t.cv1 .

slide-14
SLIDE 14

'{

J-rr flrrc-lr's q

lhera er;rl

Uo,.- Cxa. t

weth,{,

ODF tl"o.f

ex'.et O,F b/ a*r bg couves teJ lu lo "." ttt plyt" 7 lte apuo. f..ov,

,rppropri. le f.r- e f,,'o 1 , ^rf,? l.cf ,'!'l f,"c for. 4a v,a r,r ('z + lt

slide-15
SLIDE 15

Thrwr I

<5

I I ttn

l-

I N{t,Y)

L

aS hof

I I \/1/

  • ,io(

a'

r

  • bE

l'rt\ , *)y

fhd

l/of /eperol avl

t\e € luc- fsp",

tA thY)

fhcf

/v1 I

J

fu"c f

  • "

]

tJ )

  • {oCl

,5 Qx'tet , sc/* fr'cu . I whdr, ,/4(t I

,'s

/'(.1 = h* L

\Aft,Y1

  • )/""4j1'

I

L )/,\ft,y) _ )tNtt,vt l

/ttt lvtt,vt

Y' + ,t &) Attrl) = u

/tt)

slide-16
SLIDE 16

;:g:r3,

So( ,'

VerifY

3.(t. I

r (t2

(

l

I

j

i""' o'(

l(+t*t^)

ex,tc t

/')

at

the

t'

el. rl

t (sr)+

=O

G", oy),

tz t t I lt /+Yz

+

i

!>

l---------------1

)tft

rlA

zt

3t

l',.+ 'il

7Ae 61.

.

rl

lVof ex +e t .

+tY)

e?. /t--o

v

z/

slide-17
SLIDE 17

.{t

l- N ( >rn-

4a1

(t'+ tV)

( trY)

(ta + t

,

(t+u1

t ( t+Y)

  • tzt +y)

(rt+ zt)

:J- t

eftr ls

1r'r.y'Pp.'bJd \f

  • f

,)

  • *

So, thart

l't*l

/(?) sc( '

(+n- >r,,v) =.!

t

EJ-

N

l-;t------

  • lJ-
  • t

1

ll t I

(\yA -)t,V) -

slide-18
SLIDE 18

.(|

We ,'vr fP?.a t/r1 7a.for ./

Lat

L,7tt1

  • l-(t)

I /.t , t f

/qul 7ly f,h6 ertltv( 4E

(tt +t'v) lt + (rr'r + t

  • lv

{'

J?

by

y')

l"t

FO

Veri f,7 tt^nt f,trr'

vtew dE .5 ex*e ( t

>rfr = lrfr

f! tt'y

tt'y r t y"

lstV: t.A --

3t3 3 f '

I ztl r ztl

slide-19
SLIDE 19

<T

Sdt ae

al ct

exe c

fhe

t , v./ e

4S q o-/

't

Solu trow

so/. (t)

(z)

(0 =)

)"

fr rf: y

  • f,

t^

L

nf=

Y"

(z) ':

gltI+ x yl+frr*1 -- ]f,ty+ f y.

1'ftt * o

ll',,

  • -e

ft 'Y\

h1 (t,y) = o