wth 139 L2 .' ODE P/,r.. S"pat-c.L/e d !efc rrcf,'ora r - - PDF document

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wth 139 L2 .' ODE P/,r.. S"pat-c.L/e d !efc rrcf,'ora r - - PDF document

{ wth 139 L2 .' ODE P/,r.. S"pat-c.L/e d !efc rrcf,'ora r 41o.r'u Res'+(t i i. ftar"P/e.l Qz) { :eP:gue ODE Dcf r ,lR.+R, 1,, 6.va\ lqr.tiort ,ahh ,!. 1'v! ODE lhe .'i ae b SdFara YrlR+/( l. r r'lf oDc-


slide-1
SLIDE 1

{

wth

139 L2

d S"pat-c.L/e ODE r !efc rrcf,'ora i 41o.r'u Res'+(t

  • i. ftar"P/e.l

P/,r.. .'

Qz)

slide-2
SLIDE 2

{ :eP:gue

Dcf r

t Rer.rrh

6.va\ lqr.tiort

1'v! ODE ,!.

YrlR+/( .'i r'lf thP

  • Dc-

,lR.+R,

SdFara b ae lh.' for*'

ODE

1,,

lhe ,ahh

  • l. r

a (y) l'lt1 xft)

i'l

,'{f

rll

  • 0E

sPF\

  • 4. t/P

Y'ft\ -- | t t, trtl)

\tt1

A(y) Ytltt

slide-3
SLIDE 3

.4.

r lVot.ltg't r

I.

rn

lec t( Q

t, l(t; ,

  • 7(t) + A(y)

l'ft\ , o

?axfbook r

ta),

,\ (xt + N(Y)

l'ftt -- a

fhrr I f.. p r

I v'* -Alil i

x,

A(y) . N (t)

slide-4
SLIDE 4

{

i t-l:lPfg (rt Y' = l'

t - l,

  • Itrtt. t'l

ll

,3

t?prrc.6/a, tr.. ea

l:2L::1

(2) y' + y^ cos (zt)

rl seprr'*Vc, ll ae

Yt.. - y'coslzt)

l.r;

I :af

  • - -

."r r.rl I

Frnc f,'ur.r I 7, A

4t t'?u t.'

Aty) -

Reqv

I tl'l

  • - .^

r.'r I , lt^trt=-ts

|

slide-5
SLIDE 5

\

r ,Vot evPrY oDE rs s ef.-r". blc :

. frgP4

0) l':

  • 1,

Y t 4t it Alot sevc'r'L(P. t (2) .I'.

  • c.AJ y + b(t)

(kte*

  • Dr)

wf fh b( +o ,! ttt saF4re.b4..

x RPuncch I

l-l

lY''-^rrt r|l [ | (rc.r aDE v.o)

t'l ldP..r\b/e , s.'t ?e

f Y' - - \/r) , s' i

lrr'r=

  • ^r't

l, l^,rr. U\

slide-6
SLIDE 6

.tq (f

.(.

f ,lilo,t'r^

Thrr,". r r Ra*(. h. r

I i f,.r.cf,r,,3 X, A : R-D lR qip

so !' fi'qgaut with Priv\ltrrct 6 t H, re1pe.ttvell I thl.l rrl

lo'n>.|tt)f,

t,\

IH'(4) : ,-@,1

thah, /LP scprrcb/e

  • 0D'

.l*t . r, f ,''.r' l'e /y rr'*i/

b s,r t,: f2 r'r3 ft e

lc{wf, or l, Cll rr- fre5

w.'t\

a c lR c,r lc,'lr*r/.

f ,'r' d

7, L,

lher r

a, #.

Pri hih'v?t

Ytttt

Il(var\ a 6(t\

slide-7
SLIDE 7
  • {

i A-)..P& ,

se(r

F,rJ

  • (

/'nt --

tz

fc

OD E'

(-

f Tro ,"l"tr.,r ytt\

I iv,ptet t { ctu,r. There fort,

t - ytftl

/') /' "

t2

=>

aft) z t' h (,a) ,

| - ul

4-cg

lh q'

sc/.

yttl

  • s. f,'r

f ' er f4a 43.

c qlR

(1)

\ce ? l.rah atr

Y(t\ -

y"ft)

.3

  • t

t

pC

&e'.,r.h.'

Ao

v'

4Fp e4. I rV

(L) .

slide-8
SLIDE 8

i Reb\rh. r

Ver, (t c. tsov

Pertv*te .u

botL s*let cl (t),

ylft) - !

Y'lt)

  • - !f a

tcrl

l

(-

l')

Y '/r1

slide-9
SLIDE 9

c

v

r Pc"of

Sa!. a P

ther r

{

the

A

I hrw, :

( l(tt)

Y'(t\

7ft|

by a. eowg futf,

p r, h", lt' /ai

  • {tlle"

!",

yt(tl J t

Per{orrn the I ,eLs f, f r. h'ou ,.

ra3

y(tt )

= Jr

It\ olt

?

c

*^=Y

  • lt

Y (tt '/r)

Atlt

Jq

  • ttl "lt

f

c

H ta\

6ltl +e

S,r b: 6' lufp

b*r h

t^ . y(?l

.Ir

F

'ft (vo)

slide-10
SLIDE 10

{

r IYP ?or

S6';rr-*L/e

&14

I'rrl

So(;

Tft)

tnt

)

."e s.*tpl" 6 rJe

t"/. .,

tvP

(t)

Inp t/.. r'f

etr.

rh? t2

t - y'nl

'l'"\ . t lz)

At( <otu

tt o" t

t"

&)

se f,r fy fhr a3,

cor & 1,"u lz)

t'u^ P (t'et

. /t + c

3

The

Y/o)

r'hcfr *(

  • tr")

I

f

  • *

=.

+3

s>

slide-11
SLIDE 11

(

t F-1gp!9 t

s"(.'

F.'\.J the Sc(

l'lrt s l'1s1

"* EVP

.o! (zl) . o

(t)

(zl

  • 19. 0)

t!

Itu) . t

S"fqr\ Llt , a.\c c

'l' lt ) ccs(zf)

1ft) --- cor fat )

6ft\. -

l.

z S&(2t)

,f, rul "

I

al

.=> H (,rl t

/ll !olr fr'o\r

  • {

?l . (, s\ t("t fy ll. tf.

J-

v'

lc.'

  • L u

Ta?ttcit

tor-r

e clR

slide-12
SLIDE 12

t

lut

t.

Yb)

3ch aa t)

  • ^C

2

)l/r) _-

L

5,r (et) - lc

Jclu tr'cr t

4( ? t..' t

I'lr

The

Ito).t

  • iv. p d'es

e

  • 2a

.s)

ex?ha.'l 1..,r,

€---l

a

s-!

e

S.r. (et) + I

slide-13
SLIDE 13

<.

{ f, *yfJP '

tte

  • l

,VP

2- t

tfY4)

y'/t\

(t )

(z)

Yt") .

So(.'

  • 81. (t

r'!

lln''=,', I

Th(:r'r PFa t..r'l'rl/lj .\i-a ,'

1/t): r-- t

6lt\ : zt ,l t,.) . t+ c

  • 1

H(u) .

At{ s.rr. !r; .f

1r)

s-/rr fy

thP et.

Yttl 1 yrtt)

rr-

Lt - t

L

le

  • S. P\ e

* l, r,a

wtfh

  • ta

a * qa c clN

slide-14
SLIDE 14

The r'r, i fr *1

lto) . t tvPh,Ct

t*t

/{") +

Ylct

2

,.

yftl

O-O

+c r 2f

T herelore r

y'nt

  • ,r

I

*l 2

e Tttv'. t.' t ty

Irlr) r r y1r)

  • !r + 9t + 3

SpBt

f o n.

slide-15
SLIDE 15

<t

i Sa!,.t 6'te t t

er pfi.,'t ?c

lle ro/s f,

  • \,

be

? c, tr.

Yft\ ''i tt c r-oeI o*

the pc12rrou,rt'a(.

/!ft) . -.:y ,t

  • tt ( t'- qt -tl

+

P

  • sj

t lc. /.' f. ei

Y,

(d

Y- tt1

V,-tt'-+t-tj-

a

  • l
slide-16
SLIDE 16

t Owty l* lt1 ra. fr'r f,'pr fhe ,\, t\u (

ac n .lt ffoli i

,t/o). -r*Vf : i ,/

Y-(o) . -t -t/V : -3

T.h a Sor/t &'ora ig

Ytt) ''

  • l + V't2+al

+j

Fx r.lr cc I torw,