10
/'"{*{,"/ En.r 0) - it @) = -/fr.ttr,r rEö,) (arir**r"/,;,1 , r jf (ny,ts / , [e ,x6t) le t l A lo \ : f = (-t*2) n f irrt t; = i 4 l n r J(ryä, r F, i P, a r 'J f(x'Y't)"1 I lhl.-t"'l W= 1,,1/ = ry= Aun,, =*Eh 4 Y =4u!** N*LJ,27,.*t ( r;t"-) flr^1"'"( q DXL'*,;,.,, ?G=o) = o /t( fd*l''/4 ' Po) = a't,

W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

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Page 1: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

/ '"{*{,"/

En.r 0) - it @) = -/fr.ttr,r,)

rEö , ) (a r i r * * r " / , ; , 1

, r jf (ny,ts /

, [e ,x6t) let l

A l o \: f = ( - t * 2 )

nf irrt t; =i 4 l

nrJ(ryä, r F, i

P,ar

' J f ( x 'Y ' t ) "1I

lhl.-t"'l

W =

1,,1/ =

r y =Aun,, = *Eh

4 Y =4u!** N*LJ,27,.*t( r;t"-)

flr^1"'"(

qDXL'*,;,.,, ?G=o) = o

/t(

fd*l''/4 '

Po) = a't,

Page 2: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

?r^.t*o( ß-1

Krnrru.t'*

A f{') =

G?) :

F (r,n ,l =

/y fl*,u

I GOJ;)

J

tr. G

)kz.r?. (o,,;{.t'*r}-//

b

o/ / Fb,, =^ t I t .

/f*d'*/,',/4//"-,^*l - . - /

l - r 1 A

F ( r J . e ,

-{ ,l/ ̂E b ) = _ V + ? . , ,C ' t o r y '

/unrG",) =-! ir ,

= -lcooat

or t\t Q-',r^"/4,'J.

G",,'{^f,'*'V"{".{,J

" G.,,1^/.*r/"fo/o

:)Ya= - -r

/ E** [,,!

Yra . l t4 t = - y M ( ; -

d \

Page 3: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

K*.- APle'" W'U""/"/J q,..t PJ^/J yv,>.-.h 2

dJ"lx

v

f t r - fu) =- !a*1 a '

r ä r *

ä r * } y r ö r * r f r ä r i a - f

t r J = v = 4 * , r ä r *

x.

,a fat =

fl('o 60) = Fo)

xP -,o

?/ 'r

p(ö)

? f ^- T z e ,

= _ vpk)

"*y&&( ä . b )

Vrhl,n't4,,4,-

I/Jilr'*,/,*

Page 4: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

tL"/ -^,[t "4 ,nnc.- il*ß, x :' l

F . x

tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,

.U4 V

s. ,/J",^'ru(" G"r/,

,z{rGrrc w;-"1

F = o u ' ' o

L

E, =t z

*e)- F

2 t oJ; - +eorlo

+ Jpacft'*acr tr,lr- *r"t'o(rr-ln"{t- To'lJr-

: r r r - \

6r' ft + C,. ( €,r -'.Fo, = o

a'n h// /"'/6^'^it' '

1 v = o ' f x - - / ^ { '

Tnn,pu/s

.2"^,, [Gt/t, vt. *,f^

Page 5: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

.n

z_1tr=r, n t

.l

F = O,xil&

. . /

? {t'n'l ,'-',",'hzr

%+

-)F

t ,. f2

J

- t r- t z ,

a

C14

r l r t

t F tt t

zA = t

tf.dt

S rs r / t

Gt 'e' ' r+ t

= O

/\

" Z*, a-^bot JyM"rro-n ,rLa'pe e/,.0/*6t ,r"F

t

{ o , o(*,.-. -J^ *f* ltft-'

zK r t

#Wc-,^n

('_4eß f K = +

I= COrf,c

*l

{ = r

fo, = f, f"J:ne.,4 r/", t/r*"d, "/*

,r{ 4 C-"^..{;rVn/,

ll

f..u rp u (t it^.lt-,^ r t -y , d

f,cll,,.

Page 6: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

U'*, oL'.t-t^. rr**(

4?

oPta

\V*lr.-

o&,

o*/

oez

+" r

. 9/o"{rr'(- f('fr 'I

Err= ,*,{ ; ft, - ,*r/

, k-,/-,l;rlx {t"f , E^

( f^*rt, w;.{ fo'f*u't€ ivt -Dy'"*, ̂ l'^,, ..,t(t (-2 il6--t)

f ,*,,( , /G"= ,*.,{

,t.*.y-*'4/t )

fnrn ,'n Jn (l^

tu. v?

n r ' l '

' / , ̂ rr j

+ y'6 *r r.'2

* r Y (

.*r, 1( I

/n -*'

%z" l '

Il.

E Tz{a

F ..r-t.;

V [+-,-a-r") + 2--.^r,& r ? * z

u, C*r, - *,r\ t 2.*r, qA r l e 2

y'/o.LL*

Zwa ft'4, :

1 =

Y =

+v'

Page 7: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

VrRtucH '

-Sr.orz;,(1s&.- ( "("t{"''"L lßF)

4 ,*r" = q., v, =o +/ (

4 = o , 4 = VI ,

v n = V . ; 1 ' = 1

,*l^..trrf./ ?

r ( = o

u*"/ ß. Q,n/,,'n //"f)

;4 .ytr, = &z

6^,t

* Z = $ / b z = O

gf ruF ,-*,4,.,,,4

+^';'L6 rE"{n

c:;;)

, )

+ - b(

) Y : - ? , % ' = € r

V =

(,

.'|,ry,?

= 2nr, , % = U

sg*{J(. ( '-o/.'!r',L S/:/t)

.) f r ' a t e a t % t o -) 4 = v ,' ' r t v

Zrt /r(*"C, "-';7*'J t

@ ) 5a @

"tuy*rl^rlrrft- St,f'

' f r n / 1 t ^ r ' * k * ( t " ) '

\A2. .i-*,ta Lrrrr, t\ 2,;. ir-a-p* ,n r1lu"-'tt'll

( a.tll h'.1,*... frr".4l.Yo-,u.) "

@ =

Z*f uQ tJt

?a.c,6ic fi''k-t

*a/ (

Vo

/r,"- .*,;SA'u|,

Page 8: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

' E t,P(orrr*" fl'ß

f o r = o

@*@,

+ @,

@ L

/tu4 u L

f u , * Y

- ,2 n f

#j\,

ae"4 2- ' t 'ot, V

I L.en sucal

&.= &1 = *? --. - . t tq,u!\b= 4, *V,

= n, r'A.-. vrz

ür Y ' nr'r\

n r 4 2 o t , , t J

//,- /b,4 r = a a

V 1 = V ,

Page 9: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

Ve n{uct{ , .ß"clil,rlrt fa."6.(

Z.--.y-ft

* r )

fa-,e4/e :

tb

f r r rv l

(n, r *r.) 1

z[,; L1(,

//r (*, r,.,) Vr' = (n, r 4 l L

*-'lV r ' ' = 2 t ( ( ( - r " r . )

, ^ r

h . t t / \

( ( /- cor"t-l- . /

--. - l/,& t ( * z - t

A

./,

ltarr. l .p. , WV =

_N.ÄEJ\ , -J}

) F"l. L*4',-

I

v z =

Page 10: W=f irrt t; = i4l - uni-muenchen.de · 2012-12-04 · tL"/ -^,[t "4 ,nnc.- il*ß, x : 'l F.x tC^/ -;'2t wa4,nuJ 'ar- )o'/ t ,.U4 V s. ,/J",^'ru(" G"r/,,z{rGrrc w;-"1 F= ou''o L,=E

fr^,lr/* *l*l/

r(r) = &

f ( * r d t ) = ( * 'Ä

4 J ,

7rI J,,

Jl = o

v(') -

4

l - l { a t I ,L,- | .

l v '*

I

Vr r - - v - v

[t1 . v(t)

\ r \ t* ) ( r r 4 , ) , 4 a - v

+ A. ' , ( - An,4v' u t +

äl,r"r.

Ap = ' t - ' 4v

R-lJnr!"'rLr' ö

: -

v(") n L ' - tv(r) = 4 ( v r n % + [ r

4.e_ . Jr ,ln,= z t ' v t - r -T = * 7 l r r t q = * 7