9
,1 \ C. üu*,* A*of . o.* ,U. ttU. 6 .?o(z \ 5e^spct{ ,(.1.3\ \\ \o.-c\ \n,"\ \,.actc. \;q \L*\^\''r^ \(x)= x, xe(o,z) t^l crrä g 2r'.r. ei "r ef x - Lri^\e^rao1g^ Ft .^\^h',- \t - 1e^roct..,. [-.'*\'-F'"- Rl- C t"eJaR- \ - fe^^ .'Ä^'s"'.^) e-^r1,ä,^zt . 3Gx \ _--.., 2t - \(s.'! -5=.,.rrrx + !st* .\, *f * c-^ii.. CaY), (n) S= (t c") f ,tf*) Vzr,o, f.c") (.c^) \^:4 ,8r .\,, 4_. __ ( t^.rS _ ri- _ ,8+ rl.-,, ) ' \ fi: <----r u-l q^ -Ef ,\ \*. 3tr{ 2 +!.o 2s Shx \ -t a' :\ ) c.) (3--n)' cos 5i. Qei\e- t* C,r) \e-oo,^v.^^rctt\ 1p.*. 6tc" \n **r\eHR,t\. \to- eli$e*-.*?i e=\ Qe..'\^e- t.^ ('r) d-ive-g,i er-t rtue-'1e'- #f n-{c-^Y*Lrcry)ry = I*G^i:",e) Yt: \ \4 i t

t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

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Page 1: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

,1\

C. üu*,* A*of . o.* ,U. ttU. 6 .?o(z

\5e^spct{ ,(.1.3\\\

\o.-c\ \n,"\ \,.actc.

\;q \L*\^\''r^

\(x)= x, xe(o,z)

t^l crrä g 2r'.r. ei "r ef

x - Lri^\e^rao1g^ Ft .^\^h',- \t- 1e^roct..,. [-.'*\'-F'"- Rl-

C t"eJaR- \ - fe^^ .'Ä^'s"'.^)

e-^r1,ä,^zt .

3Gx \_--..,2t

- \(s.'! -5=.,.rrrx + !st*.\, *f * c-^ii.. CaY),(n)

S=

(t c")

f ,tf*)Vzr,o,

f.c")

(.c^)

\^:4

,8r.\,, 4_. __ ( t^.rS_ ri- _

,8+rl.-,, )' \ fi: <----r

u-l

q^-Ef

,\

\*.

3tr{2 +!.o2s

Shx\ -t a'

:\

)

c.) (3--n)' cos

5i. Qei\e- t* C,r) \e-oo,^v.^^rctt\ 1p.*. 6tc" \n **r\eHR,t\.

\to- eli$e*-.*?i e=\ Qe..'\^e- t.^ ('r) d-ive-g,i er-t rtue-'1e'-

#f n-{c-^Y*Lrcry)ry = I*G^i:",e)Yt: \ \4 i t

Page 2: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

u*c^) r u-(,.) - 2 Gtf l* C+ls,t

,t'

h=\

\t.n

io

R\_'2 ./h=\

=) Fu. x s [o,z) I

(\,/ *

,l

o)

c

?

z))t,

.'(

\

(or

GI\A

)

e(e((.r

)o

2

K(

{r

o€"i

^\)

-4- ')

', S)-r^rJ,

frnsi.n / s

\

q'.*1= \J-lL-

f.,,4-t],. f-2*e, -

G,) 4^., \\= ( Iri ? .e"-,)

Qec\ts \\el*t eirae ü q*- q-)

ci.iq $^- \"\* Ä Vonl, . c,*\ \

S^ \.\* -1 \.<-s*.l c^,*\-

*"[a^ f;i"^cx) = o ) oU .o\.e.1. cl..ne otcXe*

i\K et\r e- .

TL--t>l^\ PerL,e t,n (r) cle\ui e>{,{^ r..^.ri n- \ zC.) = \.(e) -lt^ '<\ \rco) =o \.,^, ts! 8. *t \ t* Q

,, s\<F,g

cfu$'v'.-- c."ni\ \oesc\- AU\ )\rrs a.,\ a{i\ SFelte,.^* 2,t>,2 c.^ !-?,2], u.ro c$E

^ A\"\ Lr.\^\s\e\.'.";orr\-

CSt' \c-*rl-! Vo.^, cj.,*.e- Q-e.t\^e t.^ Cz) ctr}- c.. \j"d* oL\.\Uat.^tse-.,^.rc.\ \rc\.{ a .

=) qJc-l ^.., n'* ä I-h-\

^e" -D'

4 st^ [(2"-n)NÄ€"-) L ---r /

/,-, ..--.\ .

iK\^ -r)tl x\I ----_ I .\ ?_)

Page 3: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

)s

Ar^ - 4)Titfr"*a3i\^

o/

\-,/h=l

,A\s <, ,(= \n

\L ,('3.:s--

Zq*.*cr* z^^ {nk) -.i\ -&- (-,D-rl ^ [q.) ^.-i+

f 't{*)= X) re G.,.11=n

\.-tt.- \eo,^..r. oLiq Qelue- gp.-. o.r.!,\ed.e..- tr.*(.Tk-rQr*t-r.^o-Ll- [orF ,2.0.-

\.\LSi"-- L.,t\<-1*ie,e*,

\)

rK\.

>< .o(^ \ -rh+1

\ Bdt = * >_ *(-D $." C,n.'- f rz)d. go h=1 J,

ö

\"=Fäsc-^i*nG*.q>) eh_-,\ u

Y* ^r {"f. hR-x \ 2-u

rr.z z_ ät-{) [ *.h= r ..tt '\)A -i ( r *^ ltr"

Tf z- <-.= ;: -1) cos . +=Q rr"^'.'\-

\^ rr e : a, f {_ Gnf*,t,

.-4 FzZ- u.. ' ')

{

r--, A6C + *" / ,^z \:t) c,,\Ez-))h=1

FJ2

r-:

X=L

z

Page 4: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

u\a

Äaq- 2-

q,o.L "n' C =

(

\,r L

\o

:--.'/

h=1

lr\

G,.f*

Kr Q(3E+

*=.

\)

=--\..t Q r< c,cS

\ :1

AG

F"-

C+).r.,d+€

\.--<- \^za {+4L^^ ),/)

A*\a-*-Ä'. ^^ Sil"uscL'$e-'r

-^ *t, V o,,^, ou\ Qor^" crt ^-^

.Ll \Lu .Qrr.3.X^. *t o{ \"*",-

V"'-ng' \\('-t.n\e-,..,c.t\ tr-n A 5oq-1g "s'bclos .' : \ h:*.* qevecL\\e"\5\

t,s\)V..\trr \2err<-cL^e* .*; "-

_

.>("2eo = *- \ \,">. { dx = +\ ,.1a.* __

CA

:-L *3t'- 19. € -L>ä\-r= 6. T

\e:) c: T ={ = 1-; {'C-,.$-n1 , 3 n2'-\ h=1 '

{,

-1 \eti - 5- 4- 6_nf

*t-^2-- -.- <= L.'z' 2

B

Page 5: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

t-Be^'l*r.er_

^.< .3c

lus r*- beb.o.ctrfe^^ t^lNd.e.r

\x\ -Fo-*, (t. Qo=Z'r

Ir tzr\: = Ic")". --tz

{.C") ^/ A-6?(2,^-n)'

\.k) = \x\ '

Kc(-a.z):

c-o sn)trx

o0

)-.---<-ta=1

a0

z-\^ 11

Qt";+-

B

?

zn)\ ^'.t*

-L

4c3

Aao.\=-L.L

\o

)./ n\(a"-J

g'-

+ z' \+- 2_

"X."_OVu --\

\.1

<-- (<r \) -'._-_----

t\l-)-

\.1 \3z

[\

G2o_^-,e+)

t\\

\-.,,

..3t 2=^l:3 \_,

-lzlz

I6

6\

"=; tzG"-ö

Page 6: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

-z,{. r\

39<3z

^

€"-^)'

.'o

=-:a"

\n= Iu\_i./

B

Be..,,.-.Lrq-

.2-\-

<-tn=\

bsgr

Ria_LJ\)

\-(== a (2"-A*

h=1 -s- )3G

\A6\ g\

(S- c=76'1- )

s-nbs't-

. -i,,- \- <\A6 r\

4s 2{

\o

--.='<-\^ _1

(ta\

D

s3+5-\h")-)

Page 7: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

E

{cq-[d= - tt (x 15) + \' N- (x, \)*'*\'

A t. /' \arr>t\ u\K\\):J V;.*; , ":-(<.X) : e

dk,1tH)-q,\lnLO.rtb) 4. V Cr.5)e-tr2-..f,o..o1 Qi.n

,X. \-,'----1V x'+52-

*ö""''

'b\{

(*) B e\''-.t.\e- E\" + + o

-h*A-r.'

\r'lt* be*.cL.q^

tr+e.l -t*l =(t*q\- t+t)

: t**ai- tr\L _ ta"t)Ca+tr) -- >.rlr+e^\ s \{ \b-q.\ t-\al

trZ*E&+ a[ +Q[ *7

st.\ig.,,-)qa(' 6l =

l"=o ü

c.\s., ,^tc[loUttUc..,n

c..^^re1.lco,o[

\a*e"\ - \qR^oc' .P*

\e+u\+\q=

l,**u\+\ >\

\>+&\ +\+\

-) A*9^*o

\a+q\l>l\\

=- l,\ l'+ +aJ_-+-t'r

0..

l^-rc,& I a-se,.\ f\>\

[]+&\ t\+\

Page 8: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

Re\..-..ctl{e-

.Q = 8.-+ o -Qr

\(ea\u

e - _--a -- -ihl

2+d.q.

eä ----

L-=O

+(t +ä

r'\.. ria

-\3---) A*

-) CI.*

&aLn* o It +e,rl + \>\ 2 \?=\

Be\.o cUt

A = i2,-- ,, .e\-e. Qn = o

E+. eA.-o o llri[.\ +l{

\. t?e({ +-r

I C- fu) ae-c-

a\=r-2t!."+

e\El

=-

\Jt.^tr-

\+l

C l,*a-)

\LlCs\ Q- r"ickL-

\di\+b."

.L^.t u* t\)- t. [Q,o1\.\",r'g;p.-eA A.trS"^U s e.^*^ Fc.lU *=o.

.- r.\ \xc r"-<_x- ,\.Y . t-\\

[o) T=) = R.> , u(r.5) = K) as{x.1) =o'9 B = L +H =" ,k A'ttc\r$"'\$-"

. C -- a s\e\ €frKU.-. {* \ 9 (s\<-f.'5 (.^\.

b* qcE-$>J - o

o\

q

Cu)

ste$)1 t'.^ }.'c (:)2+ a-

Page 9: t^l Ft - asc.tuwien.ac.atwinfried/teaching/... · s) t r^ - 4)Ti A fr"*a 3i\^ o/ \-,/ h=l,A\s

a\J,

R e\--o"t

g"Sb-$*))= .0-i...&;\

qi$ -$+tCe --z--)

e- -"--

o, qt>r-\tu1-- ^-.xw ---^r

.---.

4. J; a: ä -""-t

,.^r,*^q Q- ScD.-^roA.9-- Qj *

h.. C+-\)2*s*-

{t*) - ((r.>1-)z---t>

>-\ t.

-q(t).o = o.

I c.(s I}.-\

!i'.L+\

Grc\

Be*"-\c,n* z, A.\.6.

l>+a\ --\g o, \a\= Ä-\ \^"\

e^!^-lo

t = a(. ,&o+.')G>o +

^ qQA t

=) kj*-=x-9^-t ., oq^

0.X,\ tn"

8"-+ o

es

g

\ei

q= tQn, Q,^--+o hco -) +

L

€s s..i

a,\t<, e.t^cL t^ict^f alrK!'a^r i..l*=o'