F swr tet - R eiLe

(1)

9 L 4

{cx I lr- Periodisch- A pp*^i nratforr- c{lr.,ctu

trig o tL ornefriscfues

r}(on eos rux

[ = l

F s w r t e t - R e i L e

{c^l ? * -lfoocosnx+bncrftru)

_lL=l

B e i s P . 2 ( - 3 ' t +

8fue>ako {cx)=fI- ß-2hrr )

a 2 h r 1 x < 2 ( k + 4 ) t

, t 5 2 '

{ c x ) ^ ' A f r c t r L x

I

{ctl *

Po(y noffL

+bnsJrun-x ) ge

z

Dacste€-Lwtg da.c-lu

N=6

(2)

{c^l f-pariodisc[ , {c^*T) == fcxl 2

2e -\.g

'Säfa"oh'-

o + T - T

1 n , - t q-3n' r' f I

J.fcxl d,x = J {cn at

o - o t T h

a f gomdc, /c-x)=[m> o Jgt rlx =Z]otldx

s.f unge*da ' fexl=-{rrl -

rfrr d,x = o

(3)

Buug.S 4*l= rr txt-jx' - T 3 X < f r 3

arr aerisotis

gto{' + Si<o

-2r _-.lr

{r

G o =

# J+"ldn = + = ? , n

o

r

[+nr- f t']:

e.=# I+rncrDttx

0

= ä [ -b-

crn *x + $ ri**x r F,^ *- (r{- *)'tr{

= F ( # 1 - r ) n + o -

$ r - r f - o - pw-o -o)

= - a

lL2-

G.

(4)

+ D ef i,nr tioru 'D t zLa'L

{

t1=-0,1L2-.

o

, ,,t *tr

b,r= h I fot cil rrx dx

&i. {cx> or{ tqarr'l d+ rund- iru+e6'ie'Sot

4 2qrl

oo- il J {,^l co,s nx d.,(

IrL-4 t2t---

0

F o wt i er -Ko e{f * i e rLteL

A

I r 7 (a-n t 1 | 1 - l cos nx #bns'i" rtx )

L l ! = l

Fou"der- R ei Ie w.'' fcx> -

,n 2Y

ö€JYL- ^ | t1

oo-ä Jfcx> Äx

0

( WoM- o,: #j+,r, c* rrx d-x n*rl-

b n--O o

^= (r2, --

&L- O

* n- 0t tl --.

ün = # .ffol cünnx d,x L4h.

o

{ uagodc-+

(5)

233-4

Sate s.1

-T

Koovet qi

s

r t /'\ | ^ t . L)

Wp-l-t ttdot rn&Yl aN'a.-

, a t . t o

t3(Lne-r-Ke,rkq_ ?

urt dir-Torrrzv-Reito

Fr

f + Z@n*s rLx +b,rs,rorcx )

gLeicnrruö-pig,

?pge', +cx)

\ ßc''.

*+ [o,err]

g{r

&w=# /+", coD rLx Lx s:o1112

. q t ro

br, = "l fa*, at n',rx dx n=lr 2r --

o

$ lrad oose-- Cn'tqraticr.r-

u^d Ad+,,EylsrilLa0&tafs &zohurgnn

(6)

4

Irr+rL

/A4'-l:L

l h + t t

lk= lL

wx= 0

c,i.lx1--.

0 r [ - L , 2 r - - . .

ET

I r f o

J e f J n t x - C [ ' ) n x d X =

1 _ .

o L f r

21r

i

J a u h h x . ö t | \ l ,

o [ f r

LT- i , n

J cpontx a*nx dx = 0

o

4t

F t -

J L L ^ = c r t '

o

ar af

n f | .

J i c b r L x - 0 l ä c ü n

0 0

I

t , e x D x , c r n 2 x r - - - , a ü x 2

or*ho gona{ und ruor wiert aqrr

(7)

Wh- n%t meL, doP f,cxl Stu.r'a-

+

&1fisr_7orrno--Reiho- b{- ? z e . k 4

W"?? Sü"L-f *d , steLige

l.t -osns-disc[aFhh.- rl'"S

I

d.,wsel-6.u

'f c*t= gc^t

-ff;, aWax

Fou-der-lße$bznh,a

Avuoe"c{"oA^' tr"|-f,cx: a{etig,2sr:goncd..

u. hmuutr3ior{- Z O se^ru- Fm.rier4.eih!- ""t

fo,9-tl ..32ac0t*.pe reo hnr.r'<r3io/r

sta- trf" f,cx) -

W"/.ßoisg,'el-

8oE- S4i qg-^; otta,Suff.nr-dt tr'"ri*Rg;k

(J

Dc.wn Scxr sl*6g ud- ru-cfl &h a-t

ttoL.r.?cxl u^,t jcx; daasells. franen

k?$e-Küede^.

(8)

Eao. Ea{z E2- : %.aS'^

g

4 ln+. "Sä, oil.-io*a -"{ar-kb'c.p -o

+ f = o '

fu f+u' J t g l + o & - * " $ e ( o , e t )

ogdÄ f(5) -c >o -

6rbK f>O rn.$

)>i xet${g+{

0 < 5{". 5+d. <2t.s-f,

g=+tE)

B+f,

-[ tx)': (4+cncx-E,) :*C) ^

*$onorru4c Po$ nnr^ ^

J}errli.cxl dx :o

5{ o 74-

I,- JfrxtTicxtoh

ö r ' -

{nL

ll2t+11+l < +

6 * 6 -

lr,t +1r"1< ä

l - + o O

I g > e o (^ ä

f{ S-e- 5 E-{ E*d I , L f 3 & r ,

f,+ -+f" 7 9 ^-.{/

ls.qs

'"'tI? .f rübr*-, t^/. laq Hd{.. Fdfi .{Pfosihr

(9)

2e .+,L-

xo Sotuno _t _dste!'h- s'rA

f(xo*) - = .{i^ f cxl u^d.

X + X o X ) X o

oxt'sfier.err

fcxll -f,,o ) Sprunghöhe

-€(x;)

fcrl str,rck ü€r se" E +.{'t}

on{ fo,t: , ,jrtrts a'k?i+

trr.d, s.l"+} bi\ *+ erJhrX

vi c{.r *9g ruvr 5dtQL.e-r...

{cxl stü.k r^rzue *+"+,b

d(.[erenzrr.bac o{ fa, L]

&ü. "ftxl o"kä+ m,t

sLBbis ar{ ud,!icl"

vta.0i &pn hqsle{ft^

l u a

fcxt , f{!s 5

f,cx;)=kf^,

x 1 x o

cxf)

J , J

(10)

&gf -C fr+04 s{e-$,

- 2C.5 a

*4"ärr*l sfuck bots{- &hl"D,. {{en^zr"h.

l.tns{eh}bri+ss{s((r/" n'"ll' ü .Bnd-tr.**g k}/.r"

DuA,r,L oo

fcx I - $ * ILn"cos ltx + b,,s _, _L ü^ rcx )

lt=l

Wrb bewe.ist

l'utvu rerc-tre.rtd" t

26.k.3

mr^l(L {* (ormcq"rce ? l o , r l + lb , " l

1'rrt qOa^"N.nuäßiq

u t o

W.ere4. ^

&"r!!"xeR.

--- o

' . 1 .

hi aLt- ortoe,r.J.b ar q+ Sn5*ur.^

(11)

,14

ßa:. l"f'txr1 . H

S- /l,."

0 = X o - 4 X r ( - Ä 7 = 2 ' l l d +

It^l es-h0f+ u"d steh} a$ (xx,xz+.,)

f'cr)t, o *l cto>)e+.) ad"r { ' t x l < o a , ' } 0 < a : x z u )

ol? -

fiGr =J P,n wnrdn

o

.F:t Xw

_ T - ( n

L ) lcxlcbrcX

R=o Xp

dN

?or+'t{qS-

\> ,t ,n ff,[rn iln'] - L-

.r-l

L=o llmfin*il"

IL+',r

( t

X 5J N

k:o (+ xp.

\lt"{iSar*t.tl

: O _rel

L=o

z

Itru

tsleKäl

"r^ |

1_- \- )

/_

k=o

lJ + c;nx dx

Xp

[rt-ar^ |

:

z

.a- I

- , / T

h = o

f,f1

r-t*"ili: {"mql

(12)

2C.+ 4

$äguo[n $x)= ri- x_&

Frkvitr-RqikL 7

h = l

Be+oc o

o< C<!.

2-

o e x < 2 t

fr cün ttx

IL

Z t ct'i^hx

- cntH+I)x t " " t ' n

* cos(rtläx) + Tliflf*... + g!rt*)x

42-

ir\>n

i";111s,(x)-sxrxr)= z"l^ra(E$x * .-rH )

' garhi{srhh a- S,.cx) =

Ir+l

lt+2- ^l.\+g ^Yl'L

üüeSl^ 2 oln*,rütF.= c.ta*)- cq)to(tp)

. #r'* *ä,tr-' ) < e $- nrÄ/.,

lEncxr-s1urf < lti.äla < ri"$ a

C < x s 2 r - f , , n > t > A /

a^ gO^clnäptgaKrnrSoet arrf f$ in-CJr* scx)

QCI,.rLtx^-* trkgl$nb "-4 f{o: oo

jst+l d+ -Z i?curt L+ J-fr *** +L

o l t = l ; ^

l t = l

$ütiltÄt&s diflrre+rlttg^, I =tlx-*xL+ö ßoi'p3

Scx) = rr-x a{ ECnl

Fi. t'r, tt-t.r t.,f

T;UF sffi:

(13)

or{ fo,2rrl , + *d{'rü} odri&A}*Un**

Dar*r.

- f,cx) f"Iß J d"b oa x

Kcr,w6erz 6Q^d.u,e|bW Fa,[1 SQk*

dom ) rlehh {w e{.+5 arf ra,L1.

ts{.,r. Riüö'b &t QJ.^h gcx) = 1r- x oex42r

xrr--, x*sgrt gsk0&nvc.f , 1,,-,h^$n5G{tc^

ftxl =fu)-h

)(x-x,) - -- - h $(x-x^y

i,i,-j,; ) = {r'I)-Jcx; ) -hn *Sn - o

olr" na,l .tb &l.m&fi5 & ]"r,ol^cr^,4

F +,r, =icy1 ,,.1.ob*n.ä4cctL

O5zrotre--

Sa{zfr! frxl lt"pmo&"&, s,luck use'*tr3

ffit .,UAo,; -l"S difle.e^m,u-brc

d

*7ßn cD nx+.bncfux = 4!CäP