ENGINEERING AND NUMERICAL ANALYSIS I II ]ceng.tu.edu.iq/eed/images/2019/Complex_Functios... ·...

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ENGINEERING AND NUMERICAL ANALYSIS I II ] BY : ABDULMUTTALIB A. HUSSEIN

Transcript of ENGINEERING AND NUMERICAL ANALYSIS I II ]ceng.tu.edu.iq/eed/images/2019/Complex_Functios... ·...

Page 1: ENGINEERING AND NUMERICAL ANALYSIS I II ]ceng.tu.edu.iq/eed/images/2019/Complex_Functios... · ENGINEERING AND NUMERICAL ANALYSIS I I2] _t_\pert\/attu( o{ a Gm i

ENGINEERING AND NUMERICAL ANALYSIS I II ]BY : ABDULMUTTALIB A. HUSSEIN

Page 2: ENGINEERING AND NUMERICAL ANALYSIS I II ]ceng.tu.edu.iq/eed/images/2019/Complex_Functios... · ENGINEERING AND NUMERICAL ANALYSIS I I2] _t_\pert\/attu( o{ a Gm i

ENGINEERING AND NUMERICAL ANALYSIS I I2]

_t_\p e r t \ / a t t u ( o { a G m i<x Fvtrct ion

L7--+o A -2-

Supp<r5"- lh^* o -*pt"X Fr.^^.tlr* f(Z) is s'^qr(VaLu<A i,r't F-rn<- t?atan. -P llrr_ &mplc( ptawe . If.Jde,ritahnc .P tt*l-t denoL.) t"5 ltU r'is d.fi,n"'{ as

E X z - \ lse- -l1nq J-frri Lt"^ ,l ind lizt ; | ",{cz ; - - t -sz

{t Z* tszl ' ( Z.* AzSt-q ( Z+ AZ)'= Zz + zzaz v(47f - 5 z - 5 Az

/ / " 7 2

."" Fizt - t- ; .^ l (zzozotazf->4-saz -r ' .F4DZ- -> " AZ

'...

= L - - i ' 1 a ' { ( z z + o z - r ) = 2 2 - tAZ=2 /)4

. ' . _

; R . i l e s - { . L i r n i l s , c - n } i n . a i L 1 , a ^ )diffev'enLi^Eto ̂ lav feol Foncli"A 5 caw be-ayylie-A &,2 c'..npLzK f,,rnc{i}yl5.

An a lyh-. Fravr c {-,> r,r awcl Ga,tchy -Rle ,n an n Fauattt

A .-.-p\ex Lr,tvtct>"t Ul= l(Z\ i s Sajd E- beantt lyl ic ab a ?oiat Z" ; [ { tZl i s / i -Ffer.e,rb' io4ol<_at Z " and AE eVerq poittL ir,r Some- h<.iqLtoor fr,ca-J

^ U l c Jo-+ Z"

_r]- /- t \,

^Jfi a- C-<"rchy - Riernarrn ez1r,,r.a Li"vt s pb$ jr{e o Lest4or'fhc- anorlshctE3 "t

o,, r-"'.pLzx F,^,^ c}-t * ,

1 : . " . V+2ZAZ

BY : ABDULMUTTALIB A. HUSSEIN

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ENGINEERING AND NUMERICAL ANALYSIS I t 3 ]

A **p\cx Pyylsf;on is anaL'Xh'cC-a"cV1- Pie*qr'ryr eluati>vt 9 all

i F f r " . & l \ " \ l tyrqsqkspi<J ; "

> v

P . " - f " . l c z ; = u ( x z ! ) * i v C x , $ ; , a Z . ^ l r i a U{ {z* xzS = L4 (x+ ax '4rbY) + i v(x+ax, bn ̂ 3)

$iz: =-?L*'#

3l ax =o, {V, ,e ,n

_!!!

-v(X,

YtaJ)J -pu t t )+

1 " .^ v(x+ /r1))A^-> o 4X

)

-+J

<,Y

U+ aJ) +i v (x+D^ tA x + i a Y

, f fr-e-^.a I

AA 2 Y)- uLx,Y) . ' ,

bx-;- >" I

r l - -z- I - \X>x_l

AX.t

(x+

, / t - . , , , ,

#(z),-L---,,^L"\o*/)x-> o

a8-->o

I ":rf '^Y -

l , i - , ulfLZ) '-L--tYi. -I ^ .x -+oI r-z- ^i ; . l l ( 1 , ) = J

I t r - \ | .

f(zL) = l..-tuv-tay _-+ o

u LXt 9+b!) -uLXzY)

i a b b5-+o

,t -l+ \- | -1 t /

Bg luatinT*t,z real *.ld irna/rtarg pa,Es .'{ at

G) + (#) Nz- abb'tnt *''q+' ""

> Xa u

- € -> l,la x

' /U)l+ by) - v(x,y)

>v .l5 t T

BY : ABDULMUTTALIB A. HUSSEIN

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ENGINEERING AND NUMERICAL ANALYSIS I Iq ]BY : ABDULMUTTALIB A. HUSSEIN

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ENGINEERING AND NUMERICAL ANALYSIS II' ]

BY : ABDULMUTTALIB A. HUSSEIN