More Related Content
More from Anwal Mirza (20)
Chap 10-solutions-ex-10-1-method
- 1. ;1;i-< ’ ' 3 ¢ ~=::4;;9l=r!’1=,L'.¢f{¢ -,-‘PI--'1‘!-5*”:-‘A-;gz<:rv'z-< ~: »
*-~:~ - I =~' » ' > tr ;_¢~ '1-».»‘-.1.‘ . . '- .1-r.=I::.'1-» -'-1..?:"I'."'.:»',r :1‘-M. ‘ »:~ -=';' .I .3; »-‘M at: -.' .9; .'- - '-*=/‘-"~.-‘J .. 1"" »; . . <4.'rj:‘;1-1 . .~»~:' , . 1 , . .. <_
-. /.-'.»
‘vii. . :‘_ _- . ~- F ~ ' 5 ;- 1-7.;-.---v.-,_~_1;'; -.‘€_'.g',~_",'.=.1- j. "'_'-».r' - '- -. ,. ._ »_' 1-,. ,._ V.-., >' _:;-,.=y " ,1’;'"/-'3 - '1 I ' 1 : ' A
' :-. '1' ‘
"-="~,‘_§‘:1‘ . .‘ 1' - -,;"'».~3?.1"‘.‘7"‘-‘Tr’; '3’ .-~.*:.E "=1 - ,~;_’l>='_""»'~ _
. , , ~- - ~*- - '4 , K - - -- " ;-;..<..-- _ 1 . .-.- -‘$3,. - -. , < '1‘ ».';; ,1. .__;~¢--_»;-;,._-_,~‘,, 1'-,_ ,; - ' . ,
1 z ~ V}
.14 A. . . -A . v.w.. »¢~ ..»~.» * . _ .- . .‘Si: ~i»,_ .‘ n v<;:.:_4___.
.
5: 4.4-» - _ .;-: " _r ~1¢"' - _._,.*l~' PF '<,.' . " .'_i?F'§"_-’ ;'..'f' "' ' =
5” "' '5 "#x:+iQ~.=a D }f{j~j.‘;»@5- 1;.
1» F» / * V
~~_¢ r@"~'§§',,»*;,=;@""¢.»':1§§I§3“’ ms’ 1» - , r » . >~~
; X ,. _ .‘-~;,,-_.,;-_, I, fa» .,_,v..,.;- __ , . . _. . , .», - -:-_'.,. - 3 , ,._-,-1.3,. .;.»-' _ ~, ~.: __, 1', k. .»
3; *’ v 'r“ . .--,~ " ' 5“ J?“ ‘ "' -‘l ' &:»."~“ .» ;:<.-~:: ~
wg ~W@,;~“~*~%~W~1,.M
‘ . r ‘-.' " ' 1‘ ! » '-' ,~.>.‘ -: ' -., , rm ,~ 1» w - '- -
' . ,:s!-.;"-.-- 5;-s~...-»»,~ r .'-U» , ’ E 4? . ~<wv<- - I-' - ‘ , ' ~ " ,_ ,, =',_-,~;:.:: -
'%§T"'7”*""’. " , '_?.'“Z:*' .. LII" J = 7 1 - u 1 -4 'A'F“" l57'5L”'1%,:-nzs ‘ M ‘!‘i"§§,,,;,;1'=‘-"55"‘§*+1=:1‘7§§Z43=§¥T'§¢» 13.37.“
7-~,».~-V-W/-" :.<+-‘-’-»‘ ff. 4»-1 ‘=1 , -I —-*A"‘*” > . . ._ , ,§’;,=1,-3;;-<2»;'n~¢=1+.w».r: '1 :-
- -,4':.€"- ~'. ' .,-,-.¢-M -;= ‘.@_;,,., Sr ,'*>:'="~‘~@.-aw1:9-"*r-+¢:@&==:4-,r¢:w¢~;z *;:}%=»'=.i'.~~’»'%*>=r==%€-~=-Y-;=~=,:.=@‘.
=_-,-1;;-}:;:,1.;iy'>.:‘l_ 'f~ ;I;-¢. .' ' _. " 1 7,,-, ;.,r;.;. ., —,~-‘,"f-<",f§;'-Q-f¢;§§,§;: mg.‘ "-'-F-§',--».;-L-AH‘-"7""E"="*{ “ "-; ' ' ‘:'->- ‘- ~~*=.-V ‘ '. :.»".;=‘ -n-:.+’u‘.i‘¢-.,-.1-', -',‘_<~=2'~-=1-» -‘ '-‘i}?.i'?';'.‘.. F‘ »-_-gz‘-57;" ‘.';4:."I.T '1' vi, ._<=,.;5, ,,_ ___, J1‘-_.>:;( 2, 17-, ,4 ,_. ‘ 1,1,‘, .
:
' ‘W? ‘M :1’ I"--4 Q1!-‘lwv
}
-..-» ' - ,-.",}-:5» ‘=-‘£51,: .-, ._ . . ' ,» , PM» ,.»,(_,+ -" .»';vg 5%,. . .. ,4 ./-.-a - '~ . Y
*":"' - '- V '1 ' >1 '-' " ' -I .:. ‘ ~ 523?‘-?*"_‘-"-' *'~'*‘-P“. -H~|'“ -L. H J-"I " X ..I " v . .‘ " ..i,'::' ‘" .“- '<"" ' ..,-.>» . . : » - .- , ~ »- --
-D " ‘ 5 u
;. - , , ' ;» »_, ~ < " " -
" ' — 4- P 6*’ JL ' "-01: gr: ""i| A '
‘ ’:'“* ‘ . J ' n , / _1
D
*O'_ I _ *m,,1C» *
- ' V
.~
1
v z
?
4
1
1
v
1
7
>
I
Y
" '..» L N '-j_g..‘
wlkntl W»--@-~»**-*’"" W 1
<- 1+
5'53‘1%’?-;7}'%fi*>¢”°5_5‘;§
3 } % ? } 8,‘,,.,__1,4__.-*1 M A = +<%*%">"*§‘”‘ ,’
V’ V.
“~
; 1 -
1 Q-D=_m>+¢¢
»
< % L’ 1 -<z::::"’*“ “ "‘ % ~
=0
" ' i “1”“;”""
.1>= L‘-+'¢',
»L»1°=?1**>.'?Z "i w: ' s-"s»+~¢"
I8 ~
I
V j .,(:D__,_)L],-_'_1,>~§..-',-'_.<> 1
» -=<-s»@1/A» 7=1(¢1*§P)¢- >' : ~ ? %
-’ ~
.D‘."-_§-
' L Q>+D'-'-9* , ".'
% "rS1> 1-.s==.1>+v- &=<> %
x *.I$+ :4-O - L
‘ D 3 V I .
. .=<'
.-,__ .
I
‘v
1
J
§
3
1
I
I
1
v
3
l
.
I, . -0,’ J1” >.
“ill I‘ , ’.
a
' " " 1‘ é
4‘ 4- —SOI“ =~<1I<1,‘1-=ELv» . . = 7 O
-;- —%1»~ %"1i3,~,,¢1>¢@1=o&% 2
; A
1% ¢=="-‘; ‘ ,
1+ ‘ '2 t J? J5 2 .‘. , , - - ~» -~ - ,_ ¢>1 -- ,,~‘ -_:,;'-1-f-1,'*; ';, -.._ ' V , _. -- v~ .' - ~ ._
.2 " Q‘ » V ‘ I . ..».!- ~"-'$"i»~_'.14=:5>.:-Y - ¢r.~- ‘ 4, ~
. -, _ . - - _»_ ‘. . . »_ ,~.-~~... -v h W.-..;-.,. ;;=., , ,
» -J-';.--J 7*’ "' . * ' 1 . _ = II) """ V
. .,,_ . , . , - .. .
x s I - v
V "' ' I 1 A '
. -%
" @
. -¢'~. »
,1.-(7 - <
'- -..»‘. ',-..."~. v ». P $;.~.,| -1 ~~ ‘- -1-.
- '- _',vw;‘;;1‘," 1" '~=-.>:<.‘,._='.': -',>,' __- __. .! _, _,.
- ’ . - '- “ ' ' ‘ " .. K‘ . "1i'7"'f~".';-".<‘--,
' . ,1“;--~ ‘.-3-_..?._11¢‘-_,¢:Z_@‘_( 5 .4 V1.5 j ‘ ,‘ :-_»,§ ;~.-- . ..-, ;,. _ -' '.v' I
m N _. ,' 23/17. V
5; ’ 4
* ~ I 351?. M* * ¢$~»>»+~€:,$"+*%** 1
' . ‘ > . ‘ - _- .' "":,~.' ;- - -» ‘~,'»'_.¢: . _1 ..: ' -. 2-'~1_'-'.".~, ' '» 1'-»:',_.' "r . .,-_ 1, V‘ ' ~ .
,, » - .. >3-;,: 1 .' -. .‘ . ‘. . ».1 , -.; _‘_~.--,.- .11‘ 1.-.—-;~-=';.,-., ~
- "4-_ ‘V. ' - . - ‘. - .- .. . ;.,;-'._,;’,¢r-_,,. ,’.v. -,-VI. - |‘,,_|.-4-1-».v,I.~;_, '1.-F.» -.; .. 1.-5 ~,..-:~._'_',;.1,)' L‘,-4,-, - -',"‘;, ' » -_ .v . U ~:_-_
_.. ._..,...:.;r,_ » . -, ;~» , 1-.‘ ‘_‘.~‘,',,__,~,;;4| >_- V» '. -.~ ':.-av: .1 -.- _"' -'
». _, , J,‘ .1, ._ _.),A,M.n,-.».;.-,4; -1 . - - ‘ ,, ».
' '...~_'. - ~ .
~'~. 1' 1 " 1 1
,.__», __ . ._...... .... ‘. 1 -_'__.;"__;g;_;_;_;i§§¥__5‘=’;,;;l-_.;_;,_ _,_'.;" ,'. 5‘ ' 1" - --" '1."',',_,‘_Q.'.§;;.--.1 2.“. . ....;,-.:.-. . ' ._:.,..-.,..._._,-;..
‘SO ‘ =
. ; 4-/4-f‘-_"‘;vfI’{:-|v:::?_'f:{;:”:%1_§‘Ef;_::-"?.__ ‘ ' 4- 2 .
» -A" - .¢--@§..'.1;A-'-.:::r'- :"r.-=.§-1="<:~*f~*~=.(@->1-#1 "»~"'*-1""’Dé .n-9" ) " ( ~. .
,¢_ <- ' -. ~.-.;'3_r';'¢-‘ ‘:".,'f_'~-‘ ~ ' ' _‘ .' . 1 ' I
‘ _--.,n ;
. .. ....-.v..-... -.-:'» '
‘i
,J
Exercise 10.1 (Solutions)
Mathematical Method
By S.M. Yusuf, A. Majeed and M. Amin
- 2. @. . . . ( , , . 1
‘ rs,-J - ‘
. ». , . -
1'z1us»4»I~°' a V351,‘-A $4;/#»M~a-*>*¢"' ;2%&EZ¢/.:i|:»§biU(L‘17C"h
A
gl) ~;'AL'*(¢;§'+¢:B*¢%+-#+*“*"'*‘°=' ’
n
~ ' Fw>'-
:-pl , -- _Dn_mt_D __"
Iwwl M "¢ *7’
1 %A % - i
n_ _8 n b-7; ,---1.. ‘ -E-»__ :- B71-_ 5"“-’%__ FC_‘0>_"0 '
'>1><=~¢‘>v »="~<‘=>‘ %°w»,%I%*§?°> F“) ,3
v‘:i)“,F..(D)(-:'7‘)=a.F_(L’)"-‘gin H. * 1‘/~'»»..Al.-“-421.1% = .‘?!-_(°~*’- >" ‘- A 79
v1 b’§u ;; 21 DJJD
Fgp) J "F5-'9) M H’ L V
uzF)iD<¢¢ . ’ ++ (D 5 "i %' ' Y ’ =1-e’ '$‘Fw':p‘
' '
bx "
=4,>w;,,_. '..Q’-":__ ‘I '_"7’?5)- I '
9‘: -- "'_ ,.:.: _" Y ' I ,1 , 4 . V ‘
~/UFCD) - pgglrb)
flu‘) ‘.“@’)nI' Q,;“on(
Fen)’ %
Fc-4*)‘ '_,,¢n75,,f;4>"
..-1 _L_§_05(p~1).-='r } -‘
v¢1)F({D;) F-c_a__2.)
_1_-_§M,,l ,>,,,.’z.. <1
+'-) ==
¢ I(.$*5""'->'*¢‘°"-
:>L='**"*i’¢‘_"““"}('-‘*L):-v.f'~ ,9 '
<5--~-> W-*"4”“
1W1;-1-"~bW'**’L A
;+vm_+rL'Y")?<-'F"4"“ Y.
W" 1 ” ‘Fan; j 11 'F(i‘b)' ' " Q;‘;'..',-.,;.;~.l%Fc->Y'i#l <»n- T‘§="5"<;#?""°"
»>_;;_@»é'»>$
.= RLF-55¢ =.-. % ' _,,L,__ $,¢ f:,r,=s, ' %
-FUD . A ~ ~
2. ’, ' 1 V ' . . ’ u
at '
N) Dzceakl ‘.D1."
m'_majh§RY.OIQ F
><i»)%D‘$‘»1=»* =: @"")§’.*“.&A’“}J-»1'{b.f V
- - A» A. I ~;
gm;-1+-‘5'">£"A.'¢' :_-£1-6°,‘ “< bi
-1». '_ __ M-.,‘_:_ ‘ _ -
‘E. , - "
, - I
- . v
<
‘ 1 '_I'. . ' I‘. ' ' V,
" 4.) ‘
‘°‘1YF"
(PI) ~°"1"-‘"423 *' “ V
?
I