Sect10.8b - Wm A 5“”ka =02 A=o WW‘bao =5 use But 44m...

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Unformatted text preview: Wm: A? 5“”ka =02; A=o WW‘bao =5 use. But 44m: dots "0+ wsfib We 8.6. 'ux(a,133:4_(®_ 3° (1’40 1% mat POQQ‘H‘C. 039‘: \{”=o =7 W137: A+B’a I ‘ ‘ Y : B :0 z? =A (Wen \(‘hpzo fim am '5 $0 +ke owm 13c. \f‘(b\=o 2% santh ) x”): beo-x, and X70): D =0 =7 Knit-C. 3" “chip-4 AC = co (Maw) vs a Mammw mam. 0:29: my: Kawifing-r gwgma, P ’V N ‘ .- th): Afiwng-BWs-‘nl’ég Do’sflfl [how «*1 So FundameMal Same/rs om. /0.8p.18 This Mar? Saxth We nmhwnogenm [3.6. 11,01,115) 93(13): u‘xahfl) = an Sin)“ (A? 60$ ".713 : £93) MWMO q60,51§:© (Mac/LA a,” 1 ' X Y 03;: M,“ X’YIYYU:O X i; ‘ ‘0” ><"+o~><:o Yaw, O Y/dsCD i(3_© YGUzCD Y 0 # CO’WSFCIP ‘ I ‘ ‘ I f‘ X Prdb/em ‘ 'T'A/b rs qn eyenuq/L/e. Prob/em ‘I’Kofl- we. have. geen several #‘mes. I105 EEO/04704 f$ A _ Mn: 1?». SM"??? 1,2,3 and gr, Che. dupi- “1?: be. ale/#erm/eeo’ .q 1 . ' (Jay V 3C7} san—LIYBCKX ‘ ‘7},y CosCh-I; O ' o a 01 q fir n j "'77 _ fl ’1)‘ \ jug fiCob(-fgy)0l)< ‘ (Org/147‘ C05 7:1)2 {35147008 or 3 y o a a 0‘1 MY 9 2 "'77)‘ 9/3 C? / I277" Ci 1 vest—n71? C 5 38 +0 7%.?) 5’” “3 )L ‘0 +377 03(3 )‘(m'rj 314(12 1 "O. Q 6:) $14(;3~O*é% 5,5617) +éflfl’ SM 1 c2 6%) 6%? 117 C - 1 Q EL)1 ‘ L/q SM (9) " a w ("11% W 5'" a» w L” @646?) a 690% = We») 90C "3' 02' (m [(20 n47?) cred] ; Problem 12 part c > u:= (x, y,m) ->sum (4*a/ ( (n*Pi) A2*cosh (n*Pi*b/a) ) *sin (n*Pi/2) *sin (n*Pi*x/a)*cosh(n*Pi*y/a),n=1..m); a sm -n 1: sm cosh 2 a a u:=(x,y,m)-—> 4 b nn nznzcosh[ J n=l a > a:=3:b:=1: ' > plot({u(x,0.3,20),u(x,0.5,20),u(x,0.7,20),u(x,1,20)};x=0. .3); 0 0 0.5 1 1.5 2 2.5 3 > plot({u(0.5,y,20),u(1,y,20),u(1.5,y,20),u(2,y,20),u(2.5,y,20) },y=0..1); 1.4 1.2 0.8 045 0.4 l 10.9,9. 2.3 > plot3d(u(x,y,20),x=0..3,y=0..1); OO O? I-‘H It. In this problem u doesn’t get as small as y increases as it did in problem 1. Also in problem 1 u=0 for y=0 while that is not true here. The general trend and shapes are the similar. 1 10.6 p. 2‘1 2L- _ Y” - >< ‘ 7 0” X”—¢”%>C5 \f)HTY=(3 «who \//0\3-O mom: A A A YA 3X6J~ 6X6 3 was: <9.- 3 +2; :3 22:4; , b , -A b - fl - V (45sz a 6* -exe b .31); 5* 193:0 sv \yO V 6:0 ” ‘HNMI sa/cflvvn CQSBQ 0:0 Y :0 :3 Y: +1; A Nt‘Cll Saldhdn YRS: E :O Y’Cé); 8:,0 ‘fY‘ +\LY:O msw Msmfléfi YMX: 3:0 Y :: )GQofiCA&b was: MmOABm flzo or mambo ’h’ w m. 6’ sa/(filTo'n cobCAQ:C> :3 [MO : 5921+“.le :7 x; 52% m, n20]? J l I 55¢ pquLb C4: 3/35,.g2 OW: SM 3%??? c/g d = - ' - ‘4 (ab 95L) ‘9 V: _Cél§j§7f COS ggflg éfif'l 1'7 mum 59%'g”\<:o~s(a7flffi/ + {‘25 c954,?ch 33%,) 09 0 .3 +5 _ _ f] , by Pan 2’ ",4 o w ' , 2 15 3 9331/») b : O‘O +‘2 (QnHM'J/ Cog) 9J9 U0 0 1o -2 (ca - cm .1 1(éélrgw3 {104,442 9111/ 1y) 9' b [mamas Problem 13 part c > u:=(x,y,m)—>sum(32*b‘2/((2*n+1)“3*Pi“3*cosh((2*n+1)*a*Pi/(2*b )))*sin( (2*n+1) *Pi*y/ (2*b) ) *cosh( (2*n+1) *Pi*x/ (2*a) ) ,n=0. .m); m . 1(2n+1)1ty . 1(2n+1)1cx b2 sm cosh 5—- 32 a 1(2n+1)an] u:=(x,y,m)—> (2 n + 1)3 n3 cosh[- 2 b 12:0 > a:=3:b:=2: . > plot({u(x,0.5,20),u(x,1,20),u(x,1.5,20),u(x,2,20)},x=0..3); 1.8 1.5 1.4 1.2 1 0.8 0.8 0.4 0 0.5 1 1.5 2 2.5 3 x > pl°t({u(o'5IYI20)lu(1IYI20)lu(1'5IYI2o)Iu(2IYI20)Iu(2°5lYI20) },y=0..2); 1.4 1.2 0.8 0.6 0.4 0.2 Ilmar-Zi > plot3d(u(x,y,20) ,x=0. .3,y=0. .2); . . . cowgmmpwamm o 0.. 000° HHHH o :( 10.8,. 7o] ...
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