Sect10.8a - g. ,_ éy-zqoo:ru+ro.+o we . (H “uni W39 =0 ,...

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Unformatted text preview: g. ,_ éy-zqoo:ru+ro.+o we . (H “uni W39 =0 , 061,465 0434) “at-gore u/kb)= 3h) ul0,3)=o 11mg) = O @ SW04 Cb Vawauls: INT, '3) -.-. X0” ' Fmst, Mume W Wm We, Probkm X. Came-cm we (mes rzol 0-70, and 0'40. As hem) W.Msu1‘t 1‘3 What $70; and X“): A003 Wx+ figsm {.331 v (see secaa,‘ {0.0 %2 3‘6. (M X “ Wo)= A"--O 5> th= Bsukfijx New SubSCA—uk m \MML {or q" M40 “We. \< ebuoduW‘. II in} Y ’ BIZY ’0 Wow-=0. & COA‘HHoLeJ (E Bo Wefme Sdmbcons one Oh wand): 3m TE" Sum £13 n=lz,-.-‘ CL ( 'x o 2x 4 4/2 'L) = 3 a‘i “’24-?! 5a. 0‘ 2 g - mm: - (75) Sw- -——- 0”” a-smk’E'G—E O (3 a ‘71 Z 8‘! Std [n26 dx 4‘ ~ rmb a a' Sunk 1 a //O.5p. 3 7. '- «- ( (‘03 rm ’ eos 4% HTT- 0'2. 1 ‘l + —— cos - 47‘ ‘ v a ‘ ’1'“ INT (“Tn a [L 2 z I Z an: 003 nrr a " at - ‘ ouswq ELIE Z Znfl" “MT 5411' a. 0 .a1‘ a1. F _— ._._. (303 MT MT. MT 0 2. 7.. L 3w» 4;: .‘L + .4,— 2’ mm" Mm" L LOW-‘17 Problem 1 parts c and d > u:=(x,y,m)->sum(4*a/((n*Pi)“2*sinh(n*Pi*b/a))*sin(n*Pi/2)*sin (n*Pi*x/a) *sinh(n*Pi*y/a) ,n=1 . .m); m .(1 ],[n1tx]_- (mm) a sm -n It sm smh 2 _ a a u := (x, y, m) ——> 4 b v n2 1:2 sinh[n 7‘ J a 11:1 > 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=O. .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.. 1 O. 0.8 0.4 0. 0 0 0.2 0.4 0,8 0.8 1 9 {laapfi Wm > plot3d(u(x,y,20) ,x=0. .3,y=0. .1); o . 0 00°F} PH ,5-.,,5Ilrlllllll ,.,.,x:zg§55: $55555, (Mme) $ubsfi~lwle Whig \mflm‘. at T uch we afiuccfia“. \I"_ (1211': __ ‘ IFY ’ O ‘Hbfio. J “v 3mm 4w: W: eabum :54. u Ylg) '— A east» “33 *— E 5.514 433 V‘ a» W A > 9‘ [[00 nfi‘fluec‘ :u (0.8r- 7'] V 3mm Bf: tor \{ [‘3 0+- ’lfizb’ma Ohm 13=O , d? CS mm; emvcnwn’c +0 .wnuz. Yhas: 7c b.‘ a: YMMV ‘ Anew" a; 8). + Ens-m 3%(5'13) ( may \Hnat Cosh (has) - 303g) wand - w 5 3w. 3 (‘cnfiwd’ Gen/1W so Wt M W jufiE mulhptomg casing and $uLh’13 kg Gems-flunk; BMW {)m gml.‘ {Iowa}. Fmdmen-‘ul Sci/och ems am. . rm‘Uo-\ 7100643).— Sat/(Ea? 3M 7 #6 ,Yl‘I,?) ~ Tl' Gnanh!%f - a E. 8 WI) 3% 9\ “T05 747$ ((0.3%? (6’) am + %ur F #7490 :0 ’ . (‘40) 0‘94? u(r,o\-:o wan-<0 2..» La u m“ ulaJQ: £093 01:851- u=o UFO ) Asmme u 1‘3. Sunle mama W bounded MAM SUM-60W Jugch. _— gem/mum 06 Van/Cables: p19," H—{g’ “12:0 GD” 4- r (9 = o (9(6)=o @(n)=o We 0- usws we (9(9) PrabW‘. is? (9/03: A-Gaskme +Bsu1b‘f539 ‘ em = A=o ' ?—7 (9(9): BSmkfiPe Gm: fismkfi-‘T" =o =7 g=o :7 (919320 We. mules w M. u(a,m=£m- so No Mot 5.5M V30 6(9): Glo3= A=o =5 @19)=be GUT): bW‘O 75? two '2; G(8) 50 L12: Possib‘e 0:? 6(9):‘ A905 (7119+ We Gm = A=o -—> (919) = (ssuk P9 (301): BSu/LTPTT :0 a) {gm-Wm :7 can? rm? ”...- (5193: wt n9 ',n=1 n 2 J)"" NOOH‘H‘HQJB New QQmSaddlA we Prom {m Rm wJfl/x T'= n2: FZR” +pf2’ ,nzfa:o Eulm Eebuotbcw,‘ M baud-tons at 60% [21(3'— r"A $°W4 {30" W“. J I - / m-Z En): rm ‘ {2mg mrm‘ . [2'm-— mun-hr _ I u g r ‘l r‘LmUn-O rm‘z *- r‘rvw”M -ner =0 g m Z_ Z .. >r [m nJvo a) m: tn n=s)2,.._. Sold/tans arm n BARF KY‘ + £6“ mvlz I ))"‘ ' Sand uCOQ) must he bound} mswud we SWJGWS (en, 03 W95 Esra/ma Wbmed-ed as r‘ ’70. go Rn“) r. )Llr" nzll?’,_._ m dehms W {20) 9W. Fund mad-M WWS ‘. unme) = Enm 6J9) = r“ 3&7. n9 J may). ,_ Them , 00 n U(r,8)= Z8; 5% m9 n=. U“ ‘W 3c. a6 r=a +1; SOUR 6m We mmas emu umje): f 0K0." SLAHQ= {(9) Tr z . g7 ena" .. :fitg {)(93 Sub n& d9 ( 10.8,» 11 0 [Coflwd] béL paNLb 43’ ‘ . Cr,“ 3v, f 679-92) $160195 0(8 a>rIT¢9—92 o‘vv’ 8/5618; C19 470 c) (jhcfi‘f’aé) 019 V: ~%c05(n9) '7 «r d COCHQ “wage ‘3‘”:‘72' 0’9 C) [3 af‘b ‘ &'p c/qz’adg V: 3,5619) ._...—’ n4. ‘77 '7‘!” a. . ‘ ,r (46:9 ’3’ [NW]. ’ COECVIM‘I' %Cos(03 + 81;) CWQXLT" {a 5%? "' o 0 o 2 W N ' 9. _ .3 m ~31, 0) — 1605019) ,n/qn ’1 d L] I) ’2. ’2. - ._ ~ 1 2-" “’6 CoSCifi/v + “EGGS/03> _ r7 5 ” C, C A 3 Problem 6 part c > u;=(r,t,m)->sum(4*(1-(—1)“n)/(Pi*n“3*a“n)*r“n*sin(n*t),n=1..m ); u:(nnm)—9 E [4 J > a:=2: n=1 > plot({u(r,Pi/6,20),u(r,Pi/4,20),u(r,Pi/3,20),u(r,Pi/2,20)},r= 0..2); ' (1 -(-1)")w sinm) 1M3 a" 2.5 1.5 1 0.5 0 0 0.5 1 I'~ > plot({u(0.5,t,20),u(1,t,20),u(1.5,t,20),u(2,t,20)},t=0..Pi); 2.5 1.5 > plot3d(u(r,t,20) ,r=0. .2,t=0. .Pi); //0.8‘/). It] - ufr 4' 31;“? +7151uw :0 04(40- ‘ O‘G‘K V 71(00)=O~ amen): o L circa, - ula,9) = Q9) . ogétgd V' ' I O- Glo)=o em: 0 239 “fine Prelim {m (919) +5 alum r. 5 3U“- Probw (é), 0—:0 and 0—40 GWadAd$ We 6.6. at— (wag. __>_0: Cam- Amp“ swims Q[°)= 14:0 é Gimafisuirée (90‘7" Bsu; [134:0 :27 F¢= m‘fl', n=!,2,.-. Zn / min?— Then Ffz*'r[2-?IZ:O E V | .‘ ‘ MAR/1 E$Wt¢o~ J Ecr) : rd“ . swgtfi’wlc 411th) DJE. J Pz[m-I)(wn rm" 4» («(Mrm“ _ nan?- rwx =0 d2. , ,_ m 7'_r_I:TLZ ‘9 P [M d7,1:o M=t flit "Z “VIZ 1 (0.8 p. [5“? 8mm, ’LL mu/S’C be kmde ‘Hne 'bulu‘n‘ms r‘n‘z musk be dam/mo!) . ‘nly gm“ f‘ d '7 00 as r—vo. 8D kz=o) and 11‘ (2,40): r"l 4‘ Fund amen-H Sch/than: m; n17 ‘ . UAW): r ‘s% r352 “(a)”: Cr‘CL Sum—2: = £(9) Hz: 0L - nTYG __> chafing : 2(9) Sm. :- dG ) n=¥,z,--.. 110.8% 16; ...
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Sect10.8a - g. ,_ éy-zqoo:ru+ro.+o we . (H “uni W39 =0 ,...

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