매트랩 이용해서 공수 문제 그래프로 그리기

방금 풀었던 공수 문제를 이번에는 그래프로 그려 달라는 요청을 받았습니다.
쉬운거라고 생각하고 바로 시작했는데, 생각만큼 간단하지가 않더군요. 그래도 다행히 제대로 풀어 냈습니다.

매트랩 코드 한번 공유해 봅니다.
Dennis Zill 공업수학 13.3 연습문제 9-(b)번 입니다.

syms p x t u; # 변수선언
>> k = 1.6352; # 상수
>> A = 320/pi^2.*((-1).^(p+1) ./(2.*p-1).^2 .* exp(-k.*(2.*p-1).^2.*(pi.^2 ./100.^2).*t) .*sin(((2.*p-1).*pi)./100 .*x)); # 수열식 선언
>> u = symsum(A,p,1,100); # symsum함수를 이용해 A를 1항부터 100항까지 더함 #이 결과는 복사해 둘 것
>> x = 0:10:100; #x범위
>> t = 0:10:200; #t범위
>> [X,T] = meshgrid(x,t) #x,t를 행렬로 선언

>> Z = (1140775112240925.*exp(-(23725923417615525281231.*T)/1441151880758558720000).*sin((101.*pi.*X)/100))/358915779678175232 - (1140775112240925.*exp(-(61795319996336328908639.*T)/1441151880758558720000).*sin((163.*pi.*X)/100))/934813582028177408 - (1140775112240925.*exp(-(81332400351984835169039.*T)/1441151880758558720000).*sin((187.*pi.*X)/100))/1230362307574366208 + (1140775112240925.*exp(-(51636038211399105653231.*T)/1441151880758558720000).*sin((149.*pi.*X)/100))/781128244744159232 + (380258370746975.*exp(-(15259855263501172568391.*T)/1441151880758558720000).*sin((81.*pi.*X)/100))/76948221758275584 + (380258370746975.*exp(-(72866332197870482456199.*T)/1441151880758558720000).*sin((177.*pi.*X)/100))/367430397723672576 - (6518714927091.*exp(-(113966302074616286519.*T)/2305843009213693952).*sin((7.*pi.*X)/4))/6157265115545600 - (6518714927091.*exp(-(113966302074616286519.*T)/57646075230342348800).*sin((7.*pi.*X)/20))/246290604621824 - (162967873177275.*exp(-(113966302074616286519.*T)/1441151880758558720000).*sin((7.*pi.*X)/100))/246290604621824 - (15210334829879.*exp(-(20932586095337685279.*T)/2305843009213693952).*sin((3.*pi.*X)/4))/2638827906662400 - (15210334829879.*exp(-(20932586095337685279.*T)/57646075230342348800).*sin((3.*pi.*X)/20))/105553116266496 - (380258370746975.*exp(-(20932586095337685279.*T)/1441151880758558720000).*sin((3.*pi.*X)/100))/105553116266496 - (1140775112240925.*exp(-(47561161451506702918919.*T)/1441151880758558720000).*sin((143.*pi.*X)/100))/719485224844525568 + (1140775112240925.*exp(-(3909741914029183217111.*T)/1441151880758558720000).*sin((41.*pi.*X)/100))/59144929481326592 + (1140775112240925.*exp(-(86635322162803715439719.*T)/1441151880758558720000).*sin((193.*pi.*X)/100))/1310582675936903168 - (54322624392425.*exp(-(50259139214905782354879.*T)/1441151880758558720000).*sin((147.*pi.*X)/100))/36204718879408128 + (2172904975697.*exp(-(1025696718671546578671.*T)/57646075230342348800).*sin((21.*pi.*X)/20))/738871813865472 + (54322624392425.*exp(-(1025696718671546578671.*T)/1441151880758558720000).*sin((21.*pi.*X)/100))/738871813865472 - (1140775112240925.*exp(-(84849074816001566295911.*T)/1441151880758558720000).*sin((191.*pi.*X)/100))/1283561078172680192 + (162967873177275.*exp(-(13789922551028570668799.*T)/1441151880758558720000).*sin((77.*pi.*X)/100))/29801163159240704 - (380258370746975.*exp(-(68009972223752139471471.*T)/1441151880758558720000).*sin((171.*pi.*X)/100))/342942074749845504 + (15210334829879.*exp(-(2532842917535859918759.*T)/57646075230342348800).*sin((33.*pi.*X)/20))/12771927068246016 + (380258370746975.*exp(-(2532842917535859918759.*T)/1441151880758558720000).*sin((33.*pi.*X)/100))/12771927068246016 - (45631004489637.*exp(-(839629286712989376191.*T)/57646075230342348800).*sin((19.*pi.*X)/20))/12701558324068352 - (1140775112240925.*exp(-(839629286712989376191.*T)/1441151880758558720000).*sin((19.*pi.*X)/100))/12701558324068352 + (1140775112240925.*exp(-(69610152138595731412799.*T)/1441151880758558720000).*sin((173.*pi.*X)/100))/1053033072246652928 - (1140775112240925.*exp(-(39913789998010001896991.*T)/1441151880758558720000).*sin((131.*pi.*X)/100))/603799009416445952 - (15210334829879.*exp(-(3537607050112068812151.*T)/57646075230342348800).*sin((39.*pi.*X)/20))/17838476649037824 - (380258370746975.*exp(-(3537607050112068812151.*T)/1441151880758558720000).*sin((39.*pi.*X)/100))/17838476649037824 - (380258370746975.*exp(-(77890152860751526923159.*T)/1441151880758558720000).*sin((183.*pi.*X)/100))/392763145627631616 - (380258370746975.*exp(-(28656710364517291146951.*T)/1441151880758558720000).*sin((111.*pi.*X)/100))/144502216168833024 + (1140775112240925.*exp(-(76196939229928656380591.*T)/1441151880758558720000).*sin((181.*pi.*X)/100))/1152675214002225152 - (1140775112240925.*exp(-(5137786964955660753479.*T)/1441151880758558720000).*sin((47.*pi.*X)/100))/77722277944229888 + (1140775112240925.*exp(-(21883855841225808976679.*T)/1441151880758558720000).*sin((97.*pi.*X)/100))/331049756983820288 - (1140775112240925.*exp(-(24674867320604167013879.*T)/1441151880758558720000).*sin((103.*pi.*X)/100))/373271003490418688 + (45631004489637.*exp(-(58146072487049125775.*T)/2305843009213693952).*sin((5.*pi.*X)/4))/21990232555520000 - (1140775112240925.*exp(-(11724574056288585721271.*T)/1441151880758558720000).*sin((71.*pi.*X)/100))/177364419699802112 - (1140775112240925.*exp(-(14515585535666943758471.*T)/1441151880758558720000).*sin((79.*pi.*X)/100))/219585666206400512 + (1140775112240925.*exp(-(34052665891315450018871.*T)/1441151880758558720000).*sin((121.*pi.*X)/100))/515134391752589312 - (380258370746975.*exp(-(6049517381552591045631.*T)/1441151880758558720000).*sin((51.*pi.*X)/100))/30504850601017344 - (380258370746975.*exp(-(22795586257822739268831.*T)/1441151880758558720000).*sin((99.*pi.*X)/100))/114947343614214144 - (1140775112240925.*exp(-(10440708775774541024159.*T)/1441151880758558720000).*sin((67.*pi.*X)/100))/157942646306766848 - (1140775112240925.*exp(-(16022731734531257098559.*T)/1441151880758558720000).*sin((83.*pi.*X)/100))/242385139319963648 + (162967873177275.*exp(-(41141835048936479433359.*T)/1441151880758558720000).*sin((133.*pi.*X)/100))/88910908268478464 + (380258370746975.*exp(-(7556663580416904385719.*T)/1441151880758558720000).*sin((57.*pi.*X)/100))/38104674972205056 - (45631004489637.*exp(-(281426990837317768751.*T)/57646075230342348800).*sin((11.*pi.*X)/20))/4257309022748672 - (1140775112240925.*exp(-(281426990837317768751.*T)/1441151880758558720000).*sin((11.*pi.*X)/100))/4257309022748672 + (1140775112240925.*exp(-(8654461428972391880351.*T)/1441151880758558720000).*sin((61.*pi.*X)/100))/130921048542543872 - (1140775112240925.*exp(-(44937610660891046363951.*T)/1441151880758558720000).*sin((139.*pi.*X)/100))/679797253128323072 + (15210334829879.*exp(-(188393274858039167511.*T)/57646075230342348800).*sin((9.*pi.*X)/20))/949978046398464 + (380258370746975.*exp(-(188393274858039167511.*T)/1441151880758558720000).*sin((9.*pi.*X)/100))/949978046398464 - (380258370746975.*exp(-(58799634341803557948711.*T)/1441151880758558720000).*sin((159.*pi.*X)/100))/296498703592587264 + (1140775112240925.*exp(-(29698687983485211480839.*T)/1441151880758558720000).*sin((113.*pi.*X)/100))/449269247202295808 + (1140775112240925.*exp(-(43653745380377001666839.*T)/1441151880758558720000).*sin((137.*pi.*X)/100))/660375479735287808 - (15210334829879.*exp(-(1695539473722352507599.*T)/57646075230342348800).*sin((27.*pi.*X)/20))/8549802417586176 - (380258370746975.*exp(-(1695539473722352507599.*T)/1441151880758558720000).*sin((27.*pi.*X)/100))/8549802417586176 + (45631004489637.*exp(-(2325842899481965031.*T)/2305843009213693952).*sin((pi.*X)/4))/879609302220800 + (45631004489637.*exp(-(2325842899481965031.*T)/57646075230342348800).*sin((pi.*X)/20))/35184372088832 + (1140775112240925.*exp(-(2325842899481965031.*T)/1441151880758558720000).*sin((pi.*X)/100))/35184372088832 + (162967873177275.*exp(-(5584348801656198039431.*T)/1441151880758558720000).*sin((49.*pi.*X)/100))/12068239626469376 - (380258370746975.*exp(-(35187677226262648953999.*T)/1441151880758558720000).*sin((123.*pi.*X)/100))/177434788443979776 - (1140775112240925.*exp(-(53031543951088284671831.*T)/1441151880758558720000).*sin((151.*pi.*X)/100))/802238867997458432 + (380258370746975.*exp(-(11073338044433635512591.*T)/1441151880758558720000).*sin((69.*pi.*X)/100))/55837598504976384 - (1140775112240925.*exp(-(4300483521142153342319.*T)/1441151880758558720000).*sin((43.*pi.*X)/100))/65055903992250368 - (1140775112240925.*exp(-(92105704662385297192631.*T)/1441151880758558720000).*sin((199.*pi.*X)/100))/1393336319089836032 - (1140775112240925.*exp(-(26628575356169017639919.*T)/1441151880758558720000).*sin((107.*pi.*X)/100))/402825876045037568 + (1140775112240925.*exp(-(57329701629330956049119.*T)/1441151880758558720000).*sin((157.*pi.*X)/100))/867259587617619968 - (1140775112240925.*exp(-(8096259133096720272911.*T)/1441151880758558720000).*sin((59.*pi.*X)/100))/122476799241224192 - (162967873177275.*exp(-(19260305050610152421711.*T)/1441151880758558720000).*sin((91.*pi.*X)/100))/41623112181088256 + (1140775112240925.*exp(-(27633339488745226533311.*T)/1441151880758558720000).*sin((109.*pi.*X)/100))/418025524787412992 + (380258370746975.*exp(-(54445656433973319410679.*T)/1441151880758558720000).*sin((153.*pi.*X)/100))/274543655409156096 + (380258370746975.*exp(-(38704351690279380080871.*T)/1441151880758558720000).*sin((129.*pi.*X)/100))/195167711976751104 - (45631004489637.*exp(-(1230370893825959501399.*T)/57646075230342348800).*sin((23.*pi.*X)/20))/18612532834992128 - (1140775112240925.*exp(-(1230370893825959501399.*T)/1441151880758558720000).*sin((23.*pi.*X)/100))/18612532834992128 + (1140775112240925.*exp(-(12394416811339391650199.*T)/1441151880758558720000).*sin((73.*pi.*X)/100))/187497518861385728 - (1140775112240925.*exp(-(37513520125744613984999.*T)/1441151880758558720000).*sin((127.*pi.*X)/100))/567488737420771328 - (45631004489637.*exp(-(2235135026402168394791.*T)/57646075230342348800).*sin((31.*pi.*X)/20))/33812181577367552 - (1140775112240925.*exp(-(2235135026402168394791.*T)/1441151880758558720000).*sin((31.*pi.*X)/100))/33812181577367552 + (380258370746975.*exp(-(31838463451008619309359.*T)/1441151880758558720000).*sin((117.*pi.*X)/100))/160546289841340416 - (162967873177275.*exp(-(32936261299564106803991.*T)/1441151880758558720000).*sin((119.*pi.*X)/100))/71177984735707136 + (1140775112240925.*exp(-(66428399052104403250391.*T)/1441151880758558720000).*sin((169.*pi.*X)/100))/1004900851229130752 + (1140775112240925.*exp(-(6533292704644839772079.*T)/1441151880758558720000).*sin((53.*pi.*X)/100))/98832901197529088 + (54322624392425.*exp(-(83081434212395272872351.*T)/1441151880758558720000).*sin((189.*pi.*X)/100))/59848616923103232 - (54322624392425.*exp(-(9231270468043919208039.*T)/1441151880758558720000).*sin((63.*pi.*X)/100))/6649846324789248 + (45631004489637.*exp(-(1956033878464332591071.*T)/57646075230342348800).*sin((29.*pi.*X)/20))/29590056926707712 + (1140775112240925.*exp(-(1956033878464332591071.*T)/1441151880758558720000).*sin((29.*pi.*X)/100))/29590056926707712 - (380258370746975.*exp(-(17604304906178993319639.*T)/1441151880758558720000).*sin((87.*pi.*X)/100))/88770170780123136 + (1140775112240925.*exp(-(90263637085995580888079.*T)/1441151880758558720000).*sin((197.*pi.*X)/100))/1365470296395481088 - (1140775112240925.*exp(-(74522332342301641558271.*T)/1441151880758558720000).*sin((179.*pi.*X)/100))/1127342466098266112 + (45631004489637.*exp(-(672168597950287893959.*T)/57646075230342348800).*sin((17.*pi.*X)/20))/10168283533672448 + (1140775112240925.*exp(-(672168597950287893959.*T)/1441151880758558720000).*sin((17.*pi.*X)/100))/10168283533672448 - (1140775112240925.*exp(-(64865432623652522749559.*T)/1441151880758558720000).*sin((167.*pi.*X)/100))/981256953185435648 + (380258370746975.*exp(-(20116215237619515553119.*T)/1441151880758558720000).*sin((93.*pi.*X)/100))/101436544732102656 + (1140775112240925.*exp(-(18423001606796645010551.*T)/1441151880758558720000).*sin((89.*pi.*X)/100))/278695411315638272 + (162967873177275.*exp(-(60288173797472015568551.*T)/1441151880758558720000).*sin((161.*pi.*X)/100))/130287729844944896 + (45631004489637.*exp(-(393067450012452090239.*T)/57646075230342348800).*sin((13.*pi.*X)/20))/5946158883012608 + (1140775112240925.*exp(-(393067450012452090239.*T)/1441151880758558720000).*sin((13.*pi.*X)/100))/5946158883012608 + (45631004489637.*exp(-(3184078929390810127439.*T)/57646075230342348800).*sin((37.*pi.*X)/20))/48167405389611008 + (1140775112240925.*exp(-(3184078929390810127439.*T)/1441151880758558720000).*sin((37.*pi.*X)/100))/48167405389611008 + (380258370746975.*exp(-(46240082684600946781311.*T)/1441151880758558720000).*sin((141.*pi.*X)/100))/233166833832689664 # 위에서 복사해 둔 Z에서 x를 X로, t를 T로,*를 .*로 바꾸었음

>> mesh(X,T,Z)


를 치면

다음의 결과를 얻을 수 있음

3차원 플롯팅 결과

이렇게 해서 연습문제를 풀어 봤습니다. 항의 합이 Inf 까지라고 하니까 자꾸 오류가 떠서 100까지로 합의를 봤고, 행렬곱일때 .*를 써야 하는데, 행렬로 바꿔야 한다는 생각 자체를 못 했었네요.