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-1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 6 6 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 } {PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "T imes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 14 5 } {PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 16 3 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 " Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Verda na" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 40 "Mat-1.192 Numeric and sym bolic computing" }}{PARA 19 "" 0 "" {TEXT -1 13 "Tammikuu 2005" }} {PARA 19 "" 0 "" {TEXT 260 80 "Maple-perusteita: www.math.hut.fi/opet us/numsym/05/maple/perusteita.mws (.html)" }{TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 154 "Language will be sometimes English, sometimes Fin nish for the time being. Stabilizes, when the course starts according \+ to the participants' nationalities." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Course directory for Maple instructions and codes: " }{TEXT 331 41 "www.math.hut.fi/teaching/numsym/05/maple/" }}{PARA 0 "" 0 "" {TEXT -1 16 "Abbreviation: " }{TEXT 332 10 ".../maple/" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Varsinainen " }{TEXT 347 25 "toiminta alkaa kohdasta 6" }{TEXT -1 40 ", lue kuitenkin ainakin 1 l \344pi huolella." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Maple 8/9" }} {PARA 0 "" 0 "" {TEXT -1 117 "Luokissa versio 8, Maplesoft on julkista nut version 9.5, milloin saataneen. Tosin ei liene mit\344\344n dramaa ttista uutta." }}{PARA 0 "" 0 "" {TEXT -1 141 "Valitettavasti nykyinen kampuslisenssi ei salli oppilask\344ytt\366\344 omissa koneissa. Et \344k\344ytt\366 toki toimii tekstitilassa (ellei ole X-emulointia)." }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 53 "1. Ty\366skentelyohjeita, ty \366arkin k\344sittelyn perusasiat" }}{PARA 0 "" 0 "" {TEXT 306 56 "Mu ista tallettaa aika ajoin/save your work often (CTR-S)" }{TEXT -1 89 " . Maple n\344ytt\344\344 luokissa silloin t\344ll\366in kaatuvan (aina kin ennen, toivottavasti ei en\344\344)." }}{PARA 0 "" 0 "" {TEXT -1 106 "Talletus on joka tapauksessa syyt\344 tehd\344 aina ennen jotain \+ potentiaalisesti isoa laskentaa. Muista lyhyt: " }{TEXT 314 5 "CTR-S" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "T\344m \344 ty\366arkki sis\344lt\344\344 ohjeita ja ohjeisiin liittyvi\344 t eht\344vi\344, joita voi samantien" }}{PARA 0 "" 0 "" {TEXT -1 84 "ryh ty\344 kokeilemaan. Voit tehd\344 muistiinpanoja ty\366arkille ja tall ettaa sen itsellesi." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 73 "Suositus: Selaa ty\366arkkia jonkin matkaa, totuttele h eti helpin k\344ytt\366\366n. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 315 29 "Harjoitusteht\344v\344dokumentti: " }} {PARA 0 "" 0 "" {TEXT -1 106 "Kannattaa aloittaa INSERT-valikon SECTIO N-valinnalla ja napsauttaa muutama sektio heti k\344ttelyss\344 arkill e." }}{PARA 0 "" 0 "" {TEXT -1 108 "Huomaa, ett\344 ty\366arkin voi ta llettaa my\366s HTML-muotoon. Tosin harjoitusratkaisuja esitelt\344ess \344 Maple ws-muoto" }}{PARA 0 "" 0 "" {TEXT -1 86 "on yleens\344 pare mpi, mutta my\366hemp\344\344 katselua varten taas htlm-doku on tosi h yv\344 juttu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 316 11 "El\344m\344nohje:" }}{PARA 0 "" 0 "" {TEXT -1 84 "Maplen filosifiaa kannattaa opetella senverran, ett\344 ty\366skentely k\344 y nautittavaksi. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 291 24 "Goals for this exercise:" }}{PARA 15 "" 0 "" {TEXT -1 40 "Ty\366arkin k\344sittely/Handling of worksheet" }}{PARA 15 "" 0 " " {TEXT -1 74 "Peruslaskutoimitukset ja sievennykset/Basic arithmetic \+ and simplifications" }}{PARA 15 "" 0 "" {TEXT -1 18 "Grafiikka/Graphic s" }}{PARA 15 "" 0 "" {TEXT -1 52 "Vapaat ja sidotut muuttujat/Free an d bound variables" }}{PARA 15 "" 0 "" {TEXT 290 46 "Lauseke vs. funkti o / Expression vs. function " }}{PARA 15 "" 0 "" {TEXT -1 82 "Matriisi t ja vertailu Matlab-ty\366skentelyyn/ Matrices and comparison to Matl ab work" }}{PARA 15 "" 0 "" {TEXT -1 27 "Perustietorakenteet, erit. " }{TEXT 292 25 "jonot, joukot, listat. / " }{TEXT 321 16 "Basic data ty pes" }{TEXT 322 2 ", " }{TEXT 323 11 "especially " }{TEXT 324 22 "sequ ences, sets, lists" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 77 "Kannattaa harjoitella my\366s teknisi\344 asioita, kuten ty\366arkin printtaamista ym." }}{PARA 0 "" 0 "" {TEXT -1 57 "K atsotaan ensin ty\366arkkiin (worksheet) liittyvi\344 asioita." }} {PARA 15 "" 0 "" {TEXT -1 57 "Uuden (laskenta)kehotteen saa hiirell \344 ty\366kalunauhasta [ " }{TEXT 256 1 ">" }{TEXT -1 42 " ] tai CTR -J (j\344lkeen) tai CTR-K (ennen)" }}{PARA 15 "" 0 "" {TEXT -1 29 "La skentakehote->tekstitila: " }{TEXT 257 3 "T (" }{TEXT 325 24 "left to the previous one" }{TEXT 326 1 ")" }}{PARA 15 "" 0 "" {TEXT -1 202 "M atemaattinen teksti ja tekstimuotojen muunnokset: Maalaa hiiren vasemm alla, klikkaa oikeaa, saat valikon.\nMaplen laajamittaisempi k\344ytt \366 matemaattiseen tekstink\344sittelyyn ei liene oikein suositeltava a." }}{PARA 15 "" 0 "" {TEXT -1 36 "Uusi luku: INSERT-valikko, ->SECTI ON" }}{PARA 15 "" 0 "" {TEXT -1 62 "Leikkaa/liimaa: UNIX/X:ss\344 oike in k\344tev\344, eli kuten aina X:ss\344" }}{PARA 14 "" 0 "" {TEXT -1 32 " - Maalataan hiiren vasemmalla" }}{PARA 14 "" 0 "" {TEXT -1 39 " - vied\344\344n kursori haluttuun kohtaan" }}{PARA 14 "" 0 "" {TEXT -1 31 " - liimataan keskimm\344isell\344" }}{PARA 14 "" 0 " " {TEXT -1 44 "(Windows:ssa maalaus, CTR-C, vienti, CTR-V)" }}{PARA 14 "" 0 "" {TEXT -1 103 "Ongelmia: Joskus cut/paste ei toimi Maplen ja komentoikkunan yms. v\344lill\344 UNIX:ssa, joskus taas toimii." }} {PARA 14 "" 0 "" {TEXT -1 42 "(Eri Maple-ikkunoiden kesken toimii aina .)" }}{PARA 14 "" 0 "" {TEXT -1 100 "Kursori voi joskus kadota kesken \+ kaiken, ikkunan minimoiminen ja palautus voi auttaa, tai sitten ei." } }{PARA 15 "" 0 "" {TEXT -1 85 "Jos ty\366arkin selaus k\344y hitaaksi \+ ja usein muutenkin, kannattaa valita EDIT-valikosta " }{TEXT 307 16 "r emove output . " }{TEXT -1 106 "\nSe on k\344tev\344 my\366s ty\366ark in pakkaamiseen, turha s\344ilytell\344 isoja kuvia ym. kun ne on tall etettuna koodiin." }}{PARA 15 "" 0 "" {TEXT -1 57 "K\344\344nteinen to imenpide on EDIT-valikon edellinen valinta: " }{TEXT 318 18 "execute w orksheet." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 327 38 "Maple as a Math tex tprocessing system:" }{TEXT -1 84 " Convenenient for student project \+ type of work. Result is not of very high quality." }}{PARA 0 "" 0 "" {TEXT -1 101 "Recommendation: Use LaTeX for serious work. Maple is a c onvenient tool for generating LaTeX-formulas." }}{PARA 0 "" 0 "" {TEXT -1 110 "Also, the export->HTML makes an html-document, which is \+ not too large, and is easy to further edit, if needed." }}{PARA 0 "" 0 "" {TEXT -1 104 "The formulas and figures are gif-images, Maple has \+ also MathML-support (but I have no experience on it.)" }}{PARA 0 "" 0 "" {TEXT -1 95 "N\344tti esimerkki Maplella generoidusta ja j\344lkeen p\344in editoimalla parannellusta html-dokusta on " }{TEXT 343 12 "Vir rankosken" }}{PARA 0 "" 0 "" {TEXT -1 11 "Maple-opas." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "For more details with illustrations see . .." }{TEXT 329 5 "maple" }{TEXT -1 1 "/" }{TEXT 328 7 "gsg.pdf" }} {PARA 0 "" 0 "" {TEXT -1 71 "Ty\366arkin painikkeita ja k\344sittely \344 on selostettu havainnollisin kuvin ." }{TEXT 330 17 "../maple/gsg .pdf:" }{TEXT -1 4 "ss\344." }}{PARA 0 "" 0 "" {TEXT -1 142 "Esim. pal etit (insert-valikosta), smartplotit, ym. \"modernit\" k\344ytt\366muk avuudet selitet\344\344n gsg:ss\344 tarkasti. Makuasia, ovatko hy\366d yllisi\344, itse" }}{PARA 0 "" 0 "" {TEXT -1 27 "en juurikaan ole k \344ytt\344nyt." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 "2. Viitteit \344, ty\366arkkeja, koodeja" }}{PARA 0 "" 0 "" {TEXT -1 31 "Samat lin ki ovat luentosivulla." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 " [HA M] Apiola: Symb ja num. lask Maple-ohjelmalla, Otatieto 588" }}{PARA 0 "" 0 "" {TEXT -1 85 " T\344m\344 teos ilmeisine puutteineenk in lienee hy\366dyllinen. Perustuu versioon 5. " }}{PARA 0 "" 0 "" {TEXT -1 75 " T\344ydennyst\344 vaatii erityisesti matriisila skentaosuus, sill\344 uusi " }{TEXT 348 13 "LinearAlgebra" }{TEXT -1 29 "-tyyli tuli vasta versioon 6." }}{PARA 0 "" 0 "" {TEXT -1 84 " \+ Kirjastossa useita, jos haluat omaksi, saat minulta alennushintaa n (10 e). " }}{PARA 0 "" 0 "" {TEXT -1 6 " " }{TEXT 317 23 "Kurss in Maple-hakemisto" }{TEXT -1 51 ": www.math.hut.fi/teaching/numsym/0 5/maple/ " }}{PARA 0 "" 0 "" {TEXT -1 96 " gsg.pdf, lrng uide.pdf, prguide.pdf (Getting Started, Learning, Programming, Mapl e 7)" }}{PARA 0 "" 0 "" {TEXT -1 82 " N\344it\344 on my\366s la itoskirjastossa manuaalihyllyss\344 ainakin kahdet kappaleet." }} {PARA 14 "" 0 "" {TEXT -1 62 "[VIR] Virrankoski: http://matta.hut.fi/m atta/mplopas.htm " }}{PARA 14 "" 0 "" {TEXT -1 171 "[PIKA] Apiola -Peltola: Maple-pikaopas http://www.math.hut.fi/teaching/k3/maple-pika opas.html\n[SOL] Solmun Maple-kirjoitus http://www.math.helsinki.fi/S olmu/solmu12/apiola" }}{PARA 14 "" 0 "" {TEXT -1 123 "[KOF] M. Kofler: Maple, an introduction and reference, Addison Wesley 1997 www.awl-he .com, eritt\344in hyv\344 Maple-yleiskirja." }}{PARA 14 "" 0 "" {TEXT -1 582 "[LYN] Lynch: Dynamical systems with Applications using Maple, \+ Birkh\344user (Mat-kirjastossa) (Maple-tutoriaalit ja paljon diffyht \344l\366koodeja) www.maplesoft.com/apps/\n[HECK] Heck: An Introductio to Maple (Springer), t\344ydellisin ja kattavin Maple-kirja\n[ISR] I srael: Calculus with Maple (pari ylim. kappaletta kirjastossa)\nIsrae l: Maple advisor database (kts. linkki luentosivulla)\n[Coomb] Coombes -Hunt-Lipsman-Osborn-Stuck: Diff. Equations with Maple (ainakin 1 kirj astossa)\nKurssia varten kirjoitettuja/tettavia Maple-ty\366arkkeja, k uten LA, ominaisarvot, lindys, fourier, numint, ..." }{TEXT 344 16 "ma ple/ns05.mpl " }{TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 19 "3. Opiskelusuositus" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "K\344y \+ samalla l\344pi [HAM]-kirjan ss. 13 - 51 (Alkutoimenpiteet)" }}}} {SECT 1 {PARA 3 "" 0 "First Things First" {TEXT -1 34 "4. Ty\366arkin \+ (worksheet) lataaminen" }{TEXT 294 0 "" }}{PARA 14 "" 0 "" {TEXT -1 100 "Kun lataat ty\366arkin FILE-valikon OPEN-valinnalla, saat k\344yt t\366\366si visuaalisen esityksen Maple-ty\366st\344." }}{PARA 14 "" 0 "" {TEXT -1 18 "Ty\366arkilla olevat " }{TEXT 295 27 "komennot suori ttuvat vasta," }{TEXT -1 39 " kun siirryt punaiseen INPUT-soluun ja " }{TEXT 296 13 "painat ENTER:" }{TEXT -1 3 "i\344." }}{PARA 0 "" 0 "" {TEXT -1 53 " Koko ty\366arkin kaikki komennot saat suoritetuksi \+ " }{TEXT 339 13 "Edit valikon " }{TEXT -1 12 "valinnalla \"" }{TEXT 338 17 "execute worksheet" }{TEXT -1 26 "\", kuten edell\344 todettiin ." }}{PARA 0 "" 0 "" {TEXT -1 93 "Jos haluat jatkaa kokeiluja t\344ll \344 kohdalla, tee lis\344\344 kehotteita joko klikkaamalla kohtaa > " }}{PARA 0 "" 0 "" {TEXT -1 42 "tai CTR-J (jos j\344lkeen) (CTR-K \+ (ennen))" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "247*3756;" }}}} {SECT 1 {PARA 3 "" 0 "Laskentoa numeroilla" {TEXT -1 24 "5. Laskentoa numeroilla" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 53 "restart: # Ty\366n alkuun kannattaa yleens\344 \+ laittaa." }}}{PARA 0 "" 0 "" {TEXT -1 33 "Laskuoperaatiot ovat \"norma alit\" " }{MPLTEXT 1 0 5 "+-*/^" }{TEXT -1 3 " , " }{TEXT 308 27 "kert omerkki\344 ei saa j\344tt\344\344 " }{TEXT -1 27 "pois (kuten Mathema ticassa)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Kokeile jotain, voit m y\366s sijoittaa muuttujiin tyyliin:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "oso:=123; nimi:=-456; luku:=oso/nimi;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Maple vaatii loppumerkin, joko" } {MPLTEXT 1 0 2 " ;" }{TEXT -1 5 " tai " }{MPLTEXT 1 0 1 ":" }{TEXT -1 28 " Kokeile, jos et jo tied\344." }}{PARA 0 "" 0 "" {TEXT 264 11 "L ue lis\344\344: " }}{PARA 15 "" 0 "" {TEXT -1 17 "[PIKA] s 1.3 s. 6" } }{PARA 15 "" 0 "" {TEXT -1 10 "[SOL] s. 8" }}{PARA 15 "" 0 "" {TEXT -1 14 "[HAM] s. 21 " }}}}{SECT 1 {PARA 0 "" 0 "Laskentoa symboleilla ja numeroilla" {TEXT 261 39 "6. Laskentoa symboleilla ja numeroilla " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 0 "" 0 "" {TEXT 319 11 "Pohdiskelua" }}{PARA 0 "" 0 "" {TEXT -1 3 "Lue" }}{PARA 16 "" 0 " " {TEXT -1 49 "[SOL] s 15-16 Symbolien hallintaa ja periaatteita" }} {PARA 16 "" 0 "" {TEXT -1 27 "[HAM] s. 70 - 71 (korjaus: " }{TEXT 293 51 "http://www.math.hut.fi/~apiola/maple/opas/eval.html" }{TEXT -1 2 " )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "(se e Heck Ch 3 Variables and names p. 65 -.. " }}{PARA 0 "" 0 "" {TEXT -1 34 "The secret behind success of CA : " }{TEXT 281 24 "free (unboun d) variables" }{TEXT -1 4 " . )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "On hyv\344 totutella laittamaan " }{TEXT 0 8 "restart " }{TEXT -1 50 "ty\366arkin alkuun (ja muihinkin h eng\344hdyspaikkoihin)" }}{PARA 0 "" 0 "" {TEXT -1 53 "Painele nyt ENT ER:i\344 ja palaa ohjeen mukaan takaisin." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 24 "restart: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "lauseke:=(a+b)^2; # Muuttujat a ja b ovat \" vapaat\" " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "lauseke :=expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=x^2 :b:= exp(c*z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "lauseke;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x:=1: " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "lauseke;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "T\344m\344 on ensimm\344inen merkitt\344v\344 havainto: Kun x muut tuu, niin " }{MPLTEXT 1 0 7 "lauseke" }{TEXT -1 79 " muuttuu, koska yl l\344 olevassa sijoituslauseessa muuttujat a ja b olivat vapaat." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Jos haluat vapauttaa vain \+ joitakin valittuja muuttujia, niin:" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 35 "Muuttujien vapauttaminen arvostaan:" }}{PARA 0 "" 0 "" {TEXT -1 5 "Joko " }{TEXT 0 7 "a:='a';" }{TEXT -1 5 " tai " }{TEXT 0 15 " un assign('a'):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "a:='a': # Vapautetaan a" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "lauseke;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "b:='b': la useke;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "T\344ss\344 on ensimm \344inen ja t\344rke\344 syy symbolilaskennan onnistumiselle." }}} {EXCHG {PARA 256 "" 0 "" {TEXT -1 14 "Vakiot Pi ja I" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "Pi,I;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(Pi,30);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "2/3+4/5;evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 297 11 "H uomaa t\344m\344" }{TEXT -1 38 ": Maple osaa vain \"tekstink\344sitell \344\" " }{TEXT 262 2 "pi" }{TEXT -1 26 ":t\344, laskentaan tarvitaan " }{TEXT 263 2 "Pi" }}{PARA 0 "" 0 "" {TEXT -1 57 "T\344ss\344 tulee \+ usein virheit\344 alkavalle Maple-urheilijalle. " }}{PARA 14 "" 0 "" {TEXT 298 25 "Virhetilanteista yleens\344:" }}{PARA 14 "" 0 "" {TEXT -1 27 "[HAM] Liite A s. 191 -198, " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" } {TEXT -1 22 "-problematiikka s. 192" }}{PARA 14 "" 0 "" {TEXT -1 48 "[ PIKA] Lopussa lyhyt lista (jossa my\366s samainen " }{XPPEDIT 18 0 "Pi ;" "6#%#PiG" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 5 "" 0 "" {TEXT -1 31 "Kompleksilukuja, imag. yksikk\366 \+ " }{TEXT 0 1 "I" }}{PARA 0 "" 0 "" {TEXT 333 18 "Kompleksisievennys" } {TEXT -1 15 ", erityisesti " }{XPPEDIT 19 1 "evalc" "6#%&evalcG" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "(1+2*I)/(2-3*I); # N umeerinen kompleksiluku muuntuu automaattisesti muotoon x+I*y ." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Jos kompleksiluku annetaan symboli sessa muodossa, Maple olettaa " }{MPLTEXT 1 0 1 "a" }{TEXT -1 6 ":n ja " }{MPLTEXT 1 0 1 "b" }{TEXT -1 27 ":n reaalisiksi esityksess\344 " } {MPLTEXT 1 0 5 "a+I*b" }{TEXT -1 2 " ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "z1:=a1+I*a2;z2:=a2+I*b2;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 6 "z1/z2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Koment o " }{MPLTEXT 1 0 5 "evalc" }{TEXT -1 62 " on varsin tehokas, kannatt aa muistaa kompleksisievennyksiss\344." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalc(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " ." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "abs" }{TEXT -1 4 " ja " } {MPLTEXT 1 0 9 "argument:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "z:=((1+2*I)/(3-4*I));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "r:=abs(z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "phi:=argu ment(z);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "r*exp(I*phi);ev alc(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 1 " " }{TEXT 340 5 "evalc " }{TEXT -1 22 " did a good job again." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Example: " }{TEXT 334 13 "complex roots" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "w:=exp(I*2*k*Pi/n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "with(plots): # load the plots-package " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "setoptions(scaling=constrained,axes =framed): # Sama skaala akseleilla\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "n:=5: ykkosen5juuret:=seq(w,k=0..n-1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "rinkulat:=complexplot([ykkosen5juur et],style=point,symbol=circle,symbolsize=15):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "yksikkoymp:=complexplot(exp(I*Pi*t),t=0..2*Pi,co lor=blue):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Grafiikat saadaan s amaan kuvaan funktiolla " }{TEXT 0 7 "display" }{TEXT -1 15 " (joka as ustaa " }{TEXT 0 5 "plots" }{TEXT -1 29 "-pakkauksessa), kts alempana. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(rinkulat,yksikk oymp);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "Huom: " }{MPLTEXT 1 0 11 "complexplot" }{TEXT -1 126 " tuli vasta versiossa 7, siksi [HAM]:s sa esitett\344v\344t pikku konversiotemput eiv\344t ole en\344\344 tar peen kompleksipiirron yhteydess\344." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 345 12 "Vrt: Matlab:" }}{PARA 0 "" 0 "" {TEXT 346 7 ">> n=5;" }}{PARA 257 "" 0 "" {TEXT -1 116 ">> K=0:n-1;\n>> w=exp(2*K*i*pi/n);\n >> plot(w,'or')\n>> hold on\n>> t=linspace(0,2*pi); plot(exp(i*t),'b') \n>> axis equal" }}}}{SECT 1 {PARA 3 "" 0 "Matemaattista tekstink\344s ittely\344" {TEXT -1 43 "7. Jono, joukko, lista, taulu(kko),vektori" }}{PARA 0 "" 0 "" {TEXT -1 31 "Lue: [HAM] s. 30 ja ss. 76 - 84" }} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 44 "Lyhyesti (North Carolinan teksti \344 mukaillen)" }}{EXCHG {PARA 4 "" 0 "" {TEXT -1 29 "Joukot \{ \}, j onot, listat [ ]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 68 "T\344ss\344 v\344h\344n University of North Caroli nan sivulta poimittua teksti\344:" }}{PARA 0 "" 0 "" {TEXT -1 247 "Obs erve that we have now employed three different kinds of grouping symbo ls: \"()\",\"\{\}\", and \"[]\". They are used for different purpose s, and Maple requires that they be used correctly. The standard paren theses \"()\" are used with functions as in " }{MPLTEXT 1 0 13 "factor (x^2-1)" }{TEXT -1 5 " and " }{MPLTEXT 1 0 7 "sin(Pi)" }{TEXT -1 15 ". The braces \"" }{MPLTEXT 1 0 2 "\{\}" }{TEXT -1 32 "\" are used to g roup a set as in " }{MPLTEXT 1 0 5 "\{x,y\}" }{TEXT -1 24 ". The squa re brackets \"" }{MPLTEXT 1 0 2 "[]" }{TEXT -1 51 "\" are used to pick a coordinate from a group as in " }{MPLTEXT 1 0 6 "sol[2]" }{TEXT -1 77 ". We will see other uses for these symbols.\nHakasulut ovat my \366s listasulut. " }{TEXT 362 26 "T\344rkeimm\344t tietorakenteet:" } }{PARA 15 "" 0 "" {TEXT 358 4 "Jono" }{TEXT -1 9 ", esim: " }}{PARA 15 "" 0 "" {TEXT 0 16 "> jono:=a,b,c; " }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 359 6 "Lista," }{TEXT -1 8 " esim: " }{TEXT 0 86 "> lista: =[a,b,c]; \n > op(lista); # Listan operandi on sis\344lt \366n\344 oleva jono" }}{PARA 15 "" 0 "" {TEXT 360 6 "Joukko" }{TEXT -1 9 ", esim: " }{TEXT 0 20 "> joukko:=\{a,b,c\}; " }}{PARA 0 "" 0 " " {TEXT -1 34 " " }{TEXT 0 45 "> op(j oukko); # Vastaavasti joukon operandi\n" }}{PARA 0 "" 0 "" {TEXT 361 4 "Huom" }{TEXT -1 161 ": Listan j\344rjestys on k\344ytt\344j\344n ha llinnassa, joukon ei. \n Joukon hy\366ty on ainakin se, e tt\344 Maple osaa poistaa toistot ja joukko-operaatiot toimivat." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 363 3 "map" } {TEXT -1 79 " - funktion soveltaminen listan (tai muun rakenteen) jok aiseen alkioon (osaan)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "l ista:=[a,b,c];map(f,lista);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "jono:=a,b,c;lista:=[a,b,c];op(lista);joukko:=\{a,b,c\}; op(joukko) ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "map(f,jono);f(jono); \+ " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 188 "Huomaa, ett\344 jono ei ole \+ samanlainen \"paketti\" kuin lista tai joukko. map-esimerkki osoittaa, ett\344 voidaksemme soveltaa t\344llaista operaatiota jonoon, se on e nsin ymp\344r\366it\344v\344 listasuluilla " }{MPLTEXT 1 0 2 "[]" } {TEXT -1 45 " ja lopuksi riisuttava sulut pois tuloksesta " }{MPLTEXT 1 0 2 "op" }{TEXT -1 12 "-komennolla:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "op(map(f,[jono]));" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 57 "Funktion soveltaminen listan t ms. kaikkiin alkioihin, map" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 130 "Matlabissa kaikki ns. \"skaala arifunktiot\", kuten kaikki matemaattiset 1:n muuttujan funktiot toimi vat automaattisesti alkioittain" }}{PARA 0 "" 0 "" {TEXT -1 77 "vektor eihin ja matriiseihin. Siten sin([1,2,3]) antaa [sin(1),sin(2),sin(3)] ." }}{PARA 0 "" 0 "" {TEXT -1 47 "Maplessa n\344in ei ole, mutta se sa adaan aikaan \"" }{TEXT 352 4 "map\"" }{TEXT -1 5 ":lla:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "x:=[ a,b,c]; fx:=map(f,x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res tart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "M:=Matrix([seq([se q((x+y)^(i+j),j=1..3)],i=1..2)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "map(expand,M);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 44 "Hiukan perusteellise mmin (osittain toistaen)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Lue: [ HAM] s. 30 ja ss. 76 - 84" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "restart: with(LinearAlgebra):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "jono1:=a,b,c; jono2:=seq(x^i,i=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "lista1:=[jono1]; lista2:=[jono2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "joukko1:=\{jono1\}; joukk o2:=\{jono2\}; # Alkioiden j\344rjestys on \"satunnainen\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "joukko1 union \{a,b,-1,1\}; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "[op(lista1),op(lista2)] ; # Listat liitet\344\344n liitt\344m\344ll\344 operandijonot ja ymp \344r\366im\344ll\344 []:lla" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "logaritmit:=seq([i,log(i)],i=1..10);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Maplessa vaakavektoreiden lista ei ole sama kuin matriis i (kuten Mathematicassa). Se voidaan muuntaa " }{TEXT 0 13 " Matrix:ll a, " }{TEXT 364 17 "takaisin saadaan " }{TEXT 0 8 "convert:" }{TEXT -1 5 "lla ." }}{PARA 0 "" 0 "" {TEXT -1 90 "Esitys listojen listana on hy\366dyllinen esimerkiksi piirrett\344ess\344, se muoto kelpaa suora an " }{TEXT 0 4 "plot" }{TEXT -1 5 ":lle." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 42 "logtaulu:=Transpose(Matrix([logaritmit]));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot([logaritmit]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "convert(logtaulu,listlist); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "convert(Transpose(logta ulu),listlist);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 365 22 "Vektorit ja m atriisit:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "pysty:=; vaaka:=<1 | \+ 2 | 3>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "M:=<<1,2,3>||>; # Sarakkeittain." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Mt:=<<1|2|3>,,>; # Riveitt\344in" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "M.Mt; # M atriisikertolasku" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "conver t(vaaka,list);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "convert(p ysty,list);\n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "convert(M.Mt,listlist);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Teht\344vi\344" }}{PARA 0 "" 0 "" {TEXT -1 47 "Miten poist aisit listasta saman alkion toistot?" }}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 5 "Ratk." }}{PARA 0 "" 0 "" {TEXT -1 18 "Otetaan esimerkki:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 37 "L:=sort([seq(seq(i,i=1..k),k=1..9)]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "J:=\{op(L)\}; # Muutetaan l ista joukoksi => toistot poistuvat!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Lriisuttu:=[op(J)]; # Takaisin listaksi" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "sort(Lriisuttu); # Joukoksi muunta minen saattaa muuttaa alkioiden j\344rjestyksen." }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 68 "Tietysti voidaan ottaa alkioita, joilla ei ole j \344rjestyst\344, silloin " }{TEXT 366 4 "sort" }{TEXT -1 15 " ei tee \+ mit\344\344n." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "L:=[seq(se q(x[i],i=1..k),k=1..6)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " \{op(L)\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "[op(%)];" }}}} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "Defining Varia bles and Functions" {TEXT -1 33 "8. Symbolinen lauseke vs. funktio" }} {PARA 14 "" 0 "" {TEXT -1 8 "T\344m\344 on " }{TEXT 265 11 "t\344rke \344 asia" }{TEXT -1 21 " ymm\344rt\344\344 kunnolla. " }}{PARA 14 " " 0 "" {TEXT -1 25 "[SOLmu] s. 17 Ohjelmointi" }}{PARA 14 "" 0 "" {TEXT -1 43 "[HAM] 2.4 Matemaattiset funktiot s. 60 - 63" }}{PARA 0 " " 0 "" {TEXT -1 56 " Israel: Advisor database ..maple/advisor/fund ef.mws" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "Pohdiskelua" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Matemaattisen funktion k\344sittely " } {TEXT 309 18 "Maple-lausekkeena " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 9 "f := x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "M\344\344rittelemme muuttujan f, jota k\344yt\344mme matemaattisen funktion tavoin. Maplen kannalta " }{TEXT 341 13 "f on muuttuja" } {TEXT -1 50 ", jonka arvoksi olemme sijoittaneet lausekkeen x^2" }} {PARA 0 "" 0 "" {TEXT -1 89 "Jos haluamme laskea lausekkeen arvon eri \+ x:n arvoilla, joudumme k\344ytt\344m\344\344n subs-komentoa." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(x=5,f);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "eval(f,x=5); # N\344inkin voidaan, \+ t\344t\344 tapaa k\344ytetty gsg:ss\344. " }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 66 "Jos haluat seurata lauseke/funktio-juonta, hypp\344\344 t\344ss\344 kohdassa " }{TEXT 353 4 "seq-" }{TEXT -1 14 "kometojen y li." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "seq(subs(x=k, f),k=0 ..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "a:=-4: b:=4: N:=1 0: h:=(b-a)/N: arvojono:=seq(subs(x=a+k*h, f),k=0..N);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(arvojono);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 146 "\nVAROITUS: Kun matemaattista funktiota k\344s itell\344\344n lausekkeena, on oltava johdonmukainen. Siit\344 ei saa \+ v\344lill\344 k\344ytt\344\344 merkint\344\344 f(x), tietenk\344\344n! " }}{PARA 0 "" 0 "" {TEXT -1 17 " Kokeile vaikka:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(x); f(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "\nMatemaattisen funktion k\344sittely " }{TEXT 310 16 "Ma ple-funktiona:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "f := x -> x^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(x),f(y),f(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 349 71 "Tyytyk\344\344mme ensialkuun t\344h\344n. Lue kuitenkin jossain va iheessa loppukin." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 " " 0 "" {TEXT 0 7 "unapply" }{TEXT -1 36 " on toinen funktion m\344\344 rittelytapa. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "g := x^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "g(5); # T\344m\344 on tuh oon tuomittu." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Huomaamme nyt, e tt\344 olis ollut mukavampi k\344sitell\344 funktiona. No seh\344n k \344y:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g := unapply(g, x );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "What is the difference " }{TEXT 282 15 "u napply vs -> " }{TEXT -1 3 " ?" }}{PARA 15 "" 0 "" {TEXT -1 49 " Nuo lim\344\344rittely evaluoi (vasta) suoritusaikana." }}{PARA 15 "" 0 " " {TEXT -1 39 " unapply evaluoi (jo) m\344\344rittelyaikana." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "a:=x^2: f:=x->a;g:=unapply(a,x);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "a:=Pi;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(3);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "g(3);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "T \344ss\344 tilanteessa siis nuolim\344\344ritys ->" }}{PARA 0 "" 0 " " {TEXT -1 30 "tomii \"omituisesti\", kun taas " }{MPLTEXT 1 0 8 "#una pply" }{TEXT -1 20 " toimi \"odotetusti\"." }}{PARA 0 "" 0 "" {TEXT -1 81 "Siniset m\344\344ritysrivit yll\344 kertovat kyll\344 asian hyv in, niit\344 kannattaa seurailla." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Jatketaan t\344st\344 (harj0):" }}{PARA 0 "" 0 "" {TEXT 289 0 "" } }{PARA 0 "" 0 "" {TEXT -1 10 "Varoitus: " }{TEXT 311 75 "Hengenvaarall ista: \304l\344 koskaan m\344\344rittele funktiota tyyliin F(x):=laus eke;" }}{PARA 0 "" 0 "" {TEXT -1 113 "T\344ll\366in tulee m\344\344rit ellyksi funktion F arvo yhdess\344 pisteess\344 x, muilla symboleilla \+ funktio f on m\344\344rittelem\344t\366n." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 313 8 "Poikkeus" }{TEXT -1 36 ": Funktion m\344\344rittely\344 t\344ydent\344vien " }{TEXT 342 15 "poikkeusarvo jen" }{TEXT -1 61 " m\344\344rittelyss\344 t\344m\344 on hy\366dyllist \344, esimerkki otetaan kohta.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 40 "Palataan nyt viel\344 tuohon hengenvaaraa n:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "F(x):=x^3; # kokeillaan kielletty \344 leikki\344." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Tuo on syntak siltaan oikein, mutta hyvin h\344m\344\344v\344\344." }}{PARA 0 "" 0 " " {TEXT -1 12 "Mit\344 on F(x)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "N\344ytt\344\344, kuin toimisi oikein. Vaan eipas toimi muilla kuin x:ll\344." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "F(x),F(3),F(a),F(sin(z));" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Toisin sanoen funktio on m\344 \344ritelty vain, kun argumenttina on symboli " }{TEXT 354 1 "x" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Esimerkki: " }{TEXT 335 51 "Funkti on m\344\344rittelyn t\344ydent\344minen poikkeusarvoilla" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 60 "Haluamme m\344\344ritell\344 funk tion, jota joskus kutsutaan nimell\344 " }{TEXT 312 7 "sinc, " } {TEXT -1 19 "olkoon t\344ss\344 vain F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "F:=x->sin(x)/x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(0);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Yleinen \+ s\344\344nt\366 ei m\344\344rittele F-funktiota 0:ssa, koska siin\344 \+ tulee 0:lla jako." }}{PARA 0 "" 0 "" {TEXT -1 66 "Annamme siksi funkti olle 0:ssa sopivan arvon suoralla asetuksella:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "F(0):=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "F(a),F(1/2),F(0),F(sin(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "seq(F(x),x=-2..2);evalf(%);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 10 "Remember: " }{MPLTEXT 1 0 7 "# evalf" }{TEXT -1 8 " mea ns: " }{TEXT 337 4 "eval" }{TEXT -1 5 "uate " }{TEXT 336 1 "f" }{TEXT -1 14 "loating point." }}}{EXCHG {PARA 14 "" 0 "" {TEXT -1 10 "Lue lis \344\344:" }}{PARA 14 "" 0 "" {TEXT -1 16 " [HAM] ss. 62-63" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 16 "Harjoitusteht\344v\344" }}{PARA 0 "" 0 "" {TEXT -1 27 "M\344\344rittele polynomifunktio " }{XPPEDIT 18 0 "p(x)=x^3-4*x^2+4*x-1" "6#/-%\"pG6#%\"xG,**$F'\"\"$\"\"\"*&\"\"%F +*$F'\"\"#F+!\"\"*&F-F+F'F+F+F+F0" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 92 " M\344\344rit\344 nollakohdat ja paikalliset minimit sek \344 maksimit. Piirr\344 funktio ja sen derivaatta." }}{PARA 0 "" 0 " " {TEXT -1 71 " Tarkista laskemalla funktion arvot, ett\344 nollakohda t ovat nollakohtia." }}{PARA 0 "" 0 "" {TEXT -1 103 "K\344sittele poly nomia ensin lausekkeena ja sitten funktiona. Mitk\344 ovat kunkin tava n hyv\344t/huonot puolet." }}{PARA 0 "" 0 "" {TEXT -1 28 "Derivaattala useke -- diff " }}{PARA 0 "" 0 "" {TEXT -1 48 "Derivaattafunktio -- D (K\344yttele helppi\344 )" }}{PARA 0 "" 0 "" {TEXT 0 32 " ?plo t, ?solve,?fsolve ?diff, ?D" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 158 "T\344m\344ntyyppisten teht\344vien, niin yksinkertaisia matema attisesti kuin ovatkin, sujuva hallinta tekee Maple-ty\366skentelyst \344 nautittavaa puuhaa ja auttaa pitk\344lle." }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 48 "10. LinearAlgebra, linalg, matriisit ja vektorit" }}{PARA 0 "" 0 "" {TEXT -1 46 "Lue: www.math.hut.fi/~apiola/maple/opas /LA.pdf" }}{PARA 0 "" 0 "" {TEXT -1 52 "[HAM]-kirjassa (kuten monissa \+ muissakin) esitell\344\344n " }{TEXT 367 7 "lianlg-" }{TEXT -1 50 "tyy li\344, joka on uuteen verrattuna luotaanty\366nt\344v\344." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "with(LinearAlgebra): # T\344m \344 olkoon standardilatauskomentomme." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "#?LinearAlgebra # Poista kommentti edest\344, niin saat funktioluettelon ja selostusta." }}}}{SECT 1 {PARA 3 "" 0 " Algebra" {TEXT -1 36 "11. Sievennyst\344 ja yht\344l\366n ratkaisua" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 " Pohdiskelua\n" }{TEXT 266 11 " simplify" }{TEXT -1 46 " - yleissieve nt\344j\344, ensimm\344iseksi tarjoiltava." }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{TEXT 267 6 "expand" }{TEXT -1 15 " - kertoo auki" }} {PARA 4 "" 0 "" {TEXT -1 3 " " }{TEXT 283 21 "collect - kokoaa \+ " }}{PARA 0 "" 0 "" {TEXT -1 10 " " }{TEXT 0 10 "? collect " }{TEXT -1 72 " ja kokeile joitakin esimerkkej\344. Varsin hyv\344 kom ento monessa paikassa." }}{PARA 0 "" 0 "" {TEXT 268 9 " factor" } {TEXT -1 25 " - Jakaa tekij\366ihin.\n " }{TEXT 284 7 "convert" } {TEXT -1 54 " - ... Monenmoisiin konversioihin sievennyksess\344 esim \+ " }{TEXT 0 39 " convert(lauseke,parfrac,muuttuja);" }}{PARA 0 "" 0 "" {TEXT -1 103 " Huomaa, ett\344 lauseke ei muutu, uusi tulos pala utetaan. Jos halutaan p\344ivitt\344\344 lauseke, on komennetava" }} {PARA 0 "" 0 "" {TEXT -1 13 " " }{TEXT 0 43 "lauseke:=conv ert(lauseke,parfrac,muuttuja);" }}{PARA 0 "" 0 "" {TEXT 269 8 " solv e" }{TEXT -1 34 " - ratkaisee yht\344\366n tai systeemin" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 320 7 " fsolve " }{TEXT -1 24 "- ratkaisee numeerisesti" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "(x^3+1)/(x^2 -x+1);simplify(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "expan d((x^2-4)*(x+1)*(x-2)*(x^2+x+1));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "factor(%);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 10 "Yh t\344l\366ist\344" }}{PARA 14 "" 0 "" {TEXT -1 14 "[SOL] s. 11-12" }} {PARA 14 "" 0 "" {TEXT -1 28 "[HAM] s. Luku 6 s. 133 - 142" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "yhtalot:=\{2*x-5*y=12, 12*x+4*y=17 \}; # Kyseess\344 on joukko" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ratk:= solve(yhtalot, \{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 106 "Maple ei sijoita ratkaisuja muuttujille arvoiksi, vaan p alauttaa sijoituss\344\344nn\366t. Ne voidaan antaa suoraan" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "#subs" }{TEXT -1 52 "-komennolle. Mieti se uraavan komentojonon logiikkaa!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "subs(ratk,x),subs(ratk,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "X:=subs(ratk,x); Y:=subs(ratk,y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Tarkistaminen k\344y vaivattomasti:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "subs(ratk,yhtalot);" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "Voidaa n my\366s k\344ytt\344\344 " }{MPLTEXT 1 0 4 "#lhs" }{TEXT -1 22 " (le ft hand side) ja " }{TEXT 355 3 "rhs" }{TEXT -1 363 " (right hand sid e)-tapaa, mutta se on hiukan v\344hemm\344n elegantti ja my\366s altis Maplen harrastamalle j\344rjestyksen vaihtumiselle ratkaisujoukossa. \+ Niinp\344 t\344t\344 tyyli\344 ei voida ajaa automaattisesti, vaan tul oksiin on puututtava interaktiivisesti, mik\344 voi olla kiusallista, \+ jos on \"vakavahenkisest\344\" dokumentista kyse. Joka tapauksessa t \344m\344kin tyyli kannattaa omaksua." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "rhs(ratk[1]);lhs(ratk[1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "lhs(ratk[2])=rhs(ratk[2]);" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 41 "Ratkaisun sijoittaminen muuttujan arvoksi" }}{PARA 0 "" 0 "" {TEXT -1 94 "T\344ss\344 nyt on toisin sanoin selitetty sama a, pyyhi omasta dokustasi pois tai j\344rjest\344 paremmin." }}{PARA 0 "" 0 "" {TEXT -1 14 "Tietysti n\344in:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "X:=rhs(ratk[1]);Y:=rhs(ratk[2]);" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 62 "Turvallisempi ja elegantimpi tapa (jota edell\344 \+ mainostettiin):" }}{PARA 0 "" 0 "" {TEXT -1 5 " " }{TEXT 299 151 " Suorita ratk-yht\344l\366iden ilmaisemat korvaamiset lausekkeessa (pel kk\344) x ja\n suorita ratk-yht\344l\366iden ilmaisemat korvaamise t lausekkeessa (pelkk\344) y ." }}{PARA 0 "" 0 "" {TEXT -1 118 "Edelli sess\344 y-yht\344l\366 j\344\344 vaille k\344ytt\366\344 (kun pelkk \344 x ei sis\344ll\344 y:t\344) ja j\344lkimm\344isella vastaavasta s yyst\344 x-yht\344l\366. " }{TEXT 356 4 "ratk" }{TEXT -1 42 "-joukon j \344rjestys ei n\344yttele mit\344\344n osaa." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "X:=subs(ratk,x);Y:=subs(ratk,y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "Tehokkain, mutta turvattomin tapa, joskus kyll\344kin tosi k\344tev\344: " }{TEXT 0 13 "assign(ratk);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "assign(ratk);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "x;y;yhtalot;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 120 "solve(yhtalot,\{x,y\}); # assign-komennon j \344lkeen x ja y eiv\344t ole vapaita muuttujia, josta syyst\344 solve menee virheeseen." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 0 13 "assign(ratk) ;" }{TEXT -1 34 " toimii ik\344\344nkuin ratk-yht\344l\366iss\344 " } {TEXT 300 52 "yht\344l\366merkki (=) vaihdettaisiin sijoitusmerkkin (: =)" }}{PARA 0 "" 0 "" {TEXT -1 87 " Yht\344l\366iden toteutuminen \+ saadaan hyvin k\344tev\344sti tarkistetuksi kirjoittamalla vain " } {TEXT 0 8 "yhtalot;" }}{PARA 0 "" 0 "" {TEXT -1 55 " Sensijaan yh t\344l\366iden ratkaisua ei voida toistaa, " }{TEXT 301 51 "ennekuin m uuttujat x ja y on vapautettu arvoistaan." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 "x:='x':y:='y':solve(yhtalot,\{x,y\});" }}}}{SECT 1 {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "Piirtoa" {TEXT -1 11 "10. Piirtoa" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 17 "[SOL] ss. 10 - 11" }}{PARA 0 "" 0 "" {TEXT -1 26 " [HAM] Luku 3 ss. 89 - 100" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "Tavallinen k\344yrien piirto" }}{PARA 0 " " 0 "" {TEXT -1 44 "K\344yr\344parven voi sulkea joko joukkosulkuihin \+ " }{MPLTEXT 1 0 3 "\{ \}" }{TEXT -1 20 " tai listasulkuihin " } {MPLTEXT 1 0 3 "[ ]" }{TEXT -1 130 " .\nJ\344lkimm\344inen lienee suos iteltavaa, koska j\344rjestys on silloin k\344ytt\344j\344n hallinnass a (esim jos halutaan v\344rit hallitusti, tms)." }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 32 "plot([sin(x),cos(x)],x=0..4*Pi);" }}}{EXCHG {PARA 15 "" 0 "" {TEXT -1 69 "Ota hiiren vasemmalla kiinni kuvasta, sa at kehyksen ja uudet valikot." }}{PARA 0 "" 0 "" {TEXT -1 46 " Val itse sama mittakaava akseleilla (1:1)" }}{PARA 15 "" 0 "" {TEXT -1 90 "Jos grafiikka alkaa hidastaa ty\366arkin selausta, kannattaa valit a EDIT-valikon alimmasta, \n" }{TEXT 302 14 "Remove output." }{TEXT -1 159 " Sit\344 kannattaa k\344ytt\344\344 muutenkin silloin t\344ll \366in. Ty\366arkki tiivistyy (ja nopeutuu) kummasti. Outputit saa tak aisin saman EDIT-valikon toiseksi alimmaisesta " }{TEXT 303 17 "execu te worksheet" }}{PARA 15 "" 0 "" {TEXT -1 170 "Huomaa: Pi on Iso P, pi eni i . (pi kirjoittuu oikean n\344k\366isesti, mutta Maple ei tunnist a sit\344\nmuuksi kuin kreikkalaiseksi kirjaimeksi. ) [No johan tuost a huomauteltiin.]" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 47 "Parametrim uotoinen piirtomatrixplot(logtaulu);\n" }}{PARA 0 "" 0 "" {TEXT -1 90 "Syntaksi poikkeaa aika v\344h\344n, t\344m\344 t\344ytyy vain oppia ( tai katsoa aina uudelleen helpist\344)." }}{PARA 0 "" 0 "" {TEXT -1 123 "Aina ei ole hauskaa joutua valitsemaan hirell\344, samaskaalaiisu us (ja monia muita) voidaan antaa plot-komennon tarkentimena." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([cos(t),sin(t),t=0..2*P i],scaling=constrained);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 276 "Pist eet voidaan yht\344 hyvin ajatella kompleksitason pistein\344. complex plot osaa k\344sitell\344 suoraan reaalimuuttujan kompleksiarvoista fu nktiota. T\344ss\344 on sekin mukava piirre, ett\344 syntaksi on luonn ollisempi ja siten helpompi muistaa kuin tuossa parametrimuotoisessa R ^2-piirrossa." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "complexplot(cos(t)+I*sin(t),t=0..2*Pi,scaling=constra ined,color=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "Edellinen v oidaan ilmaista lyhyemmin eksponenttifunktion (Eulerin kaavan) avulla. Piirret\344\344n vaihteeksi pelk\344t pisteet." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "complexplot (exp(I*t),t=0..2*Pi,scaling=constrained,color=cyan,style=point);" }}}} {SECT 1 {PARA 4 "" 0 "" {TEXT -1 40 "Taulukoidun datan piirto (\"lista plotti\")" }}{PARA 0 "" 0 "" {TEXT -1 471 "Sometimes we will be intere sted in functions defined in terms of a discrete \ntable of values rat her than a formula. For example, consider the following table of \nte mperatures recorded at various times on a spring day in Raleigh.\n \+ \n Time: | 6:00 a.m. | 10:00 a.m. | 12:00 p.m. | 4:00 p.m. | \+ 5:00 p.m.\n ----------------------------------------------\n Temp: \+ | 45 deg. | 57 deg. | 65 deg. | 67 deg. | 66 deg. \n\n " }{TEXT 275 61 "Table of Temperatures on a Spring Day in Degrees Fahrenheit " }{TEXT -1 2 " \n" }}{PARA 0 "" 0 "" {TEXT -1 218 "To plot this data you must first define the poin ts as a list. Since the time is recorded in a cyclic fashion, we will plot the times in the so-called \"military style\", i.e. 6:00 a.m. \+ is 0600 and 6:00 p.m. is 1800.\n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "ListOfPoints := [[600,45], [1000,57], [1200,65], [160 0,67], [1700,66]];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " } {TEXT 276 4 "plot" }{TEXT -1 223 " command allows you to plot a list o f points and to connect them with straight lines (unless you choose an other option). This is illustrated in the next command. Notice also \+ the option which produces a title on the plot.\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "plot(ListOfPoints, title=\"Temperatures at Va rious Times\");" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "\nWhile the d ata can be plotted in this way, because the data is given for a discr ete set of points you may prefer the " }{TEXT 0 11 "style=POINT" } {TEXT -1 73 " option as illustrated in the next command. Note also th e effect of the " }{TEXT 0 13 "symbol=CIRCLE" }{TEXT -1 9 " option.\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "plot(ListOfPoints, sty le=POINT, symbol=CIRCLE,symbolsize=15, title=`Temperatures at Various \+ Times`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 8 "Exercise" }}{PARA 0 "" 0 "" {TEXT -1 23 "1 . Plot the graph of " }{XPPEDIT 18 0 "f(x)=exp(-x)*sin(2*x)" "6#/-% \"fG6#%\"xG*&-%$expG6#,$F'!\"\"\"\"\"-%$sinG6#*&\"\"#F.F'F.F." }{TEXT -1 21 " over the interval [" }{XPPEDIT 18 0 "-pi,pi" "6$,$%#piG!\"\"F $" }{TEXT -1 3 "] ." }}{PARA 0 "" 0 "" {TEXT -1 341 "2. Make a plot o f the points in the following table:\n\n X: | -1 | 0 \+ | 1 | 2 | 3 \n --------------- ----------------------------\n Y: | 2.72 | 1 | 0. 368 | 0.135 | 0.0498 \n\nMake two plots, one with the points c onnected and the other with only the data points.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 72 "Miten saadaan k\344tev\344sti koordinaattipari en lista [[x1,y1],[x2,t2],...] ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 114 "Olkoon annettu numeeriset listat (Matlab issa sanoisimme vektorit) X ja Y. Matlabin plot toimii tyyliin plot(x ,y);" }}{PARA 0 "" 0 "" {TEXT -1 61 "Maplessa t\344ytyy muodostaa pari en lista vaikkapa t\344h\344n tapaan:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "a:=-Pi:b:=Pi:N:=20:h:=(b-a)/N:x:=seq(evalf(a+i*h),i=0 ..N);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "Olkoot y-arvot vaikkapa \+ sin-funktion arvoja x-pisteiss\344. Parijono saataisiin nyt n\344in:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "xy:=[seq([x[i],sin(x[i])] ,i=1..N+1)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "plot(xy);pl ot(xy,style=point,symbol=circle);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 304 5 "Huom:" }{TEXT -1 1 " " }{TEXT 305 5 "plots" }{TEXT -1 17 "-pakkauksessa on " }{TEXT 0 9 "listplot " } {TEXT -1 3 "ja " }{TEXT 0 9 "pointplot" }{TEXT -1 318 ". Maplelle luon teenomaista on, ett\344 siin\344 on joukko redundantteja funktioita. M ielest\344ni on parempi oppia k\344ytt\344m\344\344n harvempaa ydinfun ktiojoukkoa kuin omaksua monenlaisia synonyymej\344. Niiss\344 voi tok i olla joitakin uusia mahdollisuuksia, mutta esim. n\344iss\344 ei v \344ltt\344m\344tt\344 ole (kuka noita kaikkia tuhansia ehtii penkoa). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 11 "Taulukointi" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "T\344ss\344 teimme itse asiassa taulukon, joka on havainn ollisempi usein matriisina." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "txy:matrix(xy):linalg[transp ose](xy):" }}}{EXCHG {PARA 13 "" 0 "" {TEXT -1 74 "Tilan s\344\344st \344miseksi otetaan v\344hemm\344n dataa esimerkkiimme. J\344tet\344 \344np\344 my\366s " }{TEXT 0 6 "evalf " }{TEXT -1 5 "pois." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 " a:=-Pi:b:=Pi:N:=8:h:=(b-a)/N:x:=seq(a+i*h,i=0..N);\nxy:=[seq([x[i],sin (x[i])],i=1..N+1)];\nmatrix(xy);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "linalg[transpose](xy);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "array(xy); # Taas synonyymi, mutta tiettyj\344 eroja kin yleisyydessa / matriisilaskukyvyiss\344." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 53 "Grafiikoiden yhdist\344minen, plots[display] ja text plot" }}{PARA 0 "" 0 "" {TEXT -1 37 "T\344ss\344 tarvitaan lis\344graf iikkapakkaus " }{TEXT 258 5 "plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart:with(plots): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Selvit\344 itsellesi, mit\344 seuraavassa tehd\344\344n. Mieti tarkkaan, miksi jossain pit\344\344 antaa plot:lle argumentiksi " }}{PARA 0 "" 0 "" {TEXT -1 95 "f(x) ja miksi taas jossain esim. tang . Voit sitten huvitella vaihtelemalla funktion m\344\344ritelm\344\344 " }}{PARA 0 "" 0 "" {TEXT -1 103 "ja / tai pistett\344 x0. Kirjoitetaa n pieni malliskripti, jonkalaisia voit tehd\344 moninaisissa yhteyksis s\344." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x0:=1: f:=x->x^3: # Vaihtuva sy\366te" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " df:=diff(f(x),x): kk:=subs(x=1,df) ; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "x0:=1: tang:=f(x0)+kk *(x-x0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "fkuva:=plot(f( x),x=0..2,color=red): tangkuva:=plot(tang,x=0..2,color=blue): p0kuva:= plot([[x0,f(x0)]],style=point,symbol=circle,symbolsize=15,color=black) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "display([fkuva,tangkuv a,p0kuva]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 90 "Kokeile (mutta vain kerran el \344m\344ss\344si, silloinkin syv\344sti katuen, ett\344 olit yllytysh ullu)," }}{PARA 0 "" 0 "" {TEXT -1 50 " mit\344 tapahtuu, kun vaihdat \+ (:) -> (;) vaikkapa " }{TEXT 0 10 "fkuva:=; ." }{TEXT -1 37 ".. yll \344. PLOT-tietorakenne paljastuu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 63 "- No, mene edit-valikkoon ja -> remove ou tput, kyll\344 se siit\344." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Sometimes it will be desirable to \+ " }{TEXT 277 21 "print text on a plot." }{TEXT -1 6 " The " }{TEXT 285 5 "plots" }{TEXT -1 11 " procedure " }{TEXT 286 8 "textplot" } {TEXT -1 71 " will allow this. The following commands will serve as ex amples of the " }{TEXT 287 7 "textplo" }{TEXT -1 6 "t and " }{TEXT 288 7 "display" }{TEXT -1 89 " routines. Make sure you notice where c olons and semicolons are used in these commands.\n" }}{PARA 0 "" 0 "" {TEXT -1 322 "In the next commands it is important to use colons to p unctuate the first two statements. Otherwise Maple will ouput an enti re page of text describing the plot structure rather than the graph. \+ The textplot in the second command causes the text x=0.6356,y=0.5000 t o be printed at the point (.6356,.5000). The statement " }{TEXT 0 11 "align=RIGHT" }{TEXT -1 46 " aligns this text to the right of the poin t. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 191 "f := x -> exp(-x)* sin(3*x);\nplot1 := plot(f, 0..3):# tai plot1:=plot(f(x),x=0..3):\nplo t2 := plots[textplot]([0.6356, 0.5000, \"x=.6356, y=.5000\"], align=RI GHT):\nplots[display](\{plot1, plot2\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 278 5 "Huom:" }}{PARA 0 "" 0 "" {TEXT -1 88 "plots-pakkauksen (k uten muidenkin pakkausten) funktioita voidaan k\344ytt\344\344 my\366s lataamatta" }}{PARA 0 "" 0 "" {TEXT -1 84 "koko pakkausta, t\344ll \366in pakkauksen nime\344 ik\344\344nkuin indeksoidaan ao. funktion n imell\344" }}{PARA 0 "" 0 "" {TEXT -1 9 "tyyliin " }{TEXT 0 14 "plots [display]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 25 "3d-grafiikkaa, animaatiot" }}{PARA 0 "" 0 "" {TEXT -1 49 "Otetaan l\344mm\366njohtumisesimerkki, jossa valaist aan" }}{PARA 15 "" 0 "" {TEXT -1 18 "3d-pinnan piirtoa " }}{PARA 15 " " 0 "" {TEXT -1 11 "Animaatiota" }}{PARA 15 "" 0 "" {TEXT -1 37 "3d-ku van projektiok\344yr\344parven piirtoa" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 147 "Tarkastellaan sivuiltaan l\344mp\366 eristetty\344 sauvaa, jonka p\344\344t upotetaan hetkell\344 t=0 j\344 \344vesis\344ili\366ihin (0 astetta) ja jonka\nalkul\344mp\366tilajaka uma on \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=x->100*sin(P i*x/80);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 22 "Huomaa funktiom\344 \344ritys" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 169 "Olk oon sauvan pituus L=80.\n\nT\344ss\344 tapauksessa l\344mp\366yht\344l \366n ratkaisuna olevasta Fourier-sarjasta tulee vain yksi termi. Ratk aisu on (sopivalla l\344mm\366njohtumiskertoimella)\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "u:=(x,t)->100*sin((Pi*x)/80)*exp(-0 .001785*t);" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Pintapiirros" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot3d(u(x,t),x=0..80,t=0..400);" } }}{EXCHG {PARA 15 "" 0 "" {TEXT -1 74 "Klikkaa hiirell\344 kuvaan (ja \+ tarvittaessa valitse \"boxed\") ty\366kalunauhasta." }}{PARA 15 "" 0 " " {TEXT -1 22 "Kierr\344 kuvaa hiirell\344." }}{PARA 15 "" 0 "" {TEXT -1 63 "Kokeile STYLE-valikosta PATCH ja PATCH with contour valintoja. " }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "Animaatio" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "animate(u( x,t),x=0..80,t=0..300,frames=30,color=blue);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 0 "" }}}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 36 "L\344mp\366ti laprofiilit ja korkeusk\344yr\344t" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "plot(\{seq(u(x,t),t=[0,10,50,100,200,300,400])\},x=0. .80);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "contourplot(u(x,t) ,x=0..80,t=0..400);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} }{SECT 1 {PARA 5 "" 0 "" {TEXT -1 12 "Implicitplot" }}{PARA 0 "" 0 "" {TEXT -1 59 "T\344m\344 on periaatteessa sama kuin yhden korkeusk\344y r\344n piirto." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "implicitpl ot(\{x^2+y^2=1,x^3+y^3=1,x^10+y^10=1\},x=-2..2,y=-2..2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Tuohon tekisi mieli laittaa loppuu n esim: " }{TEXT 0 25 ",color=[red,blue,black]);" }}{PARA 0 "" 0 "" {TEXT -1 22 "mutta n\344k\366j\344\344n kaikki " }{TEXT 279 4 "plot" } {TEXT -1 39 ":n hyv\344ksym\344t optiot eiv\344t t\344ss\344 toimi." } }}}}}}{MARK "14" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }