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-1 325 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 326 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 327 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 328 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Tim es" 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 "Ti mes" 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 "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 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 "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 37 "Mat-1.415 Matematiikan pe ruskurssi V3" }}{PARA 19 "" 0 "" {TEXT 262 18 "Maple-perusteita, " }} {PARA 19 "" 0 "" {TEXT 327 10 "harj0.mws " }{TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 42 "T\344ss\344 on perusty\366arkki Mapleharjoitteluun ." }}{PARA 0 "" 0 "" {TEXT -1 69 "T\344t\344 voi k\344yd\344 lis\344n \344 to 19.9., varsinaiset teht\344v\344th\344n ovat lyhyit\344." }}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Yleisi\344 toimintaohjeita" }} {PARA 0 "" 0 "" {TEXT 311 27 "Muista tallettaa aika ajoin" }{TEXT -1 98 ". Maple oon ainakin joskus entisaikaan joskus kaatuilluta, toivott avasti ei en\344\344. Silti kannattaa!" }}{PARA 0 "" 0 "" {TEXT -1 106 "Talletus on joka tapauksessa syyt\344 tehd\344 aina ennen jotain \+ potentiaalisesti isoa laskentaa. Muista lyhyt: " }{TEXT 319 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 320 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 321 11 "El\344m\344nohje:" }}{PARA 0 "" 0 "" {TEXT -1 294 "Maple n filosifiaa kannattaa opetella senverran, ett\344 ty\366skentely k \344y nautittavaksi. Kannattaa yritt\344\344 itse ja kaverien kanssa \+ (ja kirjoista) selvitell\344 my\366s pulmatilanteita, t\344llaiseen om atoimisuuteen on nyt ainutlaatuinen tilaisuus, kun puolet neuvontaharj oituksista on \"vapaita opettajasta\"." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 293 23 "Viikon oppitavoitteita:" }}{PARA 15 "" 0 "" {TEXT -1 18 "Ty\366arkin k\344sittely" }}{PARA 15 "" 0 "" {TEXT -1 37 "Peruslaskutoimitukset ja sievennykset" }}{PARA 15 "" 0 " " {TEXT -1 9 "Grafiikka" }}{PARA 15 "" 0 "" {TEXT -1 27 "Vapaat ja sid otut muuttujat" }}{PARA 15 "" 0 "" {TEXT 292 21 "Lauseke vs. funktio \+ " }}{PARA 15 "" 0 "" {TEXT -1 42 "Matriisit ja vertailu Matlab-ty\366s kentelyyn" }}{PARA 15 "" 0 "" {TEXT -1 27 "Perustietorakenteet, erit. \+ " }{TEXT 294 22 "jonot, joukot, listat." }}{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 "Katsotaan ensin ty\366arkkiin (worksheet) liittyvi \344 asioita." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT -1 31 "Uuden (laskenta)kehotteen saa " }{TEXT 257 1 ">" }{TEXT -1 44 " :lla tai CTR-J (j\344lkeen) tai CTR-K (ennen)" }}{PARA 15 "" 0 "" {TEXT -1 29 "Laskentakehote->tekstitila: " }{TEXT 258 1 "T" }} {PARA 15 "" 0 "" {TEXT -1 22 "Matemaattinen teksti: " }{TEXT 259 16 "T - tilasta -> " }{XPPEDIT 18 0 "Sigma" "6#%&SigmaG" }{TEXT -1 9 " - t ilaan" }}{PARA 15 "" 0 "" {TEXT -1 72 "Maple-sy\366te -> matem. teksti : Maalaus (hiiren vas.), vied\344\344n kursori, " }{XPPEDIT 18 0 "Si gma;" "6#%&SigmaG" }}{PARA 15 "" 0 "" {TEXT -1 36 "Uusi luku: INSERT-v alikko, ->SECTION" }}{PARA 15 "" 0 "" {TEXT -1 62 "Leikkaa/liimaa: UNI X/X:ss\344 oikein 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, C TR-V)" }}{PARA 15 "" 0 "" {TEXT -1 85 "Jos ty\366arkin selaus k\344y h itaaksi ja usein muutenkin, kannattaa valita EDIT-valikosta " }{TEXT 312 16 "remove output . " }{TEXT -1 106 "\nSe on k\344tev\344 my\366s \+ ty\366arkin pakkaamiseen, turha s\344ilytell\344 isoja kuvia ym. kun n e on talletettuna koodiin." }}{PARA 15 "" 0 "" {TEXT -1 57 "K\344\344n teinen toimenpide on EDIT-valikon edellinen valinta: " }{TEXT 323 18 " execute worksheet." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {EXCHG {PARA 5 "" 0 "" {TEXT -1 115 "Suurenna Maple-ikkuna riitt\344v \344n isoksi ja ota rinnalle ty\366arkki http://www.math.hut.fi/teachi ng/v/maple/pohja.mws " }}{PARA 0 "" 0 "" {TEXT -1 180 "T\344m\344 on \+ yleinen pohja, jota voidaan k\344ytt\344\344 harjoituksissa. Huomaa, \+ ett\344 voit leikata/liimata ty\366arkilta toiselle (tietysti). Nime \344 se uudelleen, jotta voit tallettaa itsellesi. " }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Viitteit\344" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 122 " [HAM] Apiola: Symb ja num. lask Maple-ohjelmalla, O tatieto 588 (N\344it\344 saa kurssilamme 8 euron erikoishintaan (psst! ))" }}{PARA 0 "" 0 "" {TEXT -1 227 " T\344m\344 teos ilmeisin e puutteineenkin on suositeltava, sit\344 tarvitaan niin V2 kuin V3-ku rsseilla. T\344ydennyst\344 vaatii erityisesti matriisilasken taosuus, sill\344 uusi LinearAlgebra-tyyli tuli vasta versioon 6. Kts " }{TEXT 328 6 "LA.mws" }}{PARA 0 "" 0 "" {TEXT -1 6 " " }{TEXT 322 23 "Kurssin Maple-hakemisto" }{TEXT -1 36 ": www.math.hut.fi/teac hing/v/maple/" }}{PARA 0 "" 0 "" {TEXT -1 96 " gsg.pdf, lrngui de.pdf, prguide.pdf (Getting Started, Learning, Programming, Maple \+ 7)" }}{PARA 14 "" 0 "" {TEXT -1 45 "[VIR] Virrankoski: http://matta.hu t.fi/matta/" }}{PARA 14 "" 0 "" {TEXT -1 103 "[PIKA] Apiola-Peltola: M aple-pikaopas, jaettu ja http://www.math.hut.fi/teaching/k3/maple-pika opas.html" }}{PARA 14 "" 0 "" {TEXT -1 83 "[SOL] Solmun Maple-kirjoitu s (jaettu) http://solmu.math.helsinki.fi/1999/5/apiola/" }}{PARA 14 " " 0 "" {TEXT -1 85 "[HECK] Heck: An Introductio to Maple (Springer), \+ t\344ydellisin ja kattavin Maple-kirja" }}{PARA 14 "" 0 "" {TEXT -1 33 "[ISR] Israel: Calculus with Maple" }}}}{SECT 1 {PARA 3 "" 0 "First Things First" {TEXT -1 16 "1. Aivan ensiksi" }}{PARA 0 "" 0 "" {TEXT 296 5 "Huom:" }{TEXT -1 1 " " }}{PARA 14 "" 0 "" {TEXT -1 100 "Kun lat aat ty\366arkin FILE-valikon OPEN-valinnalla, saat k\344ytt\366\366si \+ visuaalisen esityksen Maple-ty\366st\344." }}{PARA 14 "" 0 "" {TEXT -1 18 "Ty\366arkilla olevat " }{TEXT 297 27 "komennot suorittuvat vast a," }{TEXT -1 39 " kun siirryt punaiseen INPUT-soluun ja " }{TEXT 298 13 "painat ENTER:" }{TEXT -1 3 "i\344." }}{PARA 0 "" 0 "" {TEXT -1 5 " " }}{PARA 0 "" 0 "" {TEXT -1 93 "Jos haluat jatkaa kokeiluja t \344ll\344 kohdalla, tee lis\344\344 kehotteita joko klikkaamalla ko htaa >" }}{PARA 0 "" 0 "" {TEXT -1 25 "tai CTR-J (jos j\344lkeen)" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "247*3756;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Ty\366arkin painikkeita ja k\344sittely\344 on \+ sellostettu havainnollisin kuvin " }{TEXT 324 8 "gsg.pdf:" }{TEXT -1 4 "ss\344." }}}}{SECT 1 {PARA 3 "" 0 "Laskentoa numeroilla" {TEXT -1 24 "2. Laskentoa numeroilla" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 "Laskuoperaatiot ovat \"normaalit\" +-*/^ , " } {TEXT 313 27 "kertomerkki\344 ei saa j\344tt\344\344 " }{TEXT -1 27 "p ois (kuten Mathematicassa)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Harj oittelemme laskentoa. Hypp\344\344 yli, jos pitk\344stytt\344\344." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "tai:=sitten=kokeile*jotain/ tassa;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Maple vaatii loppumerki n, joko ; tai : Kokeile, jos et jo tied\344." }}{PARA 0 "" 0 "" {TEXT 266 11 "Lue 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 "Laskento a symboleilla ja numeroilla" {TEXT 263 39 "3. Laskentoa symboleilla j a numeroilla" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 0 "" 0 " " {TEXT 325 11 "Pohdiskelua" }}{PARA 0 "" 0 "" {TEXT -1 3 "Lue" }} {PARA 16 "" 0 "" {TEXT -1 49 "[SOL] s 15-16 Symbolien hallintaa ja per iaatteita" }}{PARA 16 "" 0 "" {TEXT -1 27 "[HAM] s. 70 - 71 (korjaus: \+ " }{TEXT 295 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 "(see Heck Ch 3 Variables and names p. 65 -.. " }}{PARA 0 "" 0 "" {TEXT -1 34 "The secret behind success of CA : " }{TEXT 283 24 "free (unbound) variables" }{TEXT -1 4 " . )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "On hyv\344 totute lla laittamaan " }{TEXT 0 8 "restart " }{TEXT -1 50 "ty\366arkin alkuu n (ja muihinkin heng\344hdyspaikkoihin)" }}{PARA 0 "" 0 "" {TEXT -1 53 "Painele nyt ENTER:i\344 ja palaa ohjeen mukaan takaisin." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart: # PA LUURIVI 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "(a+b)^2; \+ # PALUURIVI 1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " expand(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=x^2 :b:=ex p(c*z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "1) Palaa alkuu kohtaan " }{TEXT 0 11 "PA LUURIVI 1" }{TEXT -1 29 " ja napsuttele komennot l\344pi." }}{PARA 0 " " 0 "" {TEXT -1 24 "2) Palaa alkuu kohtaan " }{TEXT 0 11 "PALUURIVI 2 " }{TEXT -1 29 " ja napsuttele komennot l\344pi." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{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'):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a:='a':b:=' b':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "a:=1: b:=kissa; unas sign('a','b'); a,b; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "c:= exp(x^ 3); unassign('c'); c;" }}}{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(P i,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 299 11 "Huomaa t\344m\344" }{TEXT -1 38 ": Maple osaa vain \"tekstink\344sitell\344\" " }{TEXT 264 2 "pi" }{TEXT -1 26 ":t\344, laskentaan tarvitaan " }{TEXT 265 2 "Pi" }}{PARA 0 "" 0 " " {TEXT -1 57 "T\344ss\344 tulee usein virheit\344 alkavalle Maple-urh eilijalle. " }}{PARA 14 "" 0 "" {TEXT 301 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\366 s samainen " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 5 "" 0 "" {TEXT -1 31 "Kompleksi lukuja, imag. yksikk\366 " }{TEXT 0 1 "I" }}{PARA 0 "" 0 "" {TEXT -1 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 "" {MPLTEXT 1 0 24 "z1:=a1+I*a2;z2:=a2+I*b2;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "z1/z2;evalc(%);polar(%%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Maple olettaa symbolit a1,b1, . .. reaalisiksi, ellei tyyppim\344\344rityksi\344 anneta." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "T\344ss\344 voit l askea vaikka joitakin KRE-kirjan teht\344vi\344." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "polar((1+2* I)/(3-4*I));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "w:=exp(I*2* k*Pi/n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "with(plots): se toptions(scaling=constrained,axes=framed): # Sama skaala akseleilla\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "w:=exp(I*2*k*Pi/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 70 "complexplot( [ykkosen5juuret],style=point,symbol=circle,symbolsize=15);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "complexplot(exp(I*Pi*t),t=0..2*Pi,c olor=blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Grafiikat saadaan \+ samaan kuvaan funktiolla " }{TEXT 0 7 "display" }{TEXT -1 15 " (joka a sustaa " }{TEXT 0 5 "plots" }{TEXT -1 29 "-pakkauksessa), kts alempana ." }}}}{SECT 1 {PARA 3 "" 0 "Matemaattista tekstink\344sittely\344" {TEXT -1 59 "4. Komentojen \"hidastusmuodot\" alkavat isolla kirjaime lla." }}{PARA 0 "" 0 "" {TEXT -1 116 "Usein on hyv\344 est\344\344 lop ullinen evaluointi ainakin aluksi. Joillakin funktioilla on iso-kirjai nalkuinen \"inert form\"." }}{PARA 0 "" 0 "" {TEXT -1 62 "Yleens\344 e tuhipsukoita ' ' voi my\366s k\344ytt\344\344 evaluoinnin estoon." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "Int(x*sin(x),x); # hidastusmuoto (inert form), alkaa isolla I:ll \344" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(x*sin(x),x);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Int(x*sin(x),x);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "value(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 72 "Aika k\344tev\344 tyyli (ala Heck): (N\344et het i, ymm\344rsik\366 Maple sinut oikein.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "Int(x*sin(x),x); value(%);" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 302 31 "Hidastusmuoto est\344\344 evaluoinnin" }{TEXT -1 96 ", se tarjoaa k\344tev\344n tavan kirjoittaa matemaattisia kaavoja k\344 ytt\344m\344ll\344 Maplen yht\344l\366rakennetta." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 32 "Int(x*sin(x),x)=int(x*sin(x),x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Int(x*sin(x),x): %=value(%); # Kir joitusty\366t\344 s\344\344st\344v\344 (Heck-)tyyli." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 303 44 "Evaluointi voidaan est\344\344 my\366s 'hipsuk oilla' " }{TEXT -1 105 ", vrt [SOL] s. 9 rivi 1 ja s. 15. T\344h\344np \344 tuo edell\344 ollut muuttujan vapauttaminen arvostaankin perustuu ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "'int(x*sin(x),x)'=int( x*sin(x),x);\n'diff(x*sin(x),x)'=diff(x*sin(x),x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Otetaan viel\344 sin:n ja cos:n yhteenlaskukaava t (Maple korvaa MAOL-taulukkoja):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "sin(alpha+beta): %=expand(%);\ncos(alpha+beta): %=exp and(%);\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "D efining Variables and Functions" {TEXT -1 35 "5. Defining Variables an d Functions" }}{PARA 14 "" 0 "" {TEXT -1 8 "T\344m\344 on " }{TEXT 267 11 "t\344rke\344 asia" }{TEXT -1 21 " ymm\344rt\344\344 kunnolla. \+ " }}{PARA 14 "" 0 "" {TEXT -1 10 "[ALK] 1.4" }}{PARA 14 "" 0 "" {TEXT -1 23 "[SOL] s. 17 Ohjelmointi" }}{PARA 14 "" 0 "" {TEXT -1 43 " [HAM] 2.4 Matemaattiset funktiot s. 60 - 63" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 11 "Pohdiskelua" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 33 "Matemaattisen funktion k\344sittely " } {TEXT 314 18 "Maple-lausekkeena " }}{PARA 0 "" 0 "" {TEXT -1 62 "perus tuu samaan ilmi\366\366n kuin edell\344 PALUURIVI1 ja 2-tilanteet." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "f := x^2;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 153 "M\344\344rittelemme muuttujan f, jota k\344yt \344mme matemaattisen funktion tavoin. Maplen kannalta f on muuttuja, \+ jonka arvoksi olemme sijoittaneet lausekkeen x^2 ." }}{PARA 0 "" 0 "" {TEXT -1 89 "Jos haluamme laskea lausekkeen arvon eri x:n arvoilla, jo udumme k\344ytt\344m\344\344n subs-komentoa." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=5, f);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Jos haluat seurata lauseke/funktio-juonta, hypp\344\344 t\344ss \344 kohdassa seq-kometojen yli." }}}{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:=10: h:=(b-a)/N: arvojono:=seq(subs (x=a+k*h, f),k=0..N);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ev alf(arvojono);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 134 "\nVAROITUS: Ku n matemaattista funktiota k\344sitell\344\344n lausekkeena, on oltava \+ johdonmukainen. Siit\344 ei saa v\344lill\344 k\344ytt\344\344 merkint \344\344 f(x)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Maple on inhottavan pikkutarkka. Kokeile vaikka:\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(x); f(5);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "\nMatemaattisen funktion k\344sittely " } {TEXT 315 16 "Maple-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 0 7 "unapply" }{TEXT -1 36 " on toinen funktion m\344 \344rittelytapa. " }}}{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 tuhoon tuomittu." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 76 "Huomaamme ny t, ett\344 olis ollut mukavampi k\344sitell\344 funktiona. No seh\344 n 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 284 15 "u napply vs -> " }{TEXT -1 4 " ?\n" }}{PARA 15 "" 0 "" {TEXT -1 42 " N uolim\344\344rittely evaluoi suoritusaikana." }}{PARA 15 "" 0 "" {TEXT -1 35 " unapply evaluoi m\344\344rittelyaikana." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 125 "Ensi tutustumisvaiheessa voidaan j\344tt \344\344 unapply v\344hemm\344lle huomiolle, mutta se on useissa yhtey ksiss\344 varsin k\344ytt\366kelpoinen." }}}{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 24 "J atketaan t\344st\344 (harj0):" }}{PARA 0 "" 0 "" {TEXT 291 0 "" }} {PARA 0 "" 0 "" {TEXT -1 10 "Varoitus: " }{TEXT 316 75 "Hengenvaaralli sta: \304l\344 koskaan m\344\344rittele funktiota tyyliin F(x):=lause ke;" }}{PARA 0 "" 0 "" {TEXT -1 93 "T\344ll\366in nimitt\344in et tosi aankaan m\344\344rittele funktiota, vaan kummallisennimisen muuttujan \+ F(x)" }}{PARA 0 "" 0 "" {TEXT -1 30 "arvon (n\344in on hyv\344 ajatell a)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 318 8 "Po ikkeus" }{TEXT -1 109 ": Funktion m\344\344rittely\344 t\344ydent\344v ien poikkeusarvojen m\344\344rittelyss\344 t\344\344 on ihan JEES, esi merkki otetaan kohta.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 40 "Palataan nyt viel\344 tuohon hengenvaaraan:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "restart:F(x):=x^3; # N\344i n ei sitten tosiaankaan tehd\344 paitsi alla mainitussa poikkeuspistet ilanteessa." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Tuo on syntaksilta an 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, k uin 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 35 "Nyt se sallittu (hallittu) k\344y tt\366:" }}{PARA 0 "" 0 "" {TEXT -1 72 "Haluamme m\344\344ritell\344 f unktion, jota esim. GLJ-kirjassa kutsutaan nimell\344 " }{TEXT 317 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 "" {MPLTEXT 1 0 8 "F(0 ):=1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "seq(F(x),x=-2..2); evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(0);" }}} {EXCHG {PARA 14 "" 0 "" {TEXT 300 39 "Funktion poikkeusarvoja m\344 \344ritelt\344ess\344 " }{TEXT -1 84 "on eritt\344in hy\366dyllist\344 , ett\344 niit\344 voidaan tallettaa ns. proseduurin muistitauluun." } }{PARA 14 "" 0 "" {TEXT -1 10 "Lue lis\344\344:" }}{PARA 14 "" 0 "" {TEXT -1 20 " [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 funkti o ja sen derivaatta." }}{PARA 0 "" 0 "" {TEXT -1 71 " Tarkista laskema lla funktion arvot, ett\344 nollakohdat ovat nollakohtia." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{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 1 " " }}{PARA 0 "" 0 "" {TEXT -1 28 "Derivaattalauseke -- diff " }}{PARA 0 "" 0 "" {TEXT -1 48 "Derivaattafunktio -- D (K\344yttele helppi\344 )" } }{PARA 0 "" 0 "" {TEXT 0 32 " ?plot, ?solve,?fsolve ?diff, ?D" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 158 "T\344m \344ntyyppisten teht\344vien, niin yksinkertaisia matemaattisesti kuin ovatkin, sujuva hallinta tekee Maple-ty\366skentelyst\344 nautittavaa puuhaa ja auttaa pitk\344lle." }}}}{SECT 1 {PARA 3 "" 0 "Algebra" {TEXT -1 35 "6. Sievennyst\344 ja yht\344l\366n ratkaisua" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 12 "Pohdiskelu a\n" }{TEXT 268 11 " simplify" }{TEXT -1 46 " - yleissievent\344j \344, ensimm\344iseksi tarjoiltava." }}{PARA 4 "" 0 "" {TEXT -1 3 " \+ " }{TEXT 269 6 "expand" }{TEXT -1 15 " - kertoo auki" }}{PARA 4 "" 0 "" {TEXT -1 3 " " }{TEXT 285 21 "collect - kokoaa " }}{PARA 0 " " 0 "" {TEXT -1 10 " " }{TEXT 0 10 "? collect " }{TEXT -1 72 " ja kokeile joitakin esimerkkej\344. Varsin hyv\344 komento monessa \+ paikassa." }}{PARA 0 "" 0 "" {TEXT 270 9 " factor" }{TEXT -1 25 " - \+ Jakaa tekij\366ihin.\n " }{TEXT 286 7 "convert" }{TEXT -1 53 " - .. . Monenmoisiin konverioihin sievennyksess\344 esim " }{TEXT 0 39 " \+ convert(lauseke,parfrac,muuttuja);" }}{PARA 0 "" 0 "" {TEXT -1 103 " \+ Huomaa, ett\344 lauseke ei muutu, uusi tulos palautetaan. Jos halutaa n p\344ivitt\344\344 lauseke, on komennetava" }}{PARA 0 "" 0 "" {TEXT -1 13 " " }{TEXT 0 43 "lauseke:=convert(lauseke,parfrac,mu uttuja);" }}{PARA 0 "" 0 "" {TEXT 271 8 " solve" }{TEXT -1 34 " - r atkaisee yht\344\366n tai systeemin" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 326 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 "expand((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 "Yht\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 -1 105 "Maple ei sijoita ratkais uja muutujille arvoiksi, vaan palauttaa sijoituss\344\344nn\366t. Ne v oidaan antaa suoraan" }}{PARA 0 "" 0 "" {TEXT -1 56 "subs-komennolle. \+ Mieti seuraavan komnetojonon 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 -1 411 "Voidaan my\366s k\344ytt\344\344 lhs (left hand side) ja rhs ( right hand side)-tapaa, mutta se on hiukan v\344hemm\344n elegantti ja my\366s altis Maplen harrastamalle j\344rjestyksen vaihtumiselle ratk aisujoukossa. Niinp\344 t\344t\344 tyyli\344 ei voida ajaa automaattis esti, vaan tuloksiin on puututtava interaktiivisesti, mik\344 voi olla kiusallista, jos on \"vakavahenkisest\344\" dokumentista kyse. Joka t apauksessa 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 25 "lhs(ratk[2])=rhs(sol[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 seli tetty samaa, 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 304 151 "Suorita ratk-yht\344l\366iden ilmaisemat korvaamiset l ausekkeessa (pelkk\344) x ja\n suorita ratk-yht\344l\366iden ilmai semat korvaamiset lausekkeessa (pelkk\344) y ." }}{PARA 0 "" 0 "" {TEXT -1 128 "Edellisess\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\344i sella vastaavasta syyst\344 x-yht\344l\366. sol-joukon" }}{PARA 0 "" 0 "" {TEXT -1 34 "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 56 "Tehokkain, mutta turvatto min tapa, joskus 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 21 "solve(yhtalot,\{x,y\});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 0 13 "assign(ratk);" }{TEXT -1 34 " toimii ik\344\344nkuin \+ ratk-yht\344l\366iss\344 " }{TEXT 305 52 "yht\344l\366merkki (=) vaihd ettaisiin sijoitusmerkkin (:=)" }}{PARA 0 "" 0 "" {TEXT -1 87 " Yh t\344l\366iden toteutuminen saadaan hyvin k\344tev\344sti tarkistetuks i kirjoittamalla vain " }{TEXT 0 8 "yhtalot;" }}{PARA 0 "" 0 "" {TEXT -1 55 " Sensijaan yht\344l\366iden ratkaisua ei voida toistaa, " }{TEXT 306 51 "ennekuin muuttujat x ja y on vapautettu arvoistaan." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "x:='x':y:='y':solve(yhtalot ,\{x,y\});" }}}{EXCHG {PARA 4 "" 0 "" {TEXT -1 29 "Joukot \{ \}, jonot , listat [ ]" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 68 "T\344ss\344 v\344h\344n University of North Carolinan s ivulta poimittua teksti\344:" }}{PARA 0 "" 0 "" {TEXT -1 486 "Observe \+ that we have now employed three different kinds of grouping symbols: \+ \"()\",\"\{\}\", and \"[]\". They are used for different purposes, an d Maple requires that they be used correctly. The standard parenthese s \"()\" are used with functions as in factor(x^2-1) and sin(Pi). The braces \"\{\}\" are used to group a set as in \{x,y\}. The square br ackets \"[]\" are used to pick a coordinate from a group as in sol[2]. We will see other uses for these symbols.\nHakasulut ovat my\366s li stasulut. " }{TEXT 276 26 "T\344rkeimm\344t tietorakenteet:" }}{PARA 15 "" 0 "" {TEXT 272 4 "Jono" }{TEXT -1 9 ", esim: " }}{PARA 15 "" 0 "" {TEXT 0 16 "> jono:=a,b,c; " }{TEXT -1 0 "" }}{PARA 15 "" 0 "" {TEXT 273 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 274 6 "Joukko" }{TEXT -1 9 " , esim: " }{TEXT 0 20 "> joukko:=\{a,b,c\}; " }}{PARA 0 "" 0 "" {TEXT -1 34 " " }{TEXT 0 45 "> op(jou kko); # Vastaavasti joukon operandi\n" }}{PARA 0 "" 0 "" {TEXT 275 4 "Huom" }{TEXT -1 161 ": Listan j\344rjestys on k\344ytt\344j\344n hall innassa, joukon ei. \n Joukon hy\366ty on ainakin se, ett \344 Maple osaa poistaa toistot ja joukko-operaatiot toimivat." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 0 4 "map " } {TEXT -1 77 "- funktion soveltaminen listan (tai muun rakenteen) jokai seen alkioon (osaan)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "lis ta:=[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 0 "" }}}}{SECT 1 {PARA 0 " " 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 3 "" 0 "Piirtoa" {TEXT -1 10 "7 . 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 -1 219 "K\344yr\344parven voi sulkea joko joukkosulkuihin \{ \} tai lista sulkuihin [ ] .\nJ\344lkimm\344inen lienee suositeltavaa, koska j\344r jestys on silloin k\344ytt\344j\344n hallinnassa (ei siin\344\nmuuta, \+ mutta jos vaikka halutaan v\344rit hallitusti).\n" }}{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 307 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 308 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 25 "Parametrim uotoinen piirto" }}{PARA 0 "" 0 "" {TEXT -1 90 "Syntaksi poikkeaa aika v\344h\344n, t\344m\344 t\344ytyy vain oppia (tai katsoa aina uudelle en helpist\344)." }}{PARA 0 "" 0 "" {TEXT -1 123 "Aina ei ole hauskaa \+ joutua valitsemaan hirell\344, samaskaalaiisuus (ja monia muita) voida an antaa plot-komennon tarkentimena." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([sin(t),cos(t),t=0..2*Pi],scaling=constrained); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 276 "Pisteet voidaan yht\344 hyvi n ajatella kompleksitason pistein\344. complexplot osaa k\344sitell \344 suoraan reaalimuuttujan kompleksiarvoista funktiota. T\344ss\344 \+ on sekin mukava piirre, ett\344 syntaksi on luonnollisempi ja siten he lpompi muistaa kuin tuossa parametrimuotoisessa R^2-piirrossa." }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "complexplot(cos(t)+I*sin(t),t=0..2*Pi,scaling=constrained,color= blue);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Kunhan opimme kompleksi sen exp-funktion, niin edellinen voidaan ilmaista lyhyemmin:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "c omplexplot(exp(I*t),t=0..2*Pi,scaling=constrained,color=cyan,style=poi nt);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 40 "Taulukoidun datan piirt o (\"listaplotti\")" }}{PARA 0 "" 0 "" {TEXT -1 471 "Sometimes we will be interested in functions defined in terms of a discrete \ntable of \+ values rather than a formula. For example, consider the following tab le of \ntemperatures recorded at various times on a spring day in Rale igh.\n \n Time: | 6:00 a.m. | 10:00 a.m. | 12:00 p.m. | 4:0 0 p.m. | 5:00 p.m.\n ---------------------------------------------- \n Temp: | 45 deg. | 57 deg. | 65 deg. | 67 deg . | 66 deg. \n\n " }{TEXT 277 61 "Table of T emperatures on a Spring Day in Degrees Fahrenheit " }{TEXT -1 2 " \n " }}{PARA 0 "" 0 "" {TEXT -1 218 "To plot this data you must first def ine the points as a list. Since the time is recorded in a cyclic fash ion, 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], [1600,67], [1700,66]];" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "The " } {TEXT 278 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 Var ious Times`);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 119 "\nWhile the dat a can be plotted in this way, because the data is given for a discret e set of points you may prefer the " }{TEXT 0 11 "style=POINT" }{TEXT -1 73 " option as illustrated in the next command. Note also the effe ct of the " }{TEXT 0 13 "symbol=CIRCLE" }{TEXT -1 9 " option.\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "plot(ListOfPoints, style=PO INT, symbol=CIRCLE,symbolsize=20, 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 of th e 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 conne cted and the other with only the data points.\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 282 72 "Miten saadaan k\344tev\344sti koordinaattiparien li sta [[x1,y1],[x2,t2],...] ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 114 "Olkoon annettu numeeriset listat (Matlabissa s anoisimme vektorit) X ja Y. Matlabin plot toimii tyyliin plot(x,y);" }}{PARA 0 "" 0 "" {TEXT -1 61 "Maplessa t\344ytyy muodostaa parien lis ta 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-funkt ion 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);plot( xy,style=point,symbol=circle);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT 309 5 "Huom:" }{TEXT -1 1 " " }{TEXT 310 5 " plots" }{TEXT -1 17 "-pakkauksessa on " }{TEXT 0 9 "listplot " }{TEXT -1 3 "ja " }{TEXT 0 9 "pointplot" }{TEXT -1 318 ". Maplelle luonteenom aista on, ett\344 siin\344 on joukko redundantteja funktioita. Mielest \344ni on parempi oppia k\344ytt\344m\344\344n harvempaa ydinfunktiojo ukkoa kuin omaksua monenlaisia synonyymej\344. Niiss\344 voi toki 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 "T aulukointi" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "T\344ss\344 teimme itse asiassa taulukon, jonka on havainnollis empi usein matriisina." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "txy:matrix(xy):linalg[transpose](xy ):" }}}{EXCHG {PARA 13 "" 0 "" {TEXT -1 74 "Tilan s\344\344st\344misek si 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 "l inalg[transpose](xy);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "ar ray(xy); # Taas synonyymi, mutta tiettyj\344 erojakin yleisyydessa / \+ matriisilaskukyvyiss\344." }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 53 "Gr afiikoiden yhdist\344minen, plots[display] ja textplot" }}{PARA 0 "" 0 "" {TEXT -1 37 "T\344ss\344 tarvitaan lis\344grafiikkapakkaus " } {TEXT 260 5 "plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restar t:with(plots): " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 108 "Selvit\344 it sellesi, mit\344 seuraavassa tehd\344\344n. Mieti tarkkaan, miksi joss ain pit\344\344 antaa plot:lle argumentiksi" }}{PARA 0 "" 0 "" {TEXT -1 95 "f(x) ja miksi taas jossain esim. tang. Voit sitten huvitella va ihtelemalla funktion m\344\344ritelm\344\344" }}{PARA 0 "" 0 "" {TEXT -1 103 "ja / tai pistett\344 x0. Kirjoitetaan pieni malliskripti, jonk alaisia voit tehd\344 moninaisissa yhteyksiss\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,tangkuva,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, silloinki n syv\344sti katuen, ett\344 olit yllytyshullu)," }}{PARA 0 "" 0 "" {TEXT -1 50 " mit\344 tapahtuu, kun vaihdat (:) -> (;) vaikkapa " } {TEXT 0 10 "fkuva:=; ." }{TEXT -1 37 ".. yll\344. PLOT-tietorakenne pa ljastuu." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "- No, mene edit-valikkoon ja -> remove output, 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 279 21 "print \+ text on a plot." }{TEXT -1 6 " The " }{TEXT 287 5 "plots" }{TEXT -1 11 " procedure " }{TEXT 288 8 "textplot" }{TEXT -1 71 " will allow thi s. The following commands will serve as examples of the " }{TEXT 289 7 "textplo" }{TEXT -1 6 "t and " }{TEXT 290 7 "display" }{TEXT -1 89 " routines. Make sure you notice where colons and semicolons are used \+ in these commands.\n" }}{PARA 0 "" 0 "" {TEXT -1 324 "In the next com mands it is important to use colons to punctuate the first two stateme nts. Otherwise Maple V will ouput an entire page of text describing t he plot structure rather than the graph. The textplot in the second c ommand causes the text x=0.6356,y=0.5000 to be printed at the point (. 6356,.5000). The statement " }{TEXT 0 11 "align=RIGHT" }{TEXT -1 159 " aligns this text to the right of the point. Also make sure you noti ce that backward quotes (`) surround the text statement. Nykyisin k \344yv\344t my\366s \" \" -merkit." }}}{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):\nplot2 := plots[textplot]([0.6356, 0.5 000, `x=.6356, y=.5000`], align=RIGHT):\nplots[display](\{plot1, plot2 \});" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 280 5 "Huom:" }}{PARA 0 "" 0 "" {TEXT -1 88 "plots-pakkauksen (kuten 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\344nku in indeksoidaan ao. funktion nimell\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-grafiikk aa, animaatiot" }}{PARA 0 "" 0 "" {TEXT -1 49 "Otetaan l\344mm\366njoh tumisesimerkki, jossa valaistaan" }}{PARA 15 "" 0 "" {TEXT -1 18 "3d-p innan piirtoa " }}{PARA 15 "" 0 "" {TEXT -1 11 "Animaatiota" }}{PARA 15 "" 0 "" {TEXT -1 37 "3d-kuvan projektiok\344yr\344parven piirtoa" } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 147 "Tarkast ellaan sivuiltaan l\344mp\366eristetty\344 sauvaa, jonka p\344\344t up otetaan hetkell\344 t=0 j\344\344vesis\344ili\366ihin (0 astetta) ja j onka\nalkul\344mp\366tilajakauma on \n" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f:=x->100*sin(Pi*x/80);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 261 22 "Huomaa funktiom\344\344ritys" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 169 "Olkoon sauvan pituus L=80.\n\nT\344ss \344 tapauksessa l\344mp\366yht\344l\366n ratkaisuna olevasta Fourier- sarjasta tulee vain yksi termi. Ratkaisu on (sopivalla l\344mm\366njoh tumiskertoimella)\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 "Kli kkaa hiirell\344 kuvaan (ja tarvittaessa valitse \"boxed\") ty\366kalu nauhasta." }}{PARA 15 "" 0 "" {TEXT -1 57 "Kierr\344 laatikkoa hiirell \344 ja valitse R (niinkuin redraw)." }}{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\366tila profiilit 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 "" {TEXT -1 43 "Tuohon tekisi mieli laittaa loppuun esim: " }{TEXT 0 25 ",colo r=[red,blue,black]);" }}{PARA 0 "" 0 "" {TEXT -1 22 "mutta n\344k\366j \344\344n kaikki " }{TEXT 281 4 "plot" }{TEXT -1 39 ":n hyv\344ksym \344t optiot eiv\344t t\344ss\344 toimi." }}}}}}}{MARK "3" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }