{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 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 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 8 4 1 0 1 0 2 2 0 1 } {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 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 10 "L13maple, " }{XPPEDIT 18 0 "e^(A*t)" "6#)%\"eG*&%\"AG\"\"\"%\"tGF'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 10 "Alustukset" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 33 "with(LinearAlgebra):with(linalg):" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 "Esim. EHY-ratk." }}{PARA 0 "" 0 " " {TEXT -1 13 "Luentoteht\344v\344" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A:=<<2,1>|<-4,-3>>;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "g:=t-><2*t^2+10*t,t^2+9*t+3>;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 29 "(lambda,ov):=Eigenvectors(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "v1:=ov[1..-1,1]: v2:=ov[1..-1,2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "yh:=C1*exp(lambda[1]*t)*v 1+C2*exp(lambda[2]*t)*v2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG }{EXCHG {PARA 0 " " 0 "" {TEXT -1 83 "LinearAlgebra on keskener\344inen. Yll\344 oleva t \344ytyy tarjoilla komponentti kerrallaan:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 104 "Y:=t-><|>;" }}}{EXCHG } {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "Y(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "T\344ss\344 on nyt " }{TEXT 256 13 "perusmatriisi" } {TEXT -1 15 ". Sen avulla sa" }}{PARA 0 "" 0 "" {TEXT -1 6 "adaan " } {XPPEDIT 18 0 "e^(A*t)" "6#)%\"eG*&%\"AG\"\"\"%\"tGF'" }{TEXT -1 2 " . " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "expA:=t->Y(t).(Y(0)^(-1 ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "expA(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "exponential(A,t); " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Oikein meni." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "Sitten se " }{TEXT 257 16 "kaunis EHY-kaava" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "y(t)=e^('A'*t)*C+Int( e^'A(t-s)'*'g(s)',s=0..t); #tekstink\344sittely\344" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "yp:=map(int,expA(t-s).g(s),s=0..t);" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Saatiin kuin saatiinkin sama tulos kuin eilen lasketulla yritteell\344 (vrt. KRE 3.6 s. 184)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "yh:=expA(t).;yh:=map(collect ,%,\{exp(-2*t),exp(t)\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "y:=yh+yp;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Saadaan yksinkertaisempaan muotoon, tee k \344sin!" }}}}}{MARK "3" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }