{VERSION 6 0 "IBM INTEL NT" "6.0" } {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 Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 37 "Inner products for problem #2 page 96" }}{PARA 0 "" 0 "" {TEXT -1 47 "(continuous inner product by definite integral)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "phi := array(0..5,[1,cos(x),cos(2*x),cos(3*x),cos(4*x),cos(5*x)]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiGK%&ARRAYG6$7#;\"\"!\"\"&7(/6#F*\"\"\" /6#F/-%$cosG6#%\"xG/6#\"\"#-F36#,$*&F8F/F5F/F//6#\"\"$-F36#,$*&F?F/F5F /F//6#\"\"%-F36#,$*&FFF/F5F/F//6#F+-F36#,$*&F+F/F5F/F/Q(pprint06\"" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "int(phi[2]*phi[3],x=0..Pi); # innder product (phi[2],phi[3])" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "int(phi[3]*phi[3], x=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"#!\"\"%#PiG\"\"\" F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "phi[0];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "int(phi[4]*(Pi^2-x^2),x=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\")!\"\"%#PiG\"\"\"F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 38 "Discrete inner product: Example 4.2. 2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x := Vector[row]([1,3, 4,6,7]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6%\"*SS?\\ \"-%'VECTORG6#7'\"\"\"\"\"$\"\"%\"\"'\"\"(&%'VectorG6#%$rowG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "phi := array(0..1,[1,t]);" } }{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$phiGK%&ARRAYG6$7#;\"\"!\"\"\"7$/6# F*F+/6#F+%\"tGQ(pprint16\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "p := array(0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG-%&arra yG6$;\"\"!\"\"\"7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "p[0] := Vector([seq(subs(t=x[j],phi[0]),j=1..5)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"!-%'RTABLEG6%\"*GhB[\"-%'MATRIXG6#7'7#\"\" \"F0F0F0F0&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "p[1] := Vector([seq(subs(t=x[j],phi[1]),j=1..5)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"\"-%'RTABLEG6%\"*cs1Z\"-%'MATRI XG6#7'7#F'7#\"\"$7#\"\"%7#\"\"'7#\"\"(&%'VectorG6#%'columnG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "f := Vector([-2.1,-0.9,-0.6, 0.6,0.9]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%'RTABLEG6%\"*OB0 \\\"-%'MATRIXG6#7'7#$!#@!\"\"7#$!\"*F07#$!\"'F07#$\"\"'F07#$\"\"*F0&%' VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "Linea rAlgebra:-DotProduct(p[0],p[0]); # (phi[0],phi[0])" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "L inearAlgebra:-DotProduct(p[0],p[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "LinearAlgebra:-Do tProduct(p[1],p[1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$6\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "LinearAlgebra:-DotProduct(p[ 0],f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!33+++++++@!#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "LinearAlgebra:-DotProduct(p[1],f); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"3;+++++++F!#<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "A, b := Matrix(2,2), Vector(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%\"AG%\"bG6$-%'RTABLEG6%\"*Gx\"*[\"-%'MAT RIXG6#7$7$\"\"!F1F0%'MatrixG-F)6%\"*c0p[\"-F-6#7$7#F1F9&%'VectorG6#%'c olumnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 167 "for j from 0 to \+ 1 do\n b[j+1] := LinearAlgebra:-DotProduct(p[j],f):\n for k from 0 to 1 do\n A[j+1,k+1] := LinearAlgebra:-DotProduct(p[j],p[k])\n \+ end do\nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A, b;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6$-%'RTABLEG6%\"*Gx\"*[\"-%'MATRIXG6#7$ 7$\"\"&\"#@7$F-\"$6\"%'MatrixG-F$6%\"*c0p[\"-F(6#7$7#$!33+++++++@!#<7# $\"3;+++++++FF:&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "c := LinearAlgebra:-LinearSolve(A,b);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cG-%'RTABLEG6%\"*w.bZ\"-%'MATRIXG6#7$7#$!3J&*y :j_5UD!#<7#$\"3qpt%*y:j_]!#=&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "22 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 149204040 148236128 147067256 149052336 148917728 148690556 147550376 }{RTABLE M7R0 I6RTABLE_SAVE/149204040X*%)anythingG6"6"[gl!$%!!!"&"&"""""$""%""'""(F& } {RTABLE M7R0 I6RTABLE_SAVE/148236128X*%)anythingG6"6"[gl!#%!!!"&"&"""F'F'F'F'F& } {RTABLE M7R0 I6RTABLE_SAVE/147067256X*%)anythingG6"6"[gl!#%!!!"&"&"""""$""%""'""(F& } {RTABLE M7R0 I6RTABLE_SAVE/149052336X*%)anythingG6"6"[gl!#%!!!"&"&$!#@!""$!"*F)$!"'F)$""'F)$ ""*F)F& } {RTABLE M7R0 I6RTABLE_SAVE/148917728X,%)anythingG6"6"[gl!"%!!!#%"#"#""&"#@F("$6"F& } {RTABLE M7R0 I6RTABLE_SAVE/148690556X*%)anythingG6"6"[gl!#%!!!"#"#$!33+++++++@!#<$"3;+++++++ FF)F& } {RTABLE M7R0 I6RTABLE_SAVE/147550376X*%)anythingG6"6"[gl'#%!!!"#"#C004563B48C205653FE02B1DA4 6102B3F& }