{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 1 236 0 76 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 48 37 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE " " -1 257 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 50 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 255 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 4 "" 0 "" {TEXT 256 14 "Ejercicios de " }}{PARA 4 "" 0 "" {TEXT 258 31 "(12) Las Ecuaciones parab\363licas" }}{PARA 4 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 15 "Ejercicio 12-01 " }}{PARA 4 "" 0 "" {TEXT -1 24 "\n\nSe considera la matriz" }}{PARA 4 "" 0 "" {TEXT -1 35 " | 2 -1 0 . . . |" }}{PARA 4 "" 0 "" {TEXT -1 35 " | -1 2 -1 . . . |" }}{PARA 4 " " 0 "" {TEXT -1 33 " B = | 0 -1 2 . . . |" }}{PARA 4 "" 0 "" {TEXT -1 37 " | . . . |" }}{PARA 4 "" 0 "" {TEXT -1 38 " | . . . | " }}{PARA 4 "" 0 "" {TEXT -1 46 "de tama\361o ( N - 1 ) x ( N - 1 ) , y la matriz" } }{PARA 4 "" 0 "" {TEXT -1 34 " | 1 - 2 " } {XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 8 " " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 27 " 0 . . . | " }}{PARA 4 "" 0 "" {TEXT -1 33 " | " } {XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 12 " 1 - 2 " } {XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 8 " " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG" }{TEXT -1 14 " . . . |" }}{PARA 4 " " 0 "" {TEXT -1 11 " A = I - " }{XPPEDIT 18 0 "lambda" "6#%'lambdaG " }{TEXT -1 26 " B = | 0 " }{XPPEDIT 18 0 "lambda" "6 #%'lambdaG" }{TEXT -1 12 " 1 - 2 " }{XPPEDIT 18 0 "lambda" "6#%'l ambdaG" }{TEXT -1 12 " . . . |" }}{PARA 4 "" 0 "" {TEXT -1 76 " \+ | . . . \+ |" }}{PARA 4 "" 0 "" {TEXT -1 77 " | . . . | " }}{PARA 4 "" 0 "" {TEXT -1 66 "del mismo tama\361o. Esta es la matriz del m\351todo de las 'di ferencias" }}{PARA 4 "" 0 "" {TEXT -1 43 "hacia adelante' para problem as parab\363licos." }}{PARA 4 "" 0 "" {TEXT -1 46 "a) Pru\351bese que \+ los valores propios de B son" }}{PARA 4 "" 0 "" {TEXT -1 13 " 2 - \+ 2 cos " }{XPPEDIT 18 0 "n pi/N" "6#*(%\"nG\"\"\"%#piGF%%\"NG!\"\"" } {TEXT -1 13 " = 4 ( sen " }{XPPEDIT 18 0 "n pi/(2 N)" "6#*(%\"nG\"\" \"%#piGF%*&\"\"#F%%\"NGF%!\"\"" }{TEXT -1 7 " ) ^2 " }}{PARA 4 "" 0 " " {TEXT -1 42 "n = 1 , ... , N - 1 , con vectores propios" }}{PARA 4 " " 0 "" {TEXT -1 4 " " }{XPPEDIT 18 0 "x^([n])" "6#)%\"xG7#%\"nG" } {TEXT -1 10 " = ( sen " }{XPPEDIT 18 0 "n pi/N" "6#*(%\"nG\"\"\"%#piG F%%\"NG!\"\"" }{TEXT -1 9 " , sen " }{XPPEDIT 18 0 "2 n pi/N" "6#** \"\"#\"\"\"%\"nGF%%#piGF%%\"NG!\"\"" }{TEXT -1 14 " , ... , sen " } {XPPEDIT 18 0 " ( N-1)*n pi)/(N)" "6#**,&%\"NG\"\"\"F&!\"\"F&%\"nGF&%# piGF&F%F'" }{TEXT -1 14 " ) " }}{PARA 4 "" 0 "" {TEXT -1 68 "b) Calc\372lense as\355 los valores propios y tambi\351n los vecto res propios" }}{PARA 4 "" 0 "" {TEXT -1 13 "de A . " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 26 "interface(labeling=false):" }}}}{MARK "3" 0 } {VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }