{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 "" 0 1 0 0 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Reziduova veta" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 160 "Chci spocitat re alny integral (od minus-nekonecna do plus-nekonecna) z funkce f= =(2x^ 3+13x*sin(x))/(x^4+13*x^2+36).Spoctu tento integral pomoci reziduove v ety." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "funkce:=x->(2*x^3+1 3*x*sin(x))/(x^4+13*x^2+36);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'f unkceGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&,&*&\"\"#\"\"\")9$\"\"$F0F0 *(\"#8F0F2F0-%$sinG6#F2F0F0F0,(*$)F2\"\"%F0F0*&F5F0)F2F/F0F0\"#OF0!\" \"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "int((2*x^3+13*x *sin(x))/(x^4+13*x^2+36),x=-infinity..infinity);\n" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%*undefinedG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"\"%*undefine dG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 37 "Prikaz int v tomto pripade \+ nefunguje." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 432 "Zvolim integracni \+ funkci (2*z^3+13z*e^(iz))/(z^4+13z^2+36).Budu integrovat pres pulkruzn ici .Pres oblouk pulkruznici se da ukazat ze, integral se blizi nule , jestlize se polomer pulkruznice bude blizit k nekonecnu.Integral pres \+ uzavrenou krivku(pulkruznici) je pak roven integralu pres \"usecku pul kruznice\" od minus-nekonecna do plus-nekonecna.Muj hledany integral v zhledem k integracni funkci bude imaginarni cast tohoto integralu." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "Poly:=[solve(z^4+13*z^2+36= 0,z)];\n \n \n \n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PolyG7&^#\"\"#^#!\"#^#\"\"$^#!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "Pomoci pravidel na vypocet rez idui zjistim ,ze reziduum se spocte dosazenim polu do funkce FR=(2z^3+ 13z*e^(iz))/(4z^3+26z)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " FR:=z->(2*z^3+13*z*exp(I*z))/(4*z^3+26*z);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#FRGf*6#%\"zG6\"6$%)operatorG%&arrowGF(*&,&*&\"\"#\" \"\")9$\"\"$F0F0*(\"#8F0F2F0-%$expG6#*&F2F0^#F0F0F0F0F0,&*&\"\"%F0F1F0 F0*&\"#EF0F2F0F0!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "FR(2*I);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&^##!\"\"\"#?\"\"\", &^#!#;F(*&^#\"#EF(-%$expG6#!\"#F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Rezidum_prvni:=simplify(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.Rezidum_prvniG,$*&#\"\"\"\"#5F(*&,&*&\"\")F(-%$expG6 #\"\"#F(F(\"#8!\"\"F(-F/6#!\"#F(F(F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "FR(3*I);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&^##\" \"\"\"#IF&,&^#!#aF&*&^#\"#RF&-%$expG6#!\"$F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Rezidum_druhy:=simplify(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%.Rezidum_druhyG,$*&#\"\"\"\"#5F(*&,&*&\"#=F(-%$e xpG6#\"\"$F(F(\"#8!\"\"F(-F/6#!\"$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "soucet_rezidui:=Rezidum_prvni+Rezidum_druhy;\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%/soucet_reziduiG,&*&#\"\"\"\"#5F(*&, &*&\"\")F(-%$expG6#\"\"#F(F(\"#8!\"\"F(-F/6#!\"#F(F(F3*&#F(F)F(*&,&*& \"#=F(-F/6#\"\"$F(F(F2F3F(-F/6#!\"$F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 39 "Integral:=Im(2*Pi*I*(soucet_rezidui));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)IntegralG,$*(\"\"#\"\"\"%#PiGF(,&*&,&*&# \"\"%\"\"&F(-%$expG6#F'F(!\"\"#\"#8\"#5F(F(-F26#!\"#F(F(*&,&*&#\"\"*F0 F(-F26#\"\"$F(F(#F6F7F4F(-F26#!\"$F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "evalf(Integral);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+y^&>)p!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "16 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }