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"plot([[-2*Pi,0],[-2*Pi,1],[-Pi,1],[-Pi, -1], [0, -1] , [0, 1],\n[Pi, 1], [Pi, -1], [2*Pi, -1], [2*Pi, 0]], thickness=3);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 0 to 50 do" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "bild(i) := plot((4/Pi)*sum(1/(2*j+1 )*sin((2*j+1)*x), j=0..i)," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "x=0.. 5*Pi)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plots[display]([seq(bild(i), i=0..50)], insequence=tr ue);" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 18 "b) Dreiecksimpulse" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot([s eq([i*Pi, (-1)^i],i=0..5)], thickness=3);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 21 "for i from 0 to 50 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "bild(i) := plot(8/Pi^2*sum(1/(2*j+1)^2*cos((2*j+1)*x) , j=0..i)," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "x=0..5*Pi)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 " plots[display]([seq(bild(i), i=0..50)], insequence=true);" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 22 "c) Saegezahnschwingung" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "plot([[0,0], [0,Pi/ 2], [2*Pi,-Pi/2], [2*Pi,Pi/2], [4*Pi,-Pi/2],\n[4*Pi,Pi/2], [5*Pi,0]], \+ thickness=3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "plot([[[0 ,Pi/2], [2*Pi,-Pi/2]], [[2*Pi,Pi/2], [4*Pi,-Pi/2]],\n[[4*Pi,Pi/2], [5* Pi,0]]], thickness=3, color=red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 1 to 50 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "bild(i) := plots[display]([plot(sum(1/j*sin(j*x), j=1..i)," }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "x=0..5*Pi), plot(Pi/2, x=0..5*Pi, c olor=green),\nplot(-Pi/2, x=0..5*Pi, color=green)]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plots[d isplay]([seq(bild(i), i=1..50)], insequence=true);" }}}{EXCHG {PARA 265 "" 0 "" {TEXT -1 39 "Das letzte Bild in hoeherer Aufloesung:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "plots[ display]([plot(sum(1/j*sin(j*x), j=1..50), x=0..5*Pi, numpoints=1000), \nplot(Pi/2, x=0..5*Pi, color=green),\nplot(-Pi/2, x=0..5*Pi, color=gr een)]);" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 35 "d) Eine gleichgerich tete Schwingung" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i fr om 1 to 50 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "a(i) := (2*i-1)*(2 *i+1) od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for i from 0 to 50 do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "bild(i) := plot(1/2+sum(1/a(j)* cos(2*j*x), j=1..i)," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "x=0..5*Pi) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "plots[display]([seq(bild(i), i=0..50)], insequence=tr ue);" }}}{EXCHG {PARA 263 "" 0 "" {TEXT -1 46 "Die Funktion sin((N+1/2 )t)/sin(t/2) fuer N=100" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 37 "plot(sin(100.5*t)/sin(t/2), t=-3..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "2 0 0" 20 }{VIEWOPTS 1 1 0 1 1 1803 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