{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 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R 3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 128 0 128 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 128 128 1 2 1 2 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "f:=(x) -> piecewise( x<0,-1,0 " 0 "" {MPLTEXT 1 0 60 "a:=proc(n) evalf((1/Pi)*(int(f(x)*cos(n*x),x=-Pi ..Pi))) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "b:=proc(n) \+ evalf((1/Pi)*(int(f(x)*sin(n*x),x=-Pi..Pi))) end;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 66 "P:=proc(x,N) a(0)/2 + sum(a(n)*cos(n*x)+b(n) *sin(n*x),n=1..N) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "w ith(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "for k from 1 by 1 to 20 do \nP||k:= plot (\{f(x),P(x,k)\}, x=-Pi..3*Pi,y =-2..2,th ickness=2):\nod:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plots [display]([seq(P||k, k=1..20)], insequence=true);\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 183 "The graph shows two cycles of the periodic fun ction with its first three terms Fourie series aproximation. Click the graph, choose Animation+Play to see the subsequent approximations." } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "5 0 0" 76 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }