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In this exampl e we compare convergence of Fourier sine and cosine series." }}{PARA 0 "" 0 "" {TEXT -1 138 " The function, f(x)=2x, 0 " 0 "" {MPLTEXT 1 0 21 "f := x -> 2*x; L:=10;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"x G6\"6$%)operatorG%&arrowGF(,$9$\"\"#F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG\"#5" }}}{PARA 13 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Now let us find the sine series." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "b := k -> 2/L*int(f(x)*sin(k *Pi*x/L),x=0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGf*6#%\"kG6 \"6$%)operatorG%&arrowGF(,$*&%\"LG!\"\"-%$intG6$*&-%\"fG6#%\"xG\"\"\"- %$sinG6#**9$F8%#PiGF8F7F8F.F/F8/F7;\"\"!F.F8\"\"#F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "ss := (x,t,n) -> sum(b(k)*sin(k*Pi* x/L)*exp(-t*(k*Pi/L)^2),k=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #ssGf*6%%\"xG%\"tG%\"nG6\"6$%)operatorG%&arrowGF*-%$sumG6$*(-%\"bG6#% \"kG\"\"\"-%$sinG6#**F5F6%#PiGF69$F6%\"LG!\"\"F6-%$expG6#,$**9%F6F5\" 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