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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 152535, 3737]*) (*NotebookOutlinePosition[ 153179, 3759]*) (* CellTagsIndexPosition[ 153135, 3755]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[StyleBox["\:56f37.3", FontSize->18]], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(u = \[Sum]\+\(n = 1\)\%30 Sin[\(n\ \[Pi]\)\/2] \((\[Integral]\_0\%t \[Tau]\ \(\ \[ExponentialE]\^\(\(-\((\(n\ \[Pi]\)\/2)\)\^2\) \((t - \[Tau])\)\)\) \ \[DifferentialD]\[Tau])\) Sin[\(n\ \[Pi]\ x\)\/2]\)], "Input"], Cell[BoxData[ \(\((\(16\ \[ExponentialE]\^\(-\(\(\[Pi]\^2\ t\)\/4\)\)\)\/\[Pi]\^4 + \(4\ \ \((\(-4\) + \[Pi]\^2\ t)\)\)\/\[Pi]\^4)\)\ Sin[\(\[Pi]\ x\)\/2] - \((\(16\ \ \[ExponentialE]\^\(-\(\(9\ \[Pi]\^2\ t\)\/4\)\)\)\/\(81\ \[Pi]\^4\) + \(4\ \ \((\(-4\) + 9\ \[Pi]\^2\ t)\)\)\/\(81\ \[Pi]\^4\))\)\ Sin[\(3\ \[Pi]\ x\)\/2] \ + \((\(16\ \[ExponentialE]\^\(-\(\(25\ \[Pi]\^2\ t\)\/4\)\)\)\/\(625\ \ \[Pi]\^4\) + \(4\ \((\(-4\) + 25\ \[Pi]\^2\ t)\)\)\/\(625\ \[Pi]\^4\))\)\ \ Sin[\(5\ \[Pi]\ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(49\ \[Pi]\^2\ \ t\)\/4\)\)\)\/\(2401\ \[Pi]\^4\) + \(4\ \((\(-4\) + 49\ \[Pi]\^2\ \ t)\)\)\/\(2401\ \[Pi]\^4\))\)\ Sin[\(7\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(81\ \[Pi]\^2\ t\)\/4\)\)\)\/\(6561\ \[Pi]\^4\) + \(4\ \ \((\(-4\) + 81\ \[Pi]\^2\ t)\)\)\/\(6561\ \[Pi]\^4\))\)\ Sin[\(9\ \[Pi]\ \ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(121\ \[Pi]\^2\ \ t\)\/4\)\)\)\/\(14641\ \[Pi]\^4\) + \(4\ \((\(-4\) + 121\ \[Pi]\^2\ \ t)\)\)\/\(14641\ \[Pi]\^4\))\)\ Sin[\(11\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(169\ \[Pi]\^2\ t\)\/4\)\)\)\/\(28561\ \[Pi]\^4\) + \ \(4\ \((\(-4\) + 169\ \[Pi]\^2\ t)\)\)\/\(28561\ \[Pi]\^4\))\)\ Sin[\(13\ \ \[Pi]\ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(225\ \[Pi]\^2\ t\)\/4\)\)\)\ \/\(50625\ \[Pi]\^4\) + \(4\ \((\(-4\) + 225\ \[Pi]\^2\ t)\)\)\/\(50625\ \ \[Pi]\^4\))\)\ Sin[\(15\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(289\ \[Pi]\^2\ t\)\/4\)\)\)\/\(83521\ \[Pi]\^4\) + \ \(4\ \((\(-4\) + 289\ \[Pi]\^2\ t)\)\)\/\(83521\ \[Pi]\^4\))\)\ Sin[\(17\ \ \[Pi]\ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(361\ \[Pi]\^2\ t\)\/4\)\)\)\ \/\(130321\ \[Pi]\^4\) + \(4\ \((\(-4\) + 361\ \[Pi]\^2\ t)\)\)\/\(130321\ \ \[Pi]\^4\))\)\ Sin[\(19\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(441\ \[Pi]\^2\ t\)\/4\)\)\)\/\(194481\ \[Pi]\^4\) + \ \(4\ \((\(-4\) + 441\ \[Pi]\^2\ t)\)\)\/\(194481\ \[Pi]\^4\))\)\ Sin[\(21\ \ \[Pi]\ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(529\ \[Pi]\^2\ t\)\/4\)\)\)\ \/\(279841\ \[Pi]\^4\) + \(4\ \((\(-4\) + 529\ \[Pi]\^2\ t)\)\)\/\(279841\ \ \[Pi]\^4\))\)\ Sin[\(23\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(625\ \[Pi]\^2\ t\)\/4\)\)\)\/\(390625\ \[Pi]\^4\) + \ \(4\ \((\(-4\) + 625\ \[Pi]\^2\ t)\)\)\/\(390625\ \[Pi]\^4\))\)\ Sin[\(25\ \ \[Pi]\ x\)\/2] - \((\(16\ \[ExponentialE]\^\(-\(\(729\ \[Pi]\^2\ t\)\/4\)\)\)\ \/\(531441\ \[Pi]\^4\) + \(4\ \((\(-4\) + 729\ \[Pi]\^2\ t)\)\)\/\(531441\ \ \[Pi]\^4\))\)\ Sin[\(27\ \[Pi]\ x\)\/2] + \((\(16\ \ \[ExponentialE]\^\(-\(\(841\ \[Pi]\^2\ t\)\/4\)\)\)\/\(707281\ \[Pi]\^4\) + \ \(4\ \((\(-4\) + 841\ \[Pi]\^2\ t)\)\)\/\(707281\ \[Pi]\^4\))\)\ Sin[\(29\ \ \[Pi]\ x\)\/2]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell["Plot3D[u,{x,0,1},{t,0,2},AxesLabel->{\"x\",\"t\",\"u\"}];", "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .81114 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% SurfaceGraphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont 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