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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[ 86615, 6102]*) (*NotebookOutlinePosition[ 87747, 6138]*) (* CellTagsIndexPosition[ 87703, 6134]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData["Laplace Transforms"], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell["<{{18, 126}, {Inherited, Inherited}}, PageBreakWithin->Automatic, InitializationCell->True, CellLabelMargins->{{18, Inherited}, {Inherited, Inherited}}, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[TextData[ "Calculating Laplace Transforms and Inverse Laplace Transforms"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ "Find the Laplace transforms of the functions\n", StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["a)", FontSlant->"Italic"], StyleBox[" E^(2t)*Sin[Pi t]", FontFamily->"Courier", FontWeight->"Bold"], "\n", StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["b)", FontSlant->"Italic"], StyleBox[" t^2*Cos[3t]\n", FontFamily->"Courier", FontWeight->"Bold"], "by integrating and by using ", StyleBox["LaplaceTransform[f[t],t,s]", FontFamily->"Courier", FontWeight->"Bold"], ".\nFind the inverse Laplace transform of the functions\n", StyleBox[" ", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["c)", FontSlant->"Italic"], StyleBox[" s^2/(s^3 + s^2 + s + 1)\n ", FontFamily->"Courier", FontWeight->"Bold"], StyleBox["d)", FontSlant->"Italic"], StyleBox[" (2s-3)/(s^2 - 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