(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 4608, 160] NotebookOptionsPosition[ 4242, 143] NotebookOutlinePosition[ 4585, 158] CellTagsIndexPosition[ 4542, 155] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"lambda1", "=", FractionBox[ RowBox[{"(", RowBox[{"5", "-", RowBox[{"Sqrt", "[", "33", "]"}]}], ")"}], "2"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"lambda2", "=", FractionBox[ RowBox[{"(", RowBox[{"5", "+", RowBox[{"Sqrt", "[", "33", "]"}]}], ")"}], "2"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"a1", "[", "t_", "]"}], ":=", RowBox[{"-", RowBox[{"Series", "[", RowBox[{ FractionBox[ RowBox[{"(", RowBox[{ RowBox[{"lambda2", " ", SuperscriptBox["E", RowBox[{"lambda1", " ", "t"}]]}], "-", RowBox[{"lambda1", " ", SuperscriptBox["E", RowBox[{"lambda2", " ", "t"}]]}]}], ")"}], RowBox[{"lambda1", "-", "lambda2"}]], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "6"}], "}"}]}], "]"}]}]}], " ", RowBox[{"(*", " ", RowBox[{"note", " ", "negative", " ", "sign"}], " ", "*)"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"a2", "[", "t_", "]"}], ":=", RowBox[{"Series", "[", RowBox[{ FractionBox[ RowBox[{"(", RowBox[{ SuperscriptBox["E", RowBox[{"lambda1", " ", "t"}]], "-", SuperscriptBox["E", RowBox[{"lambda2", " ", "t"}]]}], ")"}], RowBox[{"lambda1", "-", "lambda2"}]], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "6"}], "}"}]}], "]"}]}], "\n", RowBox[{"a1", "[", "t", "]"}], "\[IndentingNewLine]", RowBox[{"a2", "[", "t", "]"}]}], "Input", CellChangeTimes->{{3.4794598370145054`*^9, 3.479459910704364*^9}, { 3.4794599777221327`*^9, 3.4794600413647947`*^9}, {3.4795456739695473`*^9, 3.4795457097360883`*^9}, 3.4795457499871187`*^9, {3.4795458310360684`*^9, 3.4795458363330793`*^9}}], Cell[BoxData[ InterpretationBox[ RowBox[{"1", "+", SuperscriptBox["t", "2"], "+", FractionBox[ RowBox[{"5", " ", SuperscriptBox["t", "3"]}], "3"], "+", FractionBox[ RowBox[{"9", " ", SuperscriptBox["t", "4"]}], "4"], "+", FractionBox[ RowBox[{"29", " ", SuperscriptBox["t", "5"]}], "12"], "+", FractionBox[ RowBox[{"779", " ", SuperscriptBox["t", "6"]}], "360"], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "t", "]"}], "7"], SeriesData[$CellContext`t, 0, {}, 0, 7, 1], Editable->False]}], SeriesData[$CellContext`t, 0, {1, 0, 1, Rational[5, 3], Rational[9, 4], Rational[29, 12], Rational[779, 360]}, 0, 7, 1], Editable->False]], "Output", CellChangeTimes->{3.4794600499744453`*^9, 3.4795456813134856`*^9, 3.479545714376832*^9, 3.479545750674636*^9}], Cell[BoxData[ InterpretationBox[ RowBox[{"t", "+", FractionBox[ RowBox[{"5", " ", SuperscriptBox["t", "2"]}], "2"], "+", FractionBox[ RowBox[{"9", " ", SuperscriptBox["t", "3"]}], "2"], "+", FractionBox[ RowBox[{"145", " ", SuperscriptBox["t", "4"]}], "24"], "+", FractionBox[ RowBox[{"779", " ", SuperscriptBox["t", "5"]}], "120"], "+", FractionBox[ RowBox[{"93", " ", SuperscriptBox["t", "6"]}], "16"], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "t", "]"}], "7"], SeriesData[$CellContext`t, 0, {}, 1, 7, 1], Editable->False]}], SeriesData[$CellContext`t, 0, {1, Rational[5, 2], Rational[9, 2], Rational[145, 24], Rational[779, 120], Rational[93, 16]}, 1, 7, 1], Editable->False]], "Output", CellChangeTimes->{3.4794600499744453`*^9, 3.4795456813134856`*^9, 3.479545714376832*^9, 3.479545750674636*^9}] }, Open ]] }, WindowSize->{966, 750}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[567, 22, 1833, 55, 208, "Input"], Cell[2403, 79, 875, 28, 50, "Output"], Cell[3281, 109, 945, 31, 50, "Output"] }, Open ]] } ] *) (* End of internal cache information *)