Homework5Sol - (* Content-type: application/mathematica *)...

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(* 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[ 148576, 2591] NotebookOptionsPosition[ 147874, 2562] NotebookOutlinePosition[ 148279, 2579] CellTagsIndexPosition[ 148236, 2576] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Problem 1", "Section", CellChangeTimes->{{3.464014045796875*^9, 3.464014052484375*^9}, { 3.46401409125*^9, 3.4640140919375*^9}, {3.464014597703125*^9, 3.4640145978125*^9}, {3.4640165614375*^9, 3.464016562421875*^9}, { 3.46462128534375*^9, 3.46462128546875*^9}, {3.4661809535*^9, 3.466180953578125*^9}}], Cell[CellGroupData[{ Cell["Part b)", "Subsection", CellChangeTimes->{{3.4640140630625*^9, 3.464014064203125*^9}, { 3.464621288578125*^9, 3.464621288984375*^9}, {3.46618095709375*^9, 3.46618095740625*^9}, {3.46792238715625*^9, 3.467922387390625*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", "y_", ",", "\[Alpha]_"}], "]"}], "=", RowBox[{ RowBox[{"\[Alpha]", " ", "x"}], "-", "y", "-", RowBox[{"x", RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"g", "[", RowBox[{"x_", ",", "y_", ",", "\[Alpha]_"}], "]"}], "=", RowBox[{"x", "+", RowBox[{"\[Alpha]", " ", "y"}], "-", RowBox[{"y", RowBox[{"(", RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"]}], ")"}]}]}]}], ";"}]}], "Input"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"GraphicsRow", "[",
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RowBox[{ RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"StreamPlot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f", "[", RowBox[{"x", ",", "y", ",", RowBox[{"-", "0.5"}]}], "]"}], ",", RowBox[{"g", "[", RowBox[{"x", ",", "y", ",", RowBox[{"-", "0.5"}]}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"PlotLabel", "\[Rule]", "\"\<\[Alpha] = -0.5\>\""}], ",", RowBox[{"StreamPoints", "\[Rule]", "20"}], ",", RowBox[{"StreamScale", "\[Rule]", "Large"}]}], "]"}], ",", RowBox[{"StreamPlot", "[", " ", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"f", "[", RowBox[{"x", ",", "y", ",", "0.8"}], "]"}], ",", RowBox[{"g", "[", RowBox[{"x", ",", "y", ",", "0.8"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", " ", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"PlotLabel", "\[Rule]", "\"\<\[Alpha] = 0.8\>\""}], ",", RowBox[{"StreamPoints", "\[Rule]", "20"}], ",", RowBox[{"StreamScale", "\[Rule]", "Large"}]}], "]"}]}], "}"}], ",", RowBox[{"ImageSize", "\[Rule]", "500"}]}], "]"}]], "Input", CellChangeTimes->{{3.46662168065625*^9, 3.466621769921875*^9}, { 3.46662184284375*^9, 3.46662186734375*^9}, {3.467903429703125*^9,
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Homework5Sol - (* Content-type: application/mathematica *)...

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