Lab4B_Ex3 - (* Content-type: application/mathematica *) (*...

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(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 127535, 2147] NotebookOptionsPosition[ 127088, 2128] NotebookOutlinePosition[ 127431, 2143] CellTagsIndexPosition[ 127388, 2140] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"Lab4B", " ", "Exercise", " ", "3"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.434119597528811*^9, 3.4341196066488113`*^9}, { 3.4470292991669745`*^9, 3.4470293021059747`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"Fot", " ", "the", " ", "function", " ", FormBox[ RowBox[{ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "+", SuperscriptBox["z", "2"]}], " ", "=", "1"}], TraditionalForm]}], ",", " ", RowBox[{ RowBox[{"It", "'"}], "s", " ", "obvious", " ", "that", " ", RowBox[{"it", "'"}], "s", " ", "plot", " ", "should", " ", "be", " ", "a", " ", "sophere", " ", "with", " ", "diameter", " ", "1."}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{ "For", " ", "x", " ", "value", " ", "of", " ", "this", " ", "function"}], ",", " ", RowBox[{ RowBox[{"x", "^", "2"}], " ", "has", " ", "a", " ", "range", " ", "of", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], ",", " ", RowBox[{ "so", " ", "it", " ", "can", " ", "be", " ", "expressed", " ", "with", " ", "two", " ", "variables", " ", "\[Theta]", " ", "and", " ", "\[Phi]"}], ",", " ", RowBox[{ RowBox[{"where", " ",
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RowBox[{"Cos", "[", "\[Theta]", "]"}], RowBox[{"Sin", "[", "\[Phi]", "]"}]}], "=", "x"}]}], "\[IndentingNewLine]", RowBox[{"then", ",", " ", RowBox[{"y", "=", RowBox[{ RowBox[{"Sin", "[", "\[Theta]", "]"}], RowBox[{ RowBox[{"Sin", "[", "\[Phi]", "]"}], ".", "\[IndentingNewLine]", "so"}], " ", "from", " ", "original", " ", "function"}]}], ",", " ", RowBox[{"z", "=", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "\[Phi]", "]"}], ".", "\[IndentingNewLine]", "as"}], " ", "x"}]}], ",", " ", RowBox[{ "y", " ", "and", " ", "z", " ", "are", " ", "all", " ", "with", " ", "range", " ", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "1"}], "}"}]}], ",", RowBox[{ "range", " ", "for", " ", "\[Theta]", " ", "therefor", " ", "becomes", " ", RowBox[{"{", RowBox[{"0", ",", RowBox[{"2", "\[CapitalPi]"}]}], "}"}]}], ",", " ", RowBox[{ "and", " ", "rangr", " ", "for", " ", "\[Phi]", " ", "becomes", " ", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "\[Pi]"}], "}"}], ".", "\[IndentingNewLine]", "then"}], " ", "we", " ", "can", " ", "find", " ", "the", " ", "parametrization", " ", "of", " ", "this", " ", RowBox[{"function", ":"}]}]}]}], "Input", CellChangeTimes->{{3.434121366714394*^9, 3.434121646925606*^9}, { 3.434121691228948*^9, 3.4341217983818893`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"f", "[", RowBox[{"\[Theta]_", ",", "\[Phi]_"}], "]"}], "=",
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This note was uploaded on 03/07/2011 for the course MATH 2374 taught by Professor Mosher during the Spring '07 term at Minnesota.

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Lab4B_Ex3 - (* Content-type: application/mathematica *) (*...

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