Lab4B_Ex1 - (* Content-type: application/mathematica *) (*...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
(* 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[ 209037, 3472] NotebookOptionsPosition[ 208547, 3452] NotebookOutlinePosition[ 208891, 3467] CellTagsIndexPosition[ 208848, 3464] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ RowBox[{ RowBox[{"Lab4B", " ", "Exercise", " ", "1"}], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.4336012195307293`*^9, 3.433601228535796*^9}, { 3.4470292455309744`*^9, 3.4470292478799744`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{ "First", " ", "we", " ", "can", " ", "plot", " ", "and", " ", "find", " ", "the", " ", "parametrization", " ", "of", " ", "f", RowBox[{"(", RowBox[{"y", ",", "z"}], ")"}]}], " ", "=", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"y", "^", "2"}], "+", RowBox[{"z", "^", "2"}]}], ",", " ", "y", ",", "z"}], ")"}]}], "\[IndentingNewLine]", RowBox[{"Next", ",", " ", RowBox[{ "as", " ", "the", " ", "y", " ", "and", " ", "z", " ", "values", " ", "are", " ", "in", " ", "the", " ", "unit", " ", "disk"}], ",", " ", RowBox[{ RowBox[{ RowBox[{"it", " ", "corresponds", " ", "to", " ", "0"}], "\[LessEqual]", "r", "\[LessEqual]", RowBox[{"1", " ", "and", " ", "0"}], "\[LessEqual]", "\[Theta]", "\[LessEqual]", RowBox[{"2", RowBox[{"\[Pi]", ".", " ", "\[IndentingNewLine]", "So"}], " ", "we", " ", "just", " ", "need", " ", "to", " ", "describe", " ", "x"}]}], "=", RowBox[{ RowBox[{ RowBox[{"y", "^", "2"}], "+", RowBox[{ RowBox[{"z", "^", "2"}], " ", "in", " ", "terms", " ", "of", " ", "r",
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
" ", "and", " ", RowBox[{"\[Theta]", ".", "\[IndentingNewLine]", "As"}], " ", "y"}]}], "=", RowBox[{ RowBox[{ RowBox[{"rCos", "[", "\[Theta]", "]"}], " ", "and", " ", "z"}], "=", RowBox[{"rSin", "[", "\[Theta]", "]"}]}]}]}], ",", RowBox[{ RowBox[{"we", " ", "can", " ", "deduce", " ", "x"}], "=", RowBox[{"r", "^", "2"}]}]}], "\[IndentingNewLine]", RowBox[{"then", ",", " ", RowBox[{"the", " ", "parametrization", " ", RowBox[{"becomes", ":"}]}]}]}], "Input", CellChangeTimes->{{3.4470292722369747`*^9, 3.4470292732929745`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"f", "[", RowBox[{"r_", ",", "theta_"}], "]"}], "=", RowBox[{"{", " ", RowBox[{ RowBox[{"r", "^", "2"}], ",", RowBox[{"r", " ", RowBox[{"Cos", "[", "theta", "]"}]}], ",", " ", RowBox[{"r", " ", RowBox[{"Sin", "[", "theta", "]"}]}]}], "}"}]}], "\[IndentingNewLine]", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"r", ",", "theta"}], "]"}], ",", RowBox[{"{", RowBox[{"r", ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"theta", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}]}], "]"}]}], "Input", CellChangeTimes->{{3.434118916831394*^9, 3.434118922271125*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ SuperscriptBox["r", "2"], ",", RowBox[{"r", " ",
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/07/2011 for the course MATH 2374 taught by Professor Mosher during the Spring '07 term at Minnesota.

Page1 / 59

Lab4B_Ex1 - (* Content-type: application/mathematica *) (*...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online