(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 560453, 8461]*) (*NotebookOutlinePosition[ 561575, 8501]*) (* CellTagsIndexPosition[ 561501, 8495]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Lab 3.1 Tangent Planes", "Title"], Cell["\<\ Save your final work on your account and submit your solution to \ the Engineering Math 2 Digital Dropbox with a file name in the form\ \>", \ "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell["\<\ LastNameFirstInitialChapterLabNumber.nb (no spaces or other \ characters)\ \>", "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell["for example, StroyanK3Lab1.nb", "Solution", Evaluatable->False, AspectRatioFixed->True, CellTags->"eExam1"], Cell[CellGroupData[{ Cell["\<\ Your name:Seth Cohen & T.A.'s name: Lisa Powers here Section \ A05\ \>", "Section"], Cell[CellGroupData[{ Cell[TextData[{ "This Lab is focused on understanding the gradient with the help of ", StyleBox["Mathematica", FontSlant->"Italic"], ". Open eSection 3.6 from your CD or the on-line version of the text and \ work through it. Modify those examples to do the computations for the \ function in the next exercise." }], "Text"], Cell["", "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell["", "Exercise"], Cell[CellGroupData[{ Cell[TextData[{ "a) Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to graph the function ", Cell[BoxData[ \(TraditionalForm\`f[x, y] = 3 Cos[\[Pi]\ x\ y\ ] \[ExponentialE]\^\(-\((x\^2 + y\^2)\)\)\)]], " and its tangent plane together at ", Cell[BoxData[ \(TraditionalForm\`\((x, y)\) = \((1/5, 1/7)\)\)]], ". Plot with changes in ", Cell[BoxData[ \(TraditionalForm\`x\)]], " and ", Cell[BoxData[ \(TraditionalForm\`y\)]], " of \[PlusMinus]1 away from this center. Your plot will look similar to:" }], "IndentedText"], Cell[GraphicsData["PostScript", "\<\ Null\ \>"], "Graphics", ImageSize->{124.563, 199.563}, ImageMargins->{{98, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg"], ImageCacheContents->"Empty"], Cell[CellGroupData[{ Cell[BoxData[{ \(\(Clear[x, y, dx, dy, f, fX, fY, G];\)\), "\[IndentingNewLine]", \(<< RealTime3D`\), "\[IndentingNewLine]", \(f[x_, y_] = 3*Cos[\[Pi]*x* y]*\[ExponentialE]^\(-\((x^2 + y^2)\)\)\), "\[IndentingNewLine]", \(\(fX[x_, y_] = D[f[x, y], x];\)\), "\[IndentingNewLine]", \(\(fY[x_, y_] = D[f[x, y], y];\)\), "\[IndentingNewLine]", \(\(G[x_, y_] = {fX[x, y], fY[x, y]};\)\), "\[IndentingNewLine]", \(\(x = 1/5;\)\), "\[IndentingNewLine]", \(\(y = 1/7;\)\), "\[IndentingNewLine]", \(\(z = f[x, y];\)\), "\[IndentingNewLine]", \(dz = G[x, y] . {dx, dy}\), "\[IndentingNewLine]", \(\(surface = Plot3D[f[x + dx, y + dy] - z, {dx, \(-1\), 1}, {dy, \(-1\), 1}, 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ButtonFrame->None, ButtonData:>\\\"General::optx\\\"]\\)\"\>"}]], \ "Message"] }, Open ]], Cell[BoxData[""], "Input"] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "\n\n\nb) Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to graph the function ", Cell[BoxData[ \(TraditionalForm\`f[x, y] = 3 Cos[\[Pi]\ x\ y\ ] \[ExponentialE]\^\(-\((x\^2 + y\^2)\)\)\)]], " and its tangent plane together at ", Cell[BoxData[ \(TraditionalForm\`\((x, y)\) = \((1/5, 1/7)\)\)]], ". Plot with changes in ", Cell[BoxData[ \(TraditionalForm\`x\)]], " and ", Cell[BoxData[ \(TraditionalForm\`y\)]], " of \[PlusMinus]0.1 away from this center. Your plot will look similar \ to:" }], "IndentedText"], Cell[GraphicsData["PostScript", "\<\ \ \>"], "Graphics", ImageSize->{211, 199.5}, ImageMargins->{{47.5625, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgkooo[mo`03o`000?ojoOoon_go04Son_go002Yoo[mo`05o`000?ojoOoon_gooo[m ool000003_ojoOl00ol0003on_gooo[mo`18oo[mo`00ZOojoOl01Ol0003on_gooo[mooojoOoo0000 00kon_go00?o0000oo[mooojoOl0B?ojoOl00:Won_go00Go410@oo[mooojoOoon_gooa0@400>oo[m o`03o`000?ojoOoon_go04Son_go001Too[mo`08onW/k_mCE5Go0000o`000?nEUiSo0000oa0@4?oj oOl2o`0000;on_go0_l0000goo[mo`05ogAfMonEUiSon_gooiFGV?mdMWL03_ojoOl00ol0003on_go oo[mo`18oo[mo`00I?ojoOl01_mCE5GoM7Igoo[moooYk>koDeAEo`0000;on_go00KojNc^ob4Q8On5 QXOo]kVjo`000?oHfmdgoo[mo`05onW/k_lah03?ojoOl00omCE5GoI6EVo`00 001:oo[mo`00I?ojoOl01_l0003on_gooo[mooojoOoojNc^o`0000?on_go00Cof=_Mo`000?l@413o 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Cell[TextData[{ "c) Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to graph the function ", Cell[BoxData[ \(TraditionalForm\`f[x, y] = 3 Cos[\[Pi]\ x\ y\ ] \[ExponentialE]\^\(-\((x\^2 + y\^2)\)\)\)]], " and its tangent plane together at ", Cell[BoxData[ \(TraditionalForm\`\((x, y)\) = \((1/5, 1/7)\)\)]], ". Plot with changes in ", Cell[BoxData[ \(TraditionalForm\`x\)]], " and ", Cell[BoxData[ \(TraditionalForm\`y\)]], " of \[PlusMinus]0.01 away from this center. 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