(************** 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[ 112125, 3473]*) (*NotebookOutlinePosition[ 147774, 4696]*) (* CellTagsIndexPosition[ 147699, 4690]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Lab 3 - Applications of Integration", FontSize->24, FontWeight->"Bold"], "\nMath 2374 - University of Minnesota\nhttp://www.math.umn.edu/math2374\n\ Questions to: swenson@math.umn.edu, gantner@math.umn.edu" }], "Text", TextAlignment->Center, FontColor->GrayLevel[1], Background->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell["Introduction", "Section", FontSize->14, Background->None], Cell[TextData[{ "Our goal in this part of the lab is to find the volume of liquid in a \ cylindrical tank which is tilted at some angle from the horizontal. To be \ specific, we start with the cylinder with radius 2 m and length 10 m, whose \ axis is the vertical line through (2,0,0): we will put the bottom of the \ cylinder at z=0 and the top at z=10. We can plot this cylinder using ", StyleBox["ContourPlot3D", FontWeight->"Bold"], ". We've filled in most of the commands here, including the function. \ Fill in the appropriate bounds and evaluate the cell to see the cylinder. \ (Notice that we name the plot ", StyleBox["cyl", FontWeight->"Bold"], ".)" }], "Text"], Cell[BoxData[ \(\(cyl = ContourPlot3D[\((x - 2)\)^2 + y^2 - 4, {x, , }, {y, , }, {z, , }, Axes \[Rule] True, AxesLabel \[Rule] {"\", "\", "\"}];\)\)], "Input"], Cell["\<\ The surface of the liquid in our tank should be given by a \ horizontal plane: here is an example.\ \>", "Text"], Cell[BoxData[{ \(plane1 = ParametricPlot3D[{x, y, 4}, {x, \(-1\), 5}, {y, \(-3\), 3}]\), "\[IndentingNewLine]", \(Show[cyl, plane1, AxesLabel \[Rule] {x, y, z}]\)}], "Input", CellTags->"zerodeg"], Cell[TextData[{ "In this case, the volume of the liquid is \[Pi]", Cell[BoxData[ \(TraditionalForm\`\(r\^2\) h\)]], " = 16\[Pi]. (See why?)" }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Tilting Cylinders Is Too Hard", "Section", FontSize->14, Background->None], Cell["\<\ To find the volume of liquid when the cylinder is tilted, we will \ need to use integration. Evaluate the next cell to see an example of a \ tilted cylinder, with a horizontal plane representing the surface of a \ liquid.\ \>", "Text"], Cell[BoxData[{ \(\(u = Pi/4;\)\), "\[IndentingNewLine]", \(cyl2 = ParametricPlot3D[{Cos[u]*\((2*Cos[t] + 2)\) - Sin[u]*s, 2*Sin[t], Sin[u]*\((2*Cos[t] + 2)\) + Cos[u]*s}, {s, 0, 10}, {t, 0, 2 Pi}]\), "\[IndentingNewLine]", \(plane2 = ParametricPlot3D[{x, y, 4}, {x, \(-6\), 4}, {y, \(-2\), 2}]\), "\[IndentingNewLine]", \(Show[cyl2, plane2, \ AxesLabel \[Rule] {x, y, z}, ViewPoint -> {0, \ \(-3\), \ 0}, BoxRatios \[Rule] {1, 1, 1}]\)}], "Input"], Cell["\<\ This picture is not very useful for calculation: we don't know what \ to integrate, nor over what region! [It was also tricky to reparametrize the \ cylinder.]\ \>", "Text"], Cell[TextData[{ "We will take a different approach: again, we imagine the cylinder tilting, \ but to simplify the calculations, we tilt the plane instead, and reuse ", StyleBox["cyl", FontWeight->"Bold"], ", our original cylinder. To put this another way, we are tilting the \ coordinate axes along with the cylinder." }], "Text"], Cell[BoxData[{ \(plane3 = ParametricPlot3D[{x, y, 6 - x}, {x, \(-2\), 6}, {y, \(-2\), 2}]\), "\[IndentingNewLine]", \(Show[cyl, plane3, AxesLabel \[Rule] {x, y, z}, BoxRatios \[Rule] {1, 1, 1}, ViewPoint -> {0, \ \(-3\), \ 0}]\)}], "Input"], Cell["\<\ If you tilt your head,you can see that this graph shows the same \ part of the cylinder as in the tilted-cylinder graph above. If you're not \ sure about that, evaluate the next cell to see the cylinder in a \ LiveGraphics3D window. Tilt the picture until the plane is flat. (HINT: hold \ the shift button down, click on the picture, and move your mouse to the \ left.) It should look the same as the earlier picture.\ \>", "Text"], Cell[BoxData[ \(\(ShowLive[cyl, plane3, AxesLabel \[Rule] {x, y, z}, BoxRatios \[Rule] {1, 1, 1}, ViewPoint -> {0, \ \(-3\), \ 0}];\)\)], "Input"], Cell[TextData[{ "We like this new viewpoint because it makes calculation much easier: we \ can find the volume of liquid by integration. Specifically, we want the \ volume of the region below our plane, and above the bottom of the tank.\n\n\ Therefore, the region of integration should be the bottom of the tank, which \ is in the xy-plane, and given by the inequality ", Cell[BoxData[ \(TraditionalForm\`\((x - 2)\)\^2 + y\^2\)]], "\[LessEqual] 4, and the integrand should be the height of the plane." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Exercises", "Section", CellFrame->False, FontSize->14, Background->None], Cell[TextData[{ StyleBox["Exercise 1", FontWeight->"Bold"], "\na) Suppose that the fluid level in the tank is 7 m on the left edge of \ the tank (where x=0) and 5 m on the right edge (where x=4). Find the \ equation of the plane of the liquid, and use a double integral to find the \ volume of liquid in the tank. [Hint: you should use a \"dy dx\" iterated \ integral, where the bounds on y depend on x, and are given by the equation of \ the base of the cylinder.] Also find the angle at which the tank is tipped \ from its upright position. For consistency, assume that the ", ButtonBox["tank", ButtonData:>"zerodeg", ButtonStyle->"Hyperlink"], " in the ", StyleBox["Introduction", FontWeight->"Bold"], " above is tipped at a 0\[Degree] angle. [Hint: use a \"side elevation\" \ sketch, and use trigonometry to find the angle between your plane and the \ plane z=5.]\n\nb) Suppose now that the fluid level is 7 m at the left edge of \ the tank, but that there isn't enough fluid to reach the right edge; instead, \ the fluid covers the base of the tank only out to the plane x=3. [You can \ produce a graph with the commands below: you'll have to paste them into \ another cell.]\n", Cell[BoxData[{ \(plane4 = ParametricPlot3D[{x, y, 7 - 7 x/3}, {x, 0, 3}, {y, \(-2\), 2}]\), "\n", \(Show[cyl, plane4, AxesLabel \[Rule] {x, y, z}, ViewPoint -> {0, \ \(-3\), \ 0}]\)}], "Input", CellFrame->False], "\nFind the equation of the plane of the liquid,and use a double integral \ to find the volume of liquid in the tank. Also find the angle at which the \ tank is tipped from its upright position. [", StyleBox["Warning", FontWeight->"Bold"], ": the region of integration has changed -- if you reuse the bounds from \ problem 1, you'll include the \"negative volume\" from the region where z<0.]\ \n\nc) Suppose that the tank is tipped so far that the liquid touches both \ ends of the tank, touching the top (at z=10) out to the plane x=1, and \ covering the bottom out to the plane x=3. Find the volume of liquid in the \ tank using two double integrals. Explain why you can't just use one double \ integral. Lastly, find the angle at which the tank is tipped from its \ upright position.\n\nd) Suppose, finally, that the liquid touches the top of \ the tank out to the plane x=3, and reaches a level of 3 m on the right edge \ of the tank. Find the volume of liquid in the tank using two double \ integrals, and find the angle at which the tank is tipped from its upright \ position.\n\ne) Suppose that our tank is tilted at an angle of 80\[Degree] \ from its upright position. Where could you mark the surface of the tank to \ indicate when the tank is exactly one-third full? [Hint: use trigonometry to \ decide which of the first four exercises most resembles this problem. \ Calculate the volume in terms of some unknown variable, and use ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["FindRoot", FontFamily->"Courier", FontWeight->"Bold"], " command, which you can look up in the help browser.]" }], "Text", CellFrame->True, Background->RGBColor[1, 0.501961, 0.501961]], Cell[BoxData[ \(\[IndentingNewLine]\)], "Input"], Cell["\<\ In exercise 2, rather than using the tank that was described in the \ introduction, we will use an oblong tank. When intersected with the \ xy-plane, the tank will be an ellipse which goes through the points (0,0,0), \ (4,2,0), (4,-2,0), and (8,0,0). This ellipse is centered at (4,0,0), and \ every point on the ellipse satisfies the equation (1/4)(x-4)^2 + y^2 = 4. We \ will assume that the tank has height 10. The new tank looks like\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(tank\ = \ ContourPlot3D[\((1/4)\)*\((x - 4)\)^2\ + \ y^2\ - \ 4, \ {x, 0, 8}, \ {y, \(-2\), 2}, \ {z, 0, 10}, \ AxesLabel \[Rule] {x, y, z}, \ Axes \[Rule] True]\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.26566 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics3D %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.134744 1.26566 -1.30104e-18 1.26566 [ [.2521 1.27735 -3.1377 0 ] [.2521 1.27735 2.8623 9 ] [.42233 1.23522 -3.04275 0 ] [.42233 1.23522 2.95725 9 ] [.60027 1.19116 -2.94186 0 ] [.60027 1.19116 3.05814 9 ] [.78647 1.14504 -2.83448 0 ] [.78647 1.14504 3.16552 9 ] [.98152 1.0967 -2.71994 0 ] [.98152 1.0967 3.28006 9 ] [.6018 1.27025 -4.90311 0 ] [.6018 1.27025 5.09689 9.8125 ] [.00463 1.11217 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This is the same direction as in the examples above, but here it \ actually matters which direction we tip it, because the tank is no longer \ circular.\ \>", "Text"], Cell[TextData[{ StyleBox["Exercise 2\n", FontWeight->"Bold"], StyleBox["\na", FontVariations->{"CompatibilityType"->0}], ") Suppose that the fluid level in the tank is 7 m on the left edge of the \ tank (where x=0) and 5 m on the right edge (where x=8). Find the equation of \ the plane of the liquid, and use a double integral to find the volume of \ liquid in the tank. [Hint: you should use a \"dy dx\" iterated integral, \ where the bounds on y depend on x, and are given by the equation of the base \ of the cylinder.] Also find the angle at which the tank is tipped from its \ upright position. For consistency, assume that the tank in the paragraph \ before part a) above is tipped at a 0\[Degree] angle. [Hint: use a \"side \ elevation\" sketch, and use trigonometry to find the angle between your plane \ and the plane z=5.]\n\nb) Suppose now that the fluid level is 7 m at the left \ edge of the tank, but that there isn't enough fluid to reach the right edge; \ instead, the fluid covers the base of the tank only out to the plane x=4. \ [You can produce a graph with the commands below: you'll have to paste them \ into another cell.]\n", Cell[BoxData[{ \(plane5 = ParametricPlot3D[{x, y, 7 - 7 x/4}, {x, 0, 4}, {y, \(-3\), 3}]\), "\n", \(Show[tank, plane5, AxesLabel \[Rule] {x, y, z}, ViewPoint -> {0, \ \(-4\), \ 0}]\)}], "Input", CellFrame->False], "\nFind the equation of the plane of the liquid,and use a double integral \ to find the volume of liquid in the tank. Also find the angle at which the \ tank is tipped from its upright position. [", StyleBox["Warning", FontWeight->"Bold"], ": the region of integration has changed -- if you reuse the bounds from \ problem 1, you'll include the \"negative volume\" from the region where z<0.]\ \n\nc) Suppose that the tank is tipped so far that the liquid touches both \ ends of the tank, touching the top (at z=10) out to the plane x=2, and \ covering the bottom out to the plane x=4. Find the volume of liquid in the \ tank using two double integrals. Explain why you can't just use one double \ integral. Lastly, find the angle at which the tank is tipped from its \ upright position.\n\nd) Suppose, finally, that the liquid touches the top of \ the tank out to the plane x=6, and reaches a level of 4 m on the right edge \ of the tank. Find the volume of liquid in the tank using two double \ integrals, and find the angle at which the tank is tipped from its upright \ position.\n\ne) Suppose that our tank is tilted at an angle of 80\[Degree] \ from its upright position. Where could you mark the surface of the tank to \ indicate when the tank is exactly one-third full? [Hint: use trigonometry to \ decide which of the first four exercises most resembles this problem. \ Calculate the volume in terms of some unknown variable, and use ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["FindRoot", FontFamily->"Courier", FontWeight->"Bold"], " command, which you can look up in the help browser.]" }], "Text", CellFrame->True, Background->RGBColor[1, 0.501961, 0.501961]], Cell[CellGroupData[{ Cell["Credits", "Subsection", Background->None], Cell["\<\ This lab was inspired by a lab written at Lafayette College in \ Pennsylvania. Cindy Kaus (cindy.kaus@metrostate.edu) wrote the first version \ that we used at the University of Minnesota. James Swenson \ (swenson@math.umn.edu) completely rewrote the text in Spring 2002 but kept \ the same exercises. In Spring 2004 Jonathan Rogness (rogness@math.umn.edu) \ went through and added a few Live commands and polished things up a bit; Ryan \ Gantner (gantner@math.umn.edu) added new exercises, where the cylinder is no \ longer circular. This lab (or portions thereof) copyrighted by their respective authors. \ We've all agreed to use the Creative Commons \ Attribution-NonCommercial-ShareAlike License. You can find more information \ on this license at http://creativecommons.org/licenses/by-nc-sa/1.0/ Although it's not specifically required by the license, I'd appreciate it if \ you let me know at rogness@math.umn.edu if you use parts of our labs, just so \ I can keep track of it. Please send me any questions or comments!\ \>", \ "Text"] }, Closed]] }, Open ]] }, FrontEndVersion->"5.2 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{906, 761}, WindowMargins->{{Automatic, -6}, {Automatic, 60}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{"user002", "rogness"}, \ "Newlab.nb.ps", CharacterEncoding -> "iso8859-1"], "Magnification"->1}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. 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FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 18}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, DefaultNewInlineCellStyle->"None", InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, LanguageCategory->"NaturalLanguage", CounterIncrements->"Subsubsection", FontFamily->"Times", FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, InputAutoReplacements->{"TeX"->StyleBox[ RowBox[ {"T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "LaTeX"->StyleBox[ RowBox[ {"L", StyleBox[ AdjustmentBox[ "A", BoxMargins -> {{-0.36, -0.1}, {0, -0}}, BoxBaselineShift -> -0.2], FontSize -> Smaller], "T", AdjustmentBox[ "E", BoxMargins -> {{-0.075, -0.085}, {0, 0}}, BoxBaselineShift -> 0.5], "X"}]], "mma"->"Mathematica", "Mma"->"Mathematica", "MMA"->"Mathematica"}, Hyphenation->True, LineSpacing->{1, 3}, CounterIncrements->"Text"], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}, TextJustification->0.5, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, DefaultNewInlineCellStyle->"None", Hyphenation->True, LineSpacing->{1, 3}, LanguageCategory->"NaturalLanguage", CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, TextJustification->0.5, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names. Some attributes for these styles are actually set in FormatType Styles \ (in the last section of this stylesheet). \ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}, FontSize->11], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, LinebreakAdjustments->{0.85, 2, 10, 1, 1}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, LinebreakAdjustments->{0.85, 2, 10, 0, 1}, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, LanguageCategory->"Formula", FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}, FontSize->11], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontSize->11, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->7, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}, FontSize->16], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}, FontSize->11], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, LanguageCategory->None, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None, FontFamily->"Courier", FontSize->10], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageMargins->{{38, Inherited}, {Inherited, 0}}, Magnification->0.6], Cell[StyleData["Graphics", "Printout"], ImageMargins->{{30, Inherited}, {Inherited, 0}}, Magnification->0.8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Inline Formatting", "Section"], Cell["\<\ These styles are for modifying individual words or letters in a \ cell exclusive of the cell tag.\ \>", "Text"], Cell[StyleData["RM"], StyleMenuListing->None, FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["BF"], StyleMenuListing->None, FontWeight->"Bold"], Cell[StyleData["IT"], StyleMenuListing->None, FontSlant->"Italic"], Cell[StyleData["TR"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["TI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["TB"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["TBI"], StyleMenuListing->None, FontFamily->"Times", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["MR"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["MO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["MB"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["MBO"], StyleMenuListing->None, FontFamily->"Courier", FontWeight->"Bold", FontSlant->"Italic"], Cell[StyleData["SR"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Plain"], Cell[StyleData["SO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SB"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Plain"], Cell[StyleData["SBO"], StyleMenuListing->None, FontFamily->"Helvetica", FontWeight->"Bold", FontSlant->"Italic"], Cell[CellGroupData[{ Cell[StyleData["SO10"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->10, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "Printout"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"], Cell[StyleData["SO10", "EnhancedPrintout"], StyleMenuListing->None, FontFamily->"Futura", FontSize->7, FontWeight->"Plain", FontSlant->"Italic"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, HyphenationOptions->{"HyphenationCharacter"->"\[Continuation]"}, LanguageCategory->"Formula", ScriptLevel->0, SingleLetterItalics->True, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["DisplayFormula", "Printout"], FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Program"], CellFrame->{{0, 0}, {0.5, 0.5}}, CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, Hyphenation->False, LanguageCategory->"Formula", ScriptLevel->1, FontFamily->"Courier"], Cell[StyleData["Program", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}, FontSize->16], Cell[StyleData["Program", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}, FontSize->11], Cell[StyleData["Program", "Printout"], CellMargins->{{2, 0}, {6, 6}}, FontSize->9] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"], FontSize->16], Cell[StyleData["Hyperlink", "Condensed"], FontSize->11], Cell[StyleData["Hyperlink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"], FontSize->16], Cell[StyleData["MainBookLink", "Condensed"], FontSize->11], Cell[StyleData["MainBookLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"], FontSize->16], Cell[StyleData["AddOnsLink", "Condensed"], FontSize->11], Cell[StyleData["AddOnsLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuide", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"], FontSize->16], Cell[StyleData["RefGuideLink", "Condensed"], FontSize->11], Cell[StyleData["RefGuideLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"], FontSize->16], Cell[StyleData["GettingStartedLink", "Condensed"], FontSize->11], Cell[StyleData["GettingStartedLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"], FontSize->16], Cell[StyleData["OtherInformationLink", "Condensed"], FontSize->11], Cell[StyleData["OtherInformationLink", "Printout"], FontSize->10, FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, DefaultNewInlineCellStyle->"None", LanguageCategory->"NaturalLanguage", StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Placeholder->True, StyleMenuListing->None, FontSlant->"Italic", FontColor->RGBColor[0.890623, 0.864698, 0.384756], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["PrimaryPlaceholder"], StyleMenuListing->None, DrawHighlighted->True, FontSlant->"Italic", Background->RGBColor[0.912505, 0.891798, 0.507774], TagBoxOptions->{Editable->False, Selectable->False, StripWrapperBoxes->False}], Cell[StyleData["PrimaryPlaceholder", "Presentation"]], Cell[StyleData["PrimaryPlaceholder", "Condensed"]], Cell[StyleData["PrimaryPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options. 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