(* 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[ 63309, 1448] NotebookOptionsPosition[ 19521, 507] NotebookOutlinePosition[ 62397, 1419] CellTagsIndexPosition[ 62326, 1414] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) 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: rogness@math.umn.edu" }], "Text", CellChangeTimes->{{3.411781385528648*^9, 3.41178138791743*^9}}, 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[ RowBox[{"cyl", "=", RowBox[{"ContourPlot3D", "[", RowBox[{ RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "2"], "+", SuperscriptBox["y", "2"]}], "==", "4"}], ",", RowBox[{"{", RowBox[{"x", ",", "Null", ",", "Null"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", "Null", ",", "Null"}], "}"}], ",", RowBox[{"{", RowBox[{"z", ",", "Null", ",", "Null"}], "}"}], ",", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"ContourStyle", "->", RowBox[{"Opacity", "[", "0.8", "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.411780653672388*^9, 3.411780679136447*^9}, { 3.411780713466522*^9, 3.411780717138644*^9}, {3.411781251260358*^9, 3.4117812515420637`*^9}}], Cell["\<\ The surface of the liquid in our tank should be given by a horizontal plane: \ here is an example.\ \>", "Text"], Cell[BoxData[{ RowBox[{"plane1", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "1"}], ",", "5"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"cyl", ",", "plane1", ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]}], "Input", CellTags->"zerodeg"], Cell[TextData[{ "In this case, the volume of the liquid is \[Pi]", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["r", "2"], "h"}], TraditionalForm]]], " = 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[{ RowBox[{ RowBox[{"u", "=", RowBox[{"Pi", "/", "4"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"cyl2", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Cos", "[", "u", "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"2", "*", RowBox[{"Cos", "[", "t", "]"}]}], "+", "2"}], ")"}]}], "-", RowBox[{ RowBox[{"Sin", "[", "u", "]"}], "*", "s"}]}], ",", RowBox[{"2", "*", RowBox[{"Sin", "[", "t", "]"}]}], ",", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "u", "]"}], "*", RowBox[{"(", RowBox[{ RowBox[{"2", "*", RowBox[{"Cos", "[", "t", "]"}]}], "+", "2"}], ")"}]}], "+", RowBox[{ RowBox[{"Cos", "[", "u", "]"}], "*", "s"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"s", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PlotStyle", "->", RowBox[{"Opacity", "[", "0.8", "]"}]}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"plane2", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "6"}], ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"cyl2", ",", "plane2", ",", " ", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "3"}], ",", " ", "0"}], "}"}]}], ",", RowBox[{"PlotRange", "->", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", "8"}], ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "10"}], "}"}]}], "}"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.411780851970291*^9, 3.411780860567958*^9}, { 3.411780925898554*^9, 3.411780932658647*^9}, {3.411780997855345*^9, 3.4117810842880793`*^9}}], 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[{ RowBox[{ RowBox[{"plane3", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", RowBox[{"6", "-", "x"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "2"}], ",", "6"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Show", "[", RowBox[{"cyl", ",", "plane3", ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "3"}], ",", " ", "0"}], "}"}]}], ",", RowBox[{"BoxRatios", "->", RowBox[{"{", RowBox[{"1", ",", "1", ",", "2"}], "}"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.411780942723755*^9, 3.411780970801695*^9}, { 3.411781091055859*^9, 3.411781125127046*^9}}], Cell[TextData[{ "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, rotate the graph until it looks the same as the earlier picture.\n\nWe \ 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[ FormBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"x", "-", "2"}], ")"}], "2"], "+", SuperscriptBox["y", "2"]}], TraditionalForm]]], "\[LessEqual] 4, and the integrand should be the height of the plane." }], "Text", CellChangeTimes->{{3.411781153944827*^9, 3.411781202369331*^9}}] }, 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", BaseStyle->"Hyperlink", ButtonData:>"zerodeg"], " 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[{ RowBox[{ RowBox[{"plane4", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", RowBox[{"7", "-", RowBox[{"7", RowBox[{"x", "/", "3"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{"cyl", ",", "plane4", ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "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, CellChangeTimes->{{3.411781232622912*^9, 3.411781232623007*^9}}, 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[BoxData[ RowBox[{"tank", " ", "=", " ", RowBox[{"ContourPlot3D", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1", "/", "4"}], ")"}], "*", RowBox[{ RowBox[{"(", RowBox[{"x", "-", "4"}], ")"}], "^", "2"}]}], " ", "+", " ", RowBox[{"y", "^", "2"}]}], " ", "==", " ", "4"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", "0", ",", "8"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "2"}], ",", "2"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"z", ",", "0", ",", "10"}], "}"}], ",", RowBox[{"BoxRatios", "->", RowBox[{"{", RowBox[{"2", ",", "1", ",", "2.5"}], "}"}]}], ",", " ", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", " ", RowBox[{"Axes", "\[Rule]", "True"}], ",", RowBox[{"ContourStyle", "->", RowBox[{"Opacity", "[", "0.8", "]"}]}]}], "]"}]}]], "Input", CellChangeTimes->{{3.411781261883429*^9, 3.4117813264548798`*^9}}], Cell["\<\ We will continue to \"tip\" the tank towards the negative x direction. 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[{ RowBox[{ RowBox[{"plane5", "=", RowBox[{"ParametricPlot3D", "[", RowBox[{ RowBox[{"{", RowBox[{"x", ",", "y", ",", RowBox[{"7", "-", RowBox[{"7", RowBox[{"x", "/", "4"}]}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{"-", "3"}], ",", "3"}], "}"}]}], "]"}]}], ";"}], "\n", RowBox[{"Show", "[", RowBox[{"tank", ",", "plane5", ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "y", ",", "z"}], "}"}]}], ",", RowBox[{"ViewPoint", "->", RowBox[{"{", RowBox[{"0", ",", " ", RowBox[{"-", "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, CellChangeTimes->{{3.4117813393980017`*^9, 3.4117813393980627`*^9}}, Background->RGBColor[1, 0.501961, 0.501961]], Cell[CellGroupData[{ Cell["Credits", "Subsection", Background->None], Cell[TextData[{ "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. Minor updates in Spring 2008 for ", StyleBox["Mathematica", FontSlant->"Italic"], " 6.0.\n\nThis 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/\n\n\ 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", CellChangeTimes->{{3.411781356246193*^9, 3.4117813633888206`*^9}}] }, Closed]] }, Closed]] }, WindowSize->{906, 761}, WindowMargins->{{40, Automatic}, {Automatic, 0}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"Magnification"->1, "PaperOrientation"->"Portrait", "PaperSize"->{612, 792}, "PostScriptOutputFile":>FrontEnd`FileName[{"user002", "rogness"}, "Newlab.nb.ps", CharacterEncoding -> "iso8859-1"]}, FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (April 20, 2007)", 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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RGBColor[1, 0, 0]], Cell[ StyleData["Section", "Presentation"], CellMargins -> {{40, 10}, {11, 32}}, LineSpacing -> {1, 0}, FontSize -> 24], Cell[ StyleData["Section", "Condensed"], CellMargins -> {{18, Inherited}, {6, 12}}, 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, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFunction :> (FrontEndExecute[{ FrontEnd`NotebookLocate[#2]}]& ), ButtonNote -> ButtonData}], Cell[ StyleData["Hyperlink", "Presentation"], FontSize -> 16], Cell[ StyleData["Hyperlink", "Condensed"], FontSize -> 11], Cell[ StyleData["Hyperlink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, 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, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["MainBook", #]}]& )}], Cell[ StyleData["MainBookLink", "Presentation"], FontSize -> 16], Cell[ StyleData["MainBookLink", "Condensed"], FontSize -> 11], Cell[ StyleData["MainBookLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["AddOnsLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["AddOns", #]}]& )}], Cell[ StyleData["AddOnsLink", "Presentation"], FontSize -> 16], Cell[ StyleData["AddOnsLink", "Condensed"], FontSize -> 11], Cell[ StyleData["AddOnsLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["RefGuideLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontFamily -> "Courier", FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["RefGuide", #]}]& )}], Cell[ StyleData["RefGuideLink", "Presentation"], FontSize -> 16], Cell[ StyleData["RefGuideLink", "Condensed"], FontSize -> 11], Cell[ StyleData["RefGuideLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["GettingStartedLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["GettingStarted", #]}]& )}], Cell[ StyleData["GettingStartedLink", "Presentation"], FontSize -> 16], Cell[ StyleData["GettingStartedLink", "Condensed"], FontSize -> 11], Cell[ StyleData["GettingStartedLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, Closed]], Cell[ CellGroupData[{ Cell[ StyleData["OtherInformationLink"], StyleMenuListing -> None, ButtonStyleMenuListing -> Automatic, FontVariations -> {"Underline" -> True}, FontColor -> RGBColor[0, 0, 1], ButtonBoxOptions -> { Active -> True, ButtonFrame -> "None", ButtonFunction :> (FrontEndExecute[{ FrontEnd`HelpBrowserLookup["OtherInformation", #]}]& )}], Cell[ StyleData["OtherInformationLink", "Presentation"], FontSize -> 16], Cell[ StyleData["OtherInformationLink", "Condensed"], FontSize -> 11], Cell[ StyleData["OtherInformationLink", "Printout"], FontSize -> 10, FontVariations -> {"Underline" -> False}, FontColor -> GrayLevel[0]]}, 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. This is particularly true of Input and Output.", "Text"], Cell[ StyleData["CellExpression"], PageWidth -> Infinity, CellMargins -> {{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel -> False, ShowSpecialCharacters -> False, AllowInlineCells -> False, Hyphenation -> False, AutoItalicWords -> {}, StyleMenuListing -> None, FontFamily -> "Courier", FontSize -> 12, Background -> GrayLevel[1]], Cell[ StyleData["InputForm"], InputAutoReplacements -> {}, AllowInlineCells -> False, Hyphenation -> False, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["OutputForm"], PageWidth -> Infinity, TextAlignment -> Left, LineSpacing -> {0.6, 1}, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["StandardForm"], InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", Inherited}, LineSpacing -> {1.25, 0}, StyleMenuListing -> None, FontFamily -> "Courier"], Cell[ StyleData["TraditionalForm"], InputAutoReplacements -> { "->" -> "\[Rule]", ":>" -> "\[RuleDelayed]", "<=" -> "\[LessEqual]", ">=" -> "\[GreaterEqual]", "!=" -> "\[NotEqual]", "==" -> "\[Equal]", Inherited}, LineSpacing -> {1.25, 0}, SingleLetterItalics -> True, TraditionalFunctionNotation -> True, DelimiterMatching -> None, StyleMenuListing -> None], Cell[ "The style defined below is mixed in to any cell that is in an \ inline cell within another.", "Text"], Cell[ StyleData["InlineCell"], TextAlignment -> Left, ScriptLevel -> 1, StyleMenuListing -> None], Cell[ StyleData["InlineCellEditing"], StyleMenuListing -> None, Background -> RGBColor[1, 0.749996, 0.8]]}, Closed]], Cell[ CellGroupData[{ Cell["Automatic Styles", "Section"], Cell[ "The cells below define styles that are used to affect the display \ of certain types of objects in typeset expressions. For example, \ \"UnmatchedBracket\" style defines how unmatched bracket, curly bracket, and \ parenthesis characters are displayed (typically by coloring them to make them \ stand out).", "Text"], Cell[ StyleData["UnmatchedBracket"], StyleMenuListing -> None, FontColor -> RGBColor[0.760006, 0.330007, 0.8]]}, Closed]]}, Open]]}, Visible -> False, FrontEndVersion -> "6.0 for Mac OS X x86 (32-bit) (April 20, 2007)", StyleDefinitions -> "Default.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "zerodeg"->{ Cell[2652, 83, 583, 18, 40, "Input", CellTags->"zerodeg"]} } *) (*CellTagsIndex CellTagsIndex->{ {"zerodeg", 62238, 1408} } *) (*NotebookFileOutline Notebook[{ Cell[568, 21, 375, 10, 99, "Text"], Cell[CellGroupData[{ Cell[968, 35, 65, 2, 46, "Section"], Cell[1036, 39, 685, 14, 71, "Text"], Cell[1724, 55, 800, 21, 50, "Input"], Cell[2527, 78, 122, 3, 26, "Text"], Cell[2652, 83, 583, 18, 40, "Input", CellTags->"zerodeg"], Cell[3238, 103, 201, 7, 29, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[3476, 115, 82, 2, 26, "Section"], Cell[3561, 119, 244, 4, 41, "Text"], Cell[3808, 125, 2409, 73, 85, "Input"], Cell[6220, 200, 184, 4, 26, "Text"], Cell[6407, 206, 336, 7, 41, "Text"], Cell[6746, 215, 971, 28, 40, "Input"], Cell[7720, 245, 937, 18, 134, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[8694, 268, 81, 3, 26, "Section"], Cell[8778, 273, 3797, 79, 370, "Text"], Cell[12578, 354, 45, 0, 40, "Input"], Cell[12626, 356, 465, 7, 56, "Text"], Cell[13094, 365, 1069, 29, 40, "Input"], Cell[14166, 396, 248, 4, 41, "Text"], Cell[14417, 402, 3763, 75, 385, "Text"], Cell[CellGroupData[{ Cell[18205, 481, 48, 1, 42, "Subsection"], Cell[18256, 484, 1237, 19, 161, "Text"] }, Closed]] }, Closed]] } ] *) (* End of internal cache information *)