(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 20391, 671]*) (*NotebookOutlinePosition[ 21612, 709]*) (* CellTagsIndexPosition[ 21568, 705]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ " You Try ", StyleBox["Mathematica", FontSlant->"Italic"], " " }], "Title", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ " ", StyleBox[" C.T.J. Dodson\n Department of \ Mathematics, UMIST\n \ dodson@umist.ac.uk", FontSize->10] }], "Subtitle", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], Cell[TextData[StyleBox[ "Double click on the vertical check mark at the side of a cell to open or \ close each Section", FontSize->12]], "Text", FontSize->16, FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], Cell[CellGroupData[{ Cell["Introduction", "Section", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "This document is a ", StyleBox["Mathematica", FontSlant->"Italic"], " Notebook which is also available (among many others) for downloading \n\ using a web browser (say to your floppy disk drive A) from the location\n", StyleBox["http://www.ma.umist.ac.uk/kd/mmaprogs/TRYMMA.nb \n", FontWeight->"Bold"], "You might look also at the general information file \n", StyleBox["http://www.ma.umist.ac.uk/kd/mmaprogs/AREADMEFILE", FontWeight->"Bold"] }], "Text"], Cell[TextData[{ " To use this Notebook, launch ", StyleBox["Mathematica", FontSlant->"Italic"], " by double clicking its icon, then from the menu bar select `File' \ then `Open' and select the Notebook from where you saved it. ", StyleBox[" ", FontWeight->"Bold", FontSlant->"Italic"], "That procedure should open the Notebook and allow you to type into it. \ Once the Notebook is open, you can activate any of the input lines already \ there by typing together the keys . Try altering some of the \ obvious mathematical entries. \n\nNote that the whole ", StyleBox["Mathematica", FontSlant->"Italic"], " manual is on-line via `Help' and its index will guide you to a \ particular operation, then give you an example that you can cut and paste. \ Greek letters and mathematical symbols are available via the menu under \ `File' `Palettes'. To help format for printing, set to A4 paper, switch on \ Show Rule, Show Page Breaks, and set to Word Wrapping at Paper Width. Note \ that A4 paper is approximately 8.25 inches wide (", StyleBox["Mathematica", FontSlant->"Italic"], " is an American package and the ruler is in inches!) and your left hand \ margin will have been allowed for. A 10pt font is usually convenient for \ general text; you can cut and paste from this Notebook to edit in a new \ Notebook, selecting examples of section headings etc.\n\n" }], "Text", FontWeight->"Plain"] }, Open ]], Cell[CellGroupData[{ Cell["Doing Mathematics", "Section", FontColor->RGBColor[0, 0, 1]], Cell["\<\ We give example input lines for a number of common operations: using built in standard functions; defining new functions; solving equations; differentiation; integration; plotting; animation. \ \>", "Text"], Cell[CellGroupData[{ Cell["Basic operations", "Subsection", FontColor->RGBColor[0, 0, 1]], Cell["To activate an input use :", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[\((x - a)\)\^3]\)], "Input"], Cell[BoxData[ \(\(-a\^3\) + 3\ a\^2\ x - 3\ a\ x\^2 + x\^3\)], "Output"] }, Open ]], Cell["\<\ This is how we define a new function f in terms of standard operations and \ built in functions; note that we give a rule for the representative input \ symbol, x and to activate an input use :\ \>", "Text"], Cell[BoxData[ \(h[x_] := Cos[x] Sinh[x]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(h[2]\)], "Input"], Cell[BoxData[ \(Cos[2]\ Sinh[2]\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " leaves output in analytic form; to get numerical values end with // N" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(h[2] // N\)], "Input"], Cell[BoxData[ \(\(-1.50930648532361555`\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(h[a]\)], "Input"], Cell[BoxData[ \(Cos[a]\ Sinh[a]\)], "Output"] }, Open ]], Cell["\<\ Here's a simple plot; you can resize it by clicking and dragging. The \ semicolon at the end of the command just stops the output numbering (try \ omitting it):\ \>", "Text"], Cell[BoxData[ \(\(Plot[h[x], \ {x, \(-2\), 2}];\)\)], "Input"], Cell[TextData[{ "\n", StyleBox["You can click on a plot and drag the corner to enlarge it.", FontColor->RGBColor[0, 0, 1]], "\nPlot commands have many options, to change format, line thickness, \ colour etc. You can try some of these from the listing:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[Plot]\)], "Input"], Cell[BoxData[ \({AspectRatio \[Rule] 1\/GoldenRatio, Axes \[Rule] Automatic, AxesLabel \[Rule] None, AxesOrigin \[Rule] Automatic, AxesStyle \[Rule] Automatic, Background \[Rule] Automatic, ColorOutput \[Rule] Automatic, Compiled \[Rule] True, DefaultColor \[Rule] Automatic, Epilog \[Rule] {}, Frame \[Rule] False, FrameLabel \[Rule] None, FrameStyle \[Rule] Automatic, FrameTicks \[Rule] Automatic, GridLines \[Rule] None, ImageSize \[Rule] Automatic, MaxBend \[Rule] 10.`, PlotDivision \[Rule] 30.`, PlotLabel \[Rule] None, PlotPoints \[Rule] 25, PlotRange \[Rule] Automatic, PlotRegion \[Rule] Automatic, PlotStyle \[Rule] Automatic, Prolog \[Rule] {}, RotateLabel \[Rule] True, Ticks \[Rule] Automatic, DefaultFont \[RuleDelayed] $DefaultFont, DisplayFunction \[RuleDelayed] $DisplayFunction, FormatType \[RuleDelayed] $FormatType, TextStyle \[RuleDelayed] $TextStyle}\)], "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Basic calculus", "Subsection", FontColor->RGBColor[0, 0, 1]], Cell[BoxData[ \(f[x_] := Cos[x] Sinh[x]\)], "Input"], Cell["First derivative of f with respect to x:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_x\ f[x]\)], "Input"], Cell[BoxData[ \(Cos[x]\ Cosh[x] - Sin[x]\ Sinh[x]\)], "Output"] }, Open ]], Cell["Indefinite integral of that output recovers f:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\((Cos[x]\ Cosh[x] - Sin[x]\ Sinh[x])\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(Cos[x]\ Sinh[x]\)], "Output"] }, Open ]], Cell["Second derivative of f with respect to x:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_\(x, x\)f[x]\)], "Input"], Cell[BoxData[ \(\(-2\)\ Cosh[x]\ Sin[x]\)], "Output"] }, Open ]], Cell["Definite integrals:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_a\%b\((Cos[x]\ Cosh[x] - Sin[x]\ Sinh[x])\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(\(-Cos[a]\)\ Sinh[a] + Cos[b]\ Sinh[b]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%1\( \[ExponentialE]\^\(-x\^2\)\) \[DifferentialD]x // N\)], "Input"], Cell[BoxData[ \(0.746824132812427`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%a\((\[Integral]\_0\%b\((\((x\^3 - 3 x\ y\^2)\) - 1)\) \[DifferentialD]y)\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(1\/4\ a\ b\ \((\(-4\) + a\^3 - 2\ a\ b\^2)\)\)], "Output"] }, Open ]], Cell["Here are a few more examples:", "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Det", "[", RowBox[{"(", GridBox[{ {"0", \(-1\)}, {"1", "0"} }], ")"}], "]"}]], "Input"], Cell[BoxData[ \(1\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[Sum]\+\(n = 0\)\%10 1\/2\^n\)], "Input"], Cell[BoxData[ \(2047\/1024\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[PartialD]\_x\ \((x^3 - 3 x\ y^2)\)\)], "Input"], Cell[BoxData[ \(3\ x\^2 - 3\ y\^2\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Plots of functions of several variables", "Subsection", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "We can plot functions of two variables as a surface in 3-space; note that \ ", StyleBox["Mathematica", FontSlant->"Italic"], " interprets a space between symbols as a multiplication (if we change x y \ to xy then ", StyleBox["Mathematica", FontSlant->"Italic"], " thinks that xy is a new symbol; x*y also represents the product):" }], "Text"], Cell[BoxData[ \(\(Plot3D[Sin[x\ y], \ {x, 0, Pi}, {y, 0, Pi}];\)\)], "Input"], Cell[BoxData[ \(Options[Plot3D]\)], "Input"], Cell["\<\ We can define functions of several variables; here is a function defining the \ monkey saddle surface in 3-space parametrically, note that we can give the \ function any name:\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Cups, Caps, Saddles", "Subsection"], Cell[BoxData[{ \(cup[u_, v_] := {u, v, u\^2 + v\^2}\), "\[IndentingNewLine]", \(cap[u_, v_] := {u, v, \(-u\^2\) - v\^2}\), "\n", \(sad[u_, v_] := {u, v, u\^2 - v\^2}\)}], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ cup[u, v] // Evaluate, {u, \(-1\), 1}, \ {v, \(-1\), 1}];\)\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ cap[u, v] // Evaluate, {u, \(-1\), 1}, \ {v, \(-1\), 1}];\)\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ sad[u, v] // Evaluate, {u, \(-1\), 1}, \ {v, \(-1\), 1}];\)\)], "Input"], Cell[BoxData[ \(monk[x_, y_] := {x, y, x\^3 - 3 x\ y\^2}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ monk[x, y] // Evaluate, \ \n\t{x, \(-1\), 1}, \ {y, \(-1\), 1}];\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[ParametricPlot3D]\)], "Input"], Cell[BoxData[ \({AmbientLight \[Rule] GrayLevel[0.`], AspectRatio \[Rule] Automatic, Axes \[Rule] True, AxesEdge \[Rule] Automatic, AxesLabel \[Rule] None, AxesStyle \[Rule] Automatic, Background \[Rule] Automatic, Boxed \[Rule] True, BoxRatios \[Rule] Automatic, BoxStyle \[Rule] Automatic, ColorOutput \[Rule] Automatic, Compiled \[Rule] True, DefaultColor \[Rule] Automatic, Epilog \[Rule] {}, FaceGrids \[Rule] None, ImageSize \[Rule] Automatic, Lighting \[Rule] True, LightSources \[Rule] {{{1.`, 0.`, 1.`}, RGBColor[1, 0, 0]}, {{1.`, 1.`, 1.`}, RGBColor[0, 1, 0]}, {{0.`, 1.`, 1.`}, RGBColor[0, 0, 1]}}, Plot3Matrix \[Rule] Automatic, PlotLabel \[Rule] None, PlotPoints \[Rule] Automatic, PlotRange \[Rule] Automatic, PlotRegion \[Rule] Automatic, PolygonIntersections \[Rule] True, Prolog \[Rule] {}, RenderAll \[Rule] True, Shading \[Rule] True, SphericalRegion \[Rule] False, Ticks \[Rule] Automatic, ViewCenter \[Rule] Automatic, ViewPoint \[Rule] {1.30000000000000004`, \(-2.39999999999999991`\), 2.`}, ViewVertical \[Rule] {0.`, 0.`, 1.`}, DefaultFont \[RuleDelayed] $DefaultFont, DisplayFunction \[RuleDelayed] $DisplayFunction, FormatType \[RuleDelayed] $FormatType, TextStyle \[RuleDelayed] $TextStyle}\)], "Output"] }, Closed]], Cell["\<\ We can integrate the height function of a surface to find the volume above a \ given level over a given rectangle, here is the volume under the cap over the \ rectangle 0\[LessEqual]x\[LessEqual]a by 0\[LessEqual]b\[LessEqual]a :\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\[Integral]\_0\%a\((\[Integral]\_0\%b\((x\^2 + y\^2)\) \[DifferentialD]y\ )\) \[DifferentialD]x\)], "Input"], Cell[BoxData[ \(1\/3\ a\ b\ \((a\^2 + b\^2)\)\)], "Output"] }, Open ]], Cell[BoxData[ \(\(torus[a_, b_]\)[u_, v_] := {Cos[u]\ \((a + b\ Cos[v])\), \((a + b\ Cos[v])\)\ Sin[u], b\ Sin[v]}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[\(torus[3, 1]\)[u, v] // Evaluate, {u, 0, 2 \[Pi]}, {v, 0, 2 \[Pi]}];\)\)], "Input"], Cell[BoxData[ \(helicoid[u_, v_] := {u\ Cos[v], u\ Sin[v], v}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ helicoid[u, v] // Evaluate, {u, \(-1\), 1}, {v, 0, 2 \[Pi]}];\)\)], "Input"], Cell[BoxData[ \(\(catenoid[a_]\)[u_, v_] := {a\ Cos[u]\ Cosh[v\/a], a\ Cosh[v\/a]\ Sin[u], v}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[\(catenoid[1]\)[u, v] // Evaluate, {u, \(-\[Pi]\), \[Pi]}, {v, \(-1\), 1}];\)\)], "Input"], Cell[BoxData[ \(\(moebiusstrip[a_]\)[u_, v_] := {a\ \((Cos[u] + v\ Cos[u\/2]\ Cos[u])\), a\ \((Sin[u] + v\ Cos[u\/2]\ Sin[u])\), a\ v\ Sin[u\/2]}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[ Append[\(moebiusstrip[4]\)[u, v], \n\t\tFaceForm[RGBColor[1, 1, 0], RGBColor[1, 0, 1]]] // Evaluate, \ \n\t{u, 0, 2 Pi}, \ {v, \(- .3\), .3}, Axes -> None, \ Lighting -> False, \ \n\tPlotPoints -> 20\ , \ Boxed -> False];\)\)], "Input"], Cell[BoxData[ \(\(ellipsoid[a_, b_, c_]\)[u_, v_] := {a\ Cos[u]\ Cos[v], b\ Cos[v]\ Sin[u], c\ Sin[v]}\)], "Input"], Cell[BoxData[ \(\(ParametricPlot3D[\(ellipsoid[3, 2, 1]\)[u, v] // Evaluate, \ \n\t{u, 0, 2 Pi}, \ {v, 0, 2 Pi}, Axes -> None, \ \n\t PlotPoints -> 20\ , \ Boxed -> False];\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Animation ", "Subsection", FontColor->RGBColor[0, 0, 1]], Cell["\<\ The quickest way to create an animated graphic is simply to incorporate a \ parameter, t, say, in a plot then step through a sequence of values of t. \ Next select the cell containing all of the sequence of output graphics, \ double click to hide all except the first one; finally, select from the menu \ bar `Cell' followed by `Animate Selected Graphics' The control bar at bottom left during an animation allows you to speed up, \ slow down, stop or cycle.This illustrates the method:\ \>", "Text"], Cell[BoxData[ \(Do[Plot[ t\ Sin[x], {x, \(-Pi\), Pi}, \ \n\t\tPlotRange -> {\(-1\), 1}], \ {t, 0, 1, 0.2}]\)], "Input"], Cell["\<\ Note that to make the animation look correct, we set the y-axis PlotRange \ inside the basic Plot to ensure that it is the same for all of the graphs in \ the sequence.You can try similar animations for Plot3D and ParametricPlot.\ \>", "Text"], Cell[BoxData[ \(Do[\[IndentingNewLine]Plot3D[ t\ Sin[x\ y], \ {x, \(-Pi\), Pi}, {y, \(-Pi\), Pi}, PlotPoints \[Rule] 50\ , Mesh \[Rule] False, Axes \[Rule] False, Boxed \[Rule] False, \n\t\tPlotRange -> {\(-1\), 1}], \ {t, 0, 1, 0.2}]\)], "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Embedding of Klein Bottle\n", StyleBox["UMIST Mathematics Department Mural on N Floor", FontSize->18] }], "Section"], Cell["\<\ The parametric equations below give an embedding of the Klein bottle \ (originally called a Kleinsche Fl\[ADoubleDot]che [ie surface]in German but \ mistranslated into English as Kleinsche Flasche [ie flask or bottle]).The \ Klein bottle could be made by this procedure:glue two tori (tyre tubes) \ together one above the other cut through both perpendicularly to the circle \ of contact twist one side of the cut through 180 degrees and rejoin. You can change the colour of the plot using the RGBColor controls in the \ plotting command. You can change also how much of the surface you plot by \ altering the argument of kkk from 2 Pi to some fraction thereof. \ \>", "Text"], Cell[TextData[{ StyleBox["k1=(2+Cos[u/2]Sin[t]-Sin[u/2]Sin[2t])Cos[u];\n\ k2=(2+Cos[u/2]Sin[t]-Sin[u/2]Sin[2t])Sin[u]; \n\ k3=Sin[u/2]Sin[t]+Cos[u/2]Sin[2t];\n\n\ kkk[z_]:=ParametricPlot3D[{k1,k2,k3},{t,0,2Pi},{u,0,z},\nBoxed->False, \ Axes->None, PlotPoints->{40,70},\n", AspectRatioFixed->True, FontFamily->"Courier-Bold"], "LightSources\[Rule]{{{1.3,-2.4,2.},RGBColor[0.9,1,0]},{{2.7,0.,2.},\n \ RGBColor[0,1,.1]},{{-5.3,-1.4,2.},RGBColor[0,1,0]}}", StyleBox["]\n", AspectRatioFixed->True, FontFamily->"Courier-Bold"] }], "Input", AspectRatioFixed->True], Cell[TextData[StyleBox["kkk[2 Pi];", FontSize->12]], "Input", AspectRatioFixed->True, FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell["Special functions", "Section", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ "You can find special functions through the `Help' index, via `The ", StyleBox["Mathematica", FontSlant->"Italic"], " Book' `Built in Functions' then `Mathematical Functions' and via \ `Advanced Mathematics' Mathematical Functions' `Special Functions'. Here are \ some examples using these.Note that a ? before a name will give information \ on the function." }], "Text"], Cell[BoxData[ \(\(Plot[LegendreP[8, \ x], \ {x, \ \(-1\), \ 1}];\)\)], "Input"], Cell[BoxData[ \(\(Plot[\((HermiteH[4, \ x]\ Exp[\(-x^2\)/2])\)^2, \ {x, \ \(-4\), \ 4}];\)\)], "Input"], Cell[BoxData[ \(FindRoot[\ BesselJ[0, \ x] == \ 0, \ {x, \ 1}\ ]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(D[Gamma[x], \ x]\)], "Input"], Cell[BoxData[ \(Gamma[x]\ PolyGamma[0, x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?PolyGamma\)\)], "Input"], Cell[BoxData[ \("PolyGamma[z] gives the digamma function psi(z). \n\tPolyGamma[n, z] \ gives the nth derivative of \n\tthe digamma function."\)], "Print", GeneratedCell->False, CellAutoOverwrite->False] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Local Resources", "Section", FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ StyleBox["You can find a number of ", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0]], StyleBox["Mathematica", FontSize->12, FontWeight->"Bold", FontSlant->"Italic", FontColor->GrayLevel[0]], StyleBox[" resources \non the UMIST mathematics server. For example:\n\n\ http://www.ma.umist.ac.uk/kd/mmaprogs/AREADMEFILE \n(Annotated list and \ guide)\n\nhttp://www.ma.umist.ac.uk/kd/ode/ode.htm \n\ (Ordinary differential equations)\n\n\ http://www.ma.umist.ac.uk/kd/stmath/stmath.html \n(University \ calculus)\n\nhttp://www.ma.umist.ac.uk/kd/ednet/maths/readme.html \n (High \ school mathematics)", FontSize->12, FontWeight->"Bold", FontColor->GrayLevel[0]], StyleBox["\n", FontSize->12, FontColor->GrayLevel[0]] }], "Text", FontColor->RGBColor[0, 0, 1]] }, Closed]] }, Open ]] }, FrontEndVersion->"5.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 685}}, WindowToolbars->"RulerBar", WindowSize->{647, 537}, WindowMargins->{{Automatic, 92}, {Automatic, 32}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PrintingOptions->{"PaperSize"->{597.563, 842.375}, "PaperOrientation"->"Portrait", "Magnification"->1}, PrivateFontOptions->{"FontType"->"Outline"} ] (******************************************************************* Cached data follows. 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(******************************************************************* End of Mathematica Notebook file. *******************************************************************)