(************** 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). 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[ 20382, 632]*) (*NotebookOutlinePosition[ 29801, 860]*) (* CellTagsIndexPosition[ 27743, 816]*) (*WindowFrame->Normal*) Notebook[{ Cell["Graphics and Plotting", "Title"], Cell["\<\ Mathematica has a large number of built-in graphics programs for \ plotting and exploring mathematics graphically and for plotting and \ visualizing data. Graphs and plots are effective ways of conveying complex \ information. It is important to learn how to create and manipulate plots and \ graphics. Mathematica is very rich in its graphical functions\[LongDash]we \ will explore just a small subset of all its capabilities. We can get an idea \ of how many plotting routines are available byusing a wildcard:\ \>", "Text"], Cell[BoxData[ \(\(?*Plot*\)\)], "Input"], Cell["\<\ This is much less than are available in the standard packages; \ these will be discussed later, but here's what becomes available after \ loading the Graphics Packages:\ \>", "Text"], Cell[BoxData[ \(<< Graphics`\)], "Input", CellTags->"mmtag:05:Graphics_package"], Cell[TextData[{ "While Mathematica has a large number of plotting routines, no one program \ does everything we need. It can be useful to export numbers and graphics \ from Mathematica and operate on them individually or with other specialized \ programs. The number of different creative graphical solutions available \ grows geometrically with the number of different graphical tools that are \ mastered.\nHere, we will just produce a number of examples of plots and \ graphics... (Note, I use a file \"init.m\" to set some options. Your plots \ may look different from what we see in lecture. If you want to use my init.m \ you can download it from ", ButtonBox["here", ButtonData:>{ URL[ "http://pruffle.mit.edu/3.016/init.m"], None}, ButtonStyle->"Hyperlink"], ". Where to locate your init.m file depends on the operating system you are \ using, check out init.m in the Master Index in the Help Browser." }], "Text", CellTags->"mmtag:05:init.m__example_of_using_to_change_default_graphics"], Cell[CellGroupData[{ Cell["Two-Dimensional Graphics", "Subtitle"], Cell["Plot, ParametricPlot, LogPlot, etc", "Subsection"], Cell[BoxData[ \(Plot[Sin[x]/x, {x, \(-5\)\ Pi, 5 Pi}]\)], "Input", CellTags->{"mmtag:05:Plot[]", "mmtag:05:Plot__examples_with_options"}], Cell[BoxData[ \(Options[Plot]\)], "Input"], Cell[BoxData[ \(Plot[Sin[x]/x, {x, \(-5\) Pi, 5 Pi}, PlotRange \[Rule] {\(-0.25\), 1.25}]\)], "Input"], Cell[BoxData[ \(Plot[Sin[x]/x, {x, \(-5\) Pi, 5 Pi}, PlotRange \[Rule] {\(-0.25\), 1.25}, AxesLabel \[Rule] {"\", \*"\"\<\!\(\(Sin \((x)\)\)\/x\)\>\""}]\)], \ "Input", CellTags->"mmtag:05:labels_on_plots"], Cell[BoxData[ \(Plot[{Sin[x]/x, Tan[x]/x}, {x, \(-5\) Pi, 5 Pi}, PlotRange \[Rule] {\(-0.25\), 1.25}]\)], "Input"], Cell[BoxData[ \(Plot[{Sin[x]/x, Tan[x]/x}, {x, \(-5\) Pi, 5 Pi}, PlotRange \[Rule] {\(-0.25\), 1.25}, \[IndentingNewLine]PlotStyle \[Rule] {{Thickness[0.01], Hue[1]}, {Thickness[0.005], Hue[2/3]}}]\)], "Input"], Cell[CellGroupData[{ Cell[TextData[{ "ParametricPlot produces a 2-D graph as a function of a single parameter, \ e.g. ", StyleBox["t", FontSlant->"Italic"], ". The cartesian coordinates, e.g. ", StyleBox["x", FontSlant->"Italic"], " and ", StyleBox["y", FontSlant->"Italic"], ", are specified as functions ", StyleBox["x", FontSlant->"Italic"], "(", StyleBox["t", FontSlant->"Italic"], ") and ", StyleBox["y", FontSlant->"Italic"], "(", StyleBox["t", FontSlant->"Italic"], "). Thus, a continuous variation of the single parameter ", StyleBox["t", FontSlant->"Italic"], " will trace out a trajectory in the ", StyleBox["x-y\:02c6plane.", FontSlant->"Italic"] }], "Subsubsection"], Cell[BoxData[ \(\(?ParametricPlot\)\)], "Input", CellTags->{ "mmtag:05:parametric_plots", "mmtag:05:plots__2D parametric_example"}], Cell[BoxData[ \(LuckyClover[t_\ \ , \ n_]\ := \ \((1/\((n + 1)\))\) {Cos[\((n + 1)\)\ t\ - \ Pi/4]\ - \ \((n + 1)\)\ Cos[t\ - \ Pi/4], \ Sin[\((n + 1)\)\ t\ - \ Pi/4]\ - \ \((n + 1)\) Sin[t\ - \ Pi/4]}\)], "Input"], Cell[BoxData[ \(ParametricPlot[LuckyClover[t, 4], {t, 0, \ 2\ Pi}]\)], "Input", CellTags->"mmtag:05:ParametricPlot[]"], Cell[BoxData[ \(ParametricPlot[LuckyClover[t, 4], {t, 0, \ 2\ Pi}, \ AspectRatio \[Rule] 1]\)], "Input", CellTags->"mmtag:05:plots__2D parametric_example_of_superposed"] }, Open ]], Cell[CellGroupData[{ Cell["\<\ The next statement attempts to use the Table function to produce a \ list of six LuckyClover functions and then make one parametric plot of all of \ them.\ \>", "Subsubsection"], Cell["\<\ It is necessary to use the Evaluate command to get this to \ work.\ \>", "Text", CellTags->{ "mmtag:05:Evaluate[]_and_Plot[]", "mmtag:05:plot_does_not_appear__Evaluate[]"}], Cell[BoxData[ \(\(?Evaluate\)\)], "Input"], Cell[BoxData[ \(ParametricPlot[ Evaluate[Table[LuckyClover[t, i], {i, 2, 7}]], {t, 0, \ 2\ Pi}, \ AspectRatio \[Rule] 1]\)], "Input"], Cell[BoxData[ \(ParametricPlot[ Evaluate[Table[LuckyClover[t, i], {i, 2, 7}]], {t, 0, \ 2\ Pi}, \ AspectRatio \[Rule] 1, PlotStyle \[Rule] Table[{Thickness[0.005], Hue[\((2/3)\)*\((i - 2)\)/5]}, {i, 2, 7}]]\)], "Input", CellTags->{ "mmtag:05:colors__examples_in_plotting", "mmtag:05:Hue[]__use_in_graphics"}],\ Cell[BoxData[ \(<< Miscellaneous`PhysicalConstants`\)], "Input", CellTags->{ "mmtag:05:physical_constants_package", "mmtag:05:packages__PhysicalConstants"}], Cell[BoxData[{ \(BoltzmannConstant\), "\[IndentingNewLine]", \(ElectronCharge\), "\[IndentingNewLine]", \(SpeedOfLight\)}], "Input"], Cell[BoxData[ \(Kelvin[TempCelcius_\ ]\ := \ 273.15\ + \ TempCelcius\)], "Input"], Cell[BoxData[ \(Arrhenius[EnergyEV_, \ TempCelcius_\ ]\ := \ Exp[\(-\((EnergyEV*Joule*ElectronCharge)\)\)/\((Kelvin[TempCelcius]* BoltzmannConstant*Kelvin*Coulomb)\)]\)], "Input", CellTags->"mmtag:05:Arrhenius_function"], Cell[BoxData[ \(Arrhenius[e, t]\)], "Input"], Cell[BoxData[ \(ParametricPlot[{1/Kelvin[T], Log[Arrhenius[1.0, T]]}, {T, 0, 1000}]\)], "Input", CellTags->"mmtag:05:Arrhenius_plot_example"], Cell[BoxData[ \(arrhenplot\ = ParametricPlot[ Evaluate[ Table[{1/Kelvin[T], Log[Arrhenius[ev, T]]}, {ev, 1, 5, 1}]], {T, \(-200\), 1000}, PlotStyle \[Rule] Table[{Thickness[0.005], Hue[\((2/3)\)*\((5 - i)\)/4]}, {i, 1, 5, 1}]]\)], "Input"], Cell[BoxData[ \(Show[arrhenplot, Ticks \[Rule] {Table[{1/Kelvin[T], StringJoin["\<1/\>", ToString[T]]}, {T, \(-200\), 500, 100\[IndentingNewLine]}], Automatic}]\)], "Input"], Cell[BoxData[ \(BankAccount[InitialInvestment_\ , \ AnnualInterest_, \ NYears_\ ]\ := \ InitialInvestment*\((1\ + \ AnnualInterest/100)\)^NYears\)], "Input"], Cell[BoxData[ \(Plot[BankAccount[100, 8.5, t], {t, 0, 50}]\)], "Input"], Cell[BoxData[ \(Needs["\"]\)], "Input"], Cell[BoxData[ \(LogPlot[BankAccount[100, 8.5, t], {t, 0, 50}]\)], "Input", CellTags->"mmtag:05:LogPlot[]"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Plotting Data", "Subtitle"], Cell[CellGroupData[{ Cell["ListPlot, PieChart, Histogram, Barchart, etc", "Subsection"], Cell[BoxData[ \(<< Miscellaneous`ChemicalElements`\)], "Input", CellTags->{ "mmtag:05:chemical_elements_package", "mmtag:05:packages__ChemicalElements"} ], Cell[BoxData[ \(Elements\)], "Input"], Cell[BoxData[ \(e190\ = \ Elements[\([Table[i, {i, 1, 90}]]\)]\)], "Input"], Cell[BoxData[ \(mps\ = \ Map[MeltingPoint[#] &, e190] /. Kelvin \[Rule] 1\)], "Input"], Cell["\<\ The next plot illustrates the variation of melting temperature as a \ function of atomic number\[Ellipsis]\ \>", "Text"], Cell[BoxData[ \(ListPlot[mps]\)], "Input"], Cell[BoxData[ \(ListPlot[mps, PlotJoined \[Rule] True]\)], "Input"], Cell[BoxData[ \(Dens\ = \ Map[Density[#] &, e190] /. {Kilogram \[Rule] 1, \ Meter \[Rule] 1}\)], "Input", CellTags->"mmtag:05:Map[]_example"], Cell["\<\ The next line matches up values of density with melting temperature\ \[Ellipsis]\ \>", "Text"], Cell[BoxData[ \(dmdata\ = \ Transpose[{Dens, mps}]\)], "Input"], Cell[BoxData[ \(ListPlot[dmdata]\)], "Input", CellTags->"mmtag:05:ListPlot[]_example_with_chemical_elements"], Cell[BoxData[ \(ListPlot[dmdata, PlotJoined \[Rule] True]\)], "Input"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Three-Dimensional Graphics", "Subtitle"], Cell[CellGroupData[{ Cell["Plot3D, ContourPlot, DensityPlot, etc", "Subsection"], Cell[BoxData[ \(EPot[x_, \ y_\ , \ z_\ , \ xo_\ , \ yo_]\ := \ 1\/\@\(\((x - xo)\)^2\ + \ \((y - yo)\)^2\ + \ z^2\)\)], "Input", CellTags->"mmtag:05:electical_potential_above_lattice_of_charges"], Cell[BoxData[ \(SheetOLatticeCharge[x_, \ y_\ , \ z_]\ := \ Sum[EPot[x, y, z, xo, yo], {xo, \(-5\), 5}, {yo, \(-5\), 5}]\)], "Input"], Cell[TextData[{ StyleBox["SheetOLatticeCharge", FontWeight->"Bold"], " represents the electric field produced by an 11 by 11 array of point \ charges arranged on the ", StyleBox["x-y", FontSlant->"Italic"], " plane at ", StyleBox["z", FontSlant->"Italic"], " = 0. The following command evaluates and plots the field variation in the \ plane ", StyleBox["z", FontSlant->"Italic"], " = 0.25:" }], "Text"], Cell[BoxData[ \(Plot3D[ Evaluate[SheetOLatticeCharge[x, y, 0.25]], {x, \(-6\), 6}, {y, \(-6\), 6}]\)], "Input", CellTags->{ "mmtag:05:Graphics__example_of_electical_potential_above_lattice_of_\ charges", "mmtag:05:Plot3D[]"}], Cell[TextData[{ "Note below how ", StyleBox["theplot", FontWeight->"Bold"], " is set to contain the output of the Plot3D command." }], "Text"], Cell[BoxData[ \(theplot\ = Plot3D[Evaluate[SheetOLatticeCharge[x, y, 0.25]], {x, \(-6\), 6}, {y, \(-6\), 6}, PlotPoints \[Rule] 120]\)], "Input"], Cell[TextData[{ "Now we can adjust the viewpoint of ", StyleBox["theplot", FontWeight->"Bold"], ", without recalculating the entire plot, using the ", StyleBox["Show", FontWeight->"Bold"], " command:" }], "Text"], Cell[BoxData[ \(\(?Show\)\)], "Input"], Cell[BoxData[ \(\(?Show\)\)], "Input"], Cell[BoxData[ \(Show[theplot, ViewPoint \[Rule] {0, \(-5\), 2}]\)], "Input"], Cell[BoxData[ \(theconplot\ = ContourPlot[ Evaluate[SheetOLatticeCharge[x, y, 0.25]], {x, \(-6\), 6}, {y, \(-6\), 6}, PlotPoints \[Rule] 120]\)], "Input"], Cell[BoxData[ \(theconplot\ = ContourPlot[ Evaluate[SheetOLatticeCharge[x, y, 0.25]], {x, \(-4\), 4}, {y, \(-4\), 4}, PlotPoints \[Rule] 120, ColorFunction \[Rule] Hue, Contours \[Rule] 24]\)], "Input"], Cell[BoxData[ \(thedenplot\ = DensityPlot[ Evaluate[SheetOLatticeCharge[x, y, 0.25]], {x, \(-4\), 4}, {y, \(-4\), 4}, PlotPoints \[Rule] 120, ColorFunction \[Rule] \((Hue[1 - #*0.66] &)\)]\)], "Input"], Cell[BoxData[ \(Show[thedenplot, Mesh \[Rule] False]\)], "Input", CellTags->{"mmtag:05:Show[]", "mmtag:05:Graphics__superposing_with_Show[]"}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Graphics Primitives", "Subtitle"], Cell[TextData[{ "It can be useful to be able to build up arbitrary graphics objects \ piece-by-piece using simple \"graphics primitives\" like ", StyleBox["Circle", FontWeight->"Bold"], ":" }], "Text"], Cell[BoxData[ \(Show[Graphics[Circle[{2, 2}, 1.5]]]\)], "Input", CellTags->{ "mmtag:05:drawing_with_graphics_primitives", "mmtag:05:graphics_primitives"} ], Cell[BoxData[ \(Show[Graphics[Circle[{2, 2}, 1.5]], Axes -> True]\)], "Input"], Cell[BoxData[ \(Show[Graphics[Circle[{2, 2}, 1.5]], Axes -> True, AxesOrigin \[Rule] {0, 0}, AspectRatio \[Rule] 1]\)], "Input"], Cell["Now we take a simple plot\[Ellipsis]", "Text"], Cell[BoxData[ \(cosplot\ = \ Plot[Cos[x], {x, 0, 4 Pi}]\)], "Input"], Cell["\<\ and overlay some text in places of our own \ choosing\[Ellipsis]\ \>", "Text"], Cell[BoxData[ \(Show[cosplot, Graphics[Text["\", {2\ Pi, 1.1}]], Graphics[Text["\", {4\ Pi, 1.1}]], PlotRange \[Rule] All]\)], "Input", CellTags->{ "mmtag:05:plots__annotating__example", "mmtag:05:Text[]__in_graphics"}], Cell[TextData[{ "This next example shows a clever way to perform a famous thermodynamic \ graphical construction called the ", StyleBox["Wulff construction. ", FontSlant->"Italic"], "For surface tensions that are a function of their orientation, the Wulff \ construction gives the enclosing surface of lowest total energy. The \ following code creates the graphics objects corresponding to the Wulff \ construction; it will be combined with an orientation-dependent surface \ tension to produce a prediction of the energy-minimizing shape" }], "Subsubtitle"], Cell[BoxData[ \(wulffline[{x_, y_}, wulfflength_]\ = \ Module[{theta, wulffhalflength = wulfflength*0.5, x1, x2, y1, y2}, theta = ArcTan[x, y]; \[IndentingNewLine]\ x1\ = \ x\ + \ wulffhalflength*Cos[theta\ + \ Pi/2]; \[IndentingNewLine]\ x2 = \ \ x\ + \ wulffhalflength*Cos[theta\ - \ Pi/2]; \[IndentingNewLine]\ y1\ = \ y\ + \ wulffhalflength*Sin[theta\ + \ Pi/2]; \[IndentingNewLine]y2 = \ y\ + \ wulffhalflength* Sin[theta\ - \ Pi/2]; \[IndentingNewLine]Graphics[ Line[{{x1, y1}, {x2, y2}}]]\[IndentingNewLine]]\)], "Input", CellTags->"mmtag:05:Wulff_construction__function_example"], Cell[TextData[{ "These last two plots have to do with the orientation dependence of the \ surface energy of a 2-D crystal (", StyleBox["GammaPlot", FontWeight->"Bold"], ")and the equilibrium shape that a single crystal having this surface \ energy will adopt to minimize its total surface energy." }], "Text"], Cell[BoxData[ \(gammaplot[theta_\ , \ anisotropy_\ , \ nfold_]\ := \ {Cos[theta] + \ anisotropy*Cos[\((nfold + 1)\)*theta], Sin[theta]\ + \ anisotropy*Sin[\((nfold + 1)\)*theta]}\)], "Input", CellTags->{ "mmtag:05:surface_tension__in_Wulff_construction", "mmtag:05:surface_tension__anisotropic_example__Wulff_construction"}], Cell[BoxData[ \(GammaPlot\ = \ ParametricPlot[gammaplot[t, 0.1, 4], {t, 0, 2\ Pi}, AspectRatio \[Rule] 1, PlotStyle \[Rule] {{Thickness[0.005], RGBColor[1, 0, 0]}}]\)], "Input"], Cell[BoxData[ \(Show[ Table[wulffline[gammaplot[t, 0.1, 4], 2], {t, 0, \ 2\ Pi, \ 2\ Pi/100}], GammaPlot, AspectRatio \[Rule] 1]\)], "Input"], Cell[TextData[{ "The inner envelope of the tangent lines to the ", StyleBox["GammaPlot", FontWeight->"Bold"], " in the figure above illustrates the energy-minimizing shape of the \ crystal. For this particular ", StyleBox["GammaPlot", FontWeight->"Bold"], ", the shape is approximately a square but the corners are rounded." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Animations", "Subtitle"], Cell[TextData[{ "Many processes in the natural world can be modelled by ", StyleBox["random walks", FontSlant->"Italic"], ". An example is the trajectory of a particular molecule in a gas at low \ pressure. The next few lines of code produce random walks and display them \ graphically: " }], "Text"], Cell[BoxData[ \(randomwalk[0]\ = \ {0, {0, 0}}\)], "Input", CellTags->{ "mmtag:05:simulation_of_2D_random_walk", "mmtag:05:random_walk__illustration"}], Cell[BoxData[ \(\(randomwalk[0]\)[\([2]\)]\)], "Input"], Cell[BoxData[ \(randomwalk[ nstep_Integer?Positive]\ := \ \(randomwalk[ nstep] = {nstep, \(randomwalk[ nstep - 1]\)[\([2]\)]\ + \ \[IndentingNewLine]Random[ Real, {0, 0.5}]*{Cos[theta\ = 2\ Pi\ Random[]], Sin[theta]}}\)\)], "Input"], Cell[BoxData[ \(randomwalk[4]\)], "Input"], Cell[BoxData[ \(Show[ Table[Graphics[ Text[ToString[\(randomwalk[i]\)[\([1]\)]], \(randomwalk[ i]\)[\([2]\)]]], {i, 0, 100}], PlotRange \[Rule] All, AspectRatio \[Rule] 1, AxesOrigin \[Rule] {0, 0}]\)], "Input"], Cell[BoxData[ \(Show[\[IndentingNewLine]Table[ Graphics[ Text[ToString[\(randomwalk[i]\)[\([1]\)]], \(randomwalk[ i]\)[\([2]\)]]], {i, 0, 50}], \[IndentingNewLine]Table[ Graphics[ Line[{\(randomwalk[j - 1]\)[\([2]\)], \(randomwalk[ j]\)[\([2]\)]}]], {j, 1, 50}], \[IndentingNewLine]PlotRange \[Rule] All, AspectRatio \[Rule] 1, AxesOrigin \[Rule] {0, 0}]\)], "Input"], Cell[BoxData[ \(<< Graphics`Animation`\)], "Input"], Cell[BoxData[ \(ShowAnimation[ Table[\[IndentingNewLine]Graphics[\[IndentingNewLine]{Text[\ \[IndentingNewLine]ToString[\(randomwalk[i]\)[\([1]\)]], \(randomwalk[ i]\)[\([2]\)]], \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[IndentingNewLine]Line[{\(randomwalk[i]\)[\([2]\)], \(randomwalk[ i + 1]\)[\([2]\)]}]}\[IndentingNewLine]], \ \[IndentingNewLine]{i, 0, 49}\[IndentingNewLine]], \[IndentingNewLine]PlotRange \[Rule] \ {{\(-3\), 3}, {\(-3\), 3}}, AspectRatio \[Rule] 1, AxesOrigin \[Rule] {0, 0}\[IndentingNewLine]]\)], "Input"], Cell["Other Frames suppressed in pdf version of this document", \ "Subsubsection"], Cell[BoxData[ \(ShowAnimation[\[IndentingNewLine]Table[\[IndentingNewLine]Graphics[\ \[IndentingNewLine]Table[\[IndentingNewLine]{Text[\[IndentingNewLine]ToString[\ \(randomwalk[j]\)[\([1]\)]], \(randomwalk[ j]\)[\([2]\)]], \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \[IndentingNewLine]Line[{\(randomwalk[j]\)[\([2]\)], \(randomwalk[ j + 1]\)[\([2]\)]}]\[IndentingNewLine]}, \ \[IndentingNewLine]{j, 0, i}\[IndentingNewLine]]\[IndentingNewLine]], \ \[IndentingNewLine]{i, 0, 49}\[IndentingNewLine]], \[IndentingNewLine]PlotRange \[Rule] \ {{\(-3\), 3}, {\(-3\), 3}}, AspectRatio \[Rule] 1, AxesOrigin \[Rule] {0, 0}\[IndentingNewLine]]\)], "Input"], Cell["Other Frames suppressed in pdf version of this document", \ "Subsubsection"] }, Closed]] }, FrontEndVersion->"5.2 for Macintosh", ScreenRectangle->{{4, 1280}, {0, 832}}, CellGrouping->Manual, WindowSize->{1280, 806}, WindowMargins->{{109, Automatic}, {Automatic, 51}}, WindowTitle->"Lecture 05 MIT 3.016 (Fall 2006) \[Copyright] W. Craig Carter \ 2003-2006", PrintingCopies->1, PrintingPageRange->{1, Automatic}, ShowSelection->True, ShowCellLabel->False, CellLabelAutoDelete->True, StyleDefinitions -> "3016_Carter.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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*******************************************************************)