(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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[ 314574, 8529]*) (*NotebookOutlinePosition[ 315284, 8554]*) (* CellTagsIndexPosition[ 315240, 8550]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Log and Log-Log Graphing", FontWeight->"Bold"]], "Subtitle"], Cell["\<\ This notebook is a modification of Paul Wellin's EngineeringDemo.nb\ \ \>", "Text", FontSlant->"Italic"], Cell[TextData[{ StyleBox["Log Plotting", FontWeight->"Bold"], " is one of many advanced functions that reside in one of the many external \ packages that come with ", StyleBox["Mathematica", FontSlant->"Italic"], ". These packages may be loaded into ", StyleBox["Mathematica", FontSlant->"Italic"], " as their functionality is needed. Also provided is a style guide to use \ as you begin to write your own packages." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Setup", "Section"], Cell[TextData[{ "Load the Graphics package. This is done using the ", StyleBox["Get ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 0.294118]], "comand, ", StyleBox["<<", FontWeight->"Bold", FontColor->RGBColor[0, 0, 0.294118]], ", in ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "Text"], Cell[BoxData[ \(<< Graphics`\)], "Input"], Cell[TextData[{ "Define the function to be graphed. This is done in a similar format to \ the popular standards and traditional written formula criteria. The name of \ the function in on the left-hand side of the equation. The variables of the \ function are represented with an underscore attached. Everything to the \ right of the := defines the function. For instance, defined below is a \ function ", Cell[BoxData[ \(TraditionalForm\`f(x)\)]], "." }], "Text"], Cell[BoxData[ \(f[x_] := x^2\ + \ 3\)], "Input"], Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`f\)]], " is a function of ", Cell[BoxData[ \(TraditionalForm\`x\)]], ". In order that ", StyleBox["Mathematica", FontSlant->"Italic"], " knows the definitions of ", Cell[BoxData[ \(TraditionalForm\`f\)]], " you evaluate the cell. Now, if you evaluate this function at some value \ its value will be returned by ", StyleBox["Mathematica", FontSlant->"Italic"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f[2]\)], "Input"], Cell[BoxData[ \(7\)], "Output"] }, Open ]], Cell[TextData[{ " You ", "can define a function as a combination of ", StyleBox["Mathematica", FontSlant->"Italic"], " functions. For instance," }], "Text"], Cell[BoxData[ \(\(eqn[x_] := Abs[100\/\(\((I\ x)\)\^2 + 2\ I\ x + 100\)];\)\)], "Input"], Cell[TextData[{ " You can evaluate this function ", Cell[BoxData[ \(TraditionalForm\`eqn[x_]\)]], " across a collection of values and save it in a data variable using ", StyleBox["Mathematica", FontSlant->"Italic"], "'s ", StyleBox["Table ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 0.294118]], "function." }], "Text"], Cell[BoxData[ \(\(data = Table[eqn[x], {x, .1, 20, .4}];\)\)], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["Log plot of a function", "Section"], Cell[TextData[{ "Take the data you collected and produce a visualization of this data using \ ", StyleBox["LogPlot", FontWeight->"Bold"], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?LogPlot\)\)], "Input"], Cell[BoxData[ \("LogPlot[f, {x, xmin, xmax}] generates a plot of Log[f] as a function \ of x."\)], "Print"] }, Open ]], Cell[TextData[{ "You also can add options to many ", StyleBox["Mathematica", FontSlant->"Italic"], " functions. The current option settings for a particular function can be \ viewed by using the ", StyleBox["Options ", FontWeight->"Bold", FontColor->RGBColor[0, 0, 0.294118]], "command." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Options[LogPlot]\)], "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"] }, Open ]], Cell[TextData[{ "Now create a log plot of this function, setting a few options for the \ graphic output. 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