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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[ 75839, 2317]*) (*NotebookOutlinePosition[ 100139, 3174]*) (* CellTagsIndexPosition[ 100095, 3170]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["The Plot Command", "Title"], Cell["By Robin Sue Sanders (Spring 1998)", "Subsubtitle", TextAlignment->Center], Cell[TextData[{ "For additional information on the Plot command, you can work through the \ second chapter in the text, ", StyleBox["Lab 2 Plotting. ", FontSlant->"Italic"], " The on-line version is located in notebook ", StyleBox["02/Plotting.nb", FontSlant->"Italic"], " which is located in the textbook folder. ", StyleBox["We will not officially cover 02/Plotting.nb however\[LongDash]", FontSlant->"Italic"], "this notebook covers the basic information you need to know about the Plot \ command." }], "Text"], Cell[CellGroupData[{ Cell[TextData[ "Basic syntax for Plot[ ]\[LongDash]the plotting command"], "Section"], Cell[TextData[{ "If you want to have ", StyleBox["Mathematica", FontSlant->"Italic"], " make a plot (i.e. a graph) of one function, the syntax is:" }], "Text"], Cell[TextData[{ "\t\t", StyleBox["Plot[function, {x, start, end}];", FontSlant->"Italic"], "\t\t\n\n(Note the use of [ ] since Plot is a ", StyleBox["Mathematica", FontSlant->"Italic"], " function. The use of the semi-colon at the end surpresses the generation \ of a cell with the word -Graphics- in it)" }], "Text"], Cell[TextData[{ "This will make a \"plain-jane\" plot\[LongDash]", StyleBox["Mathematica", FontSlant->"Italic"], " will choose the y-range that it thinks is best, and the function will be \ drawn in black. The x-range will be \n\t\t\t", StyleBox["start", FontSlant->"Italic"], " \[LessEqual] x \[LessEqual] ", StyleBox["end", FontSlant->"Italic"], "\nIf you want to graph more than one function at the same time, the syntax \ is:" }], "Text"], Cell[TextData[{ "\t\t", StyleBox["Plot[{function1, function2}, {x, start, end}];", FontSlant->"Italic"], "\t" }], "Text"], Cell[TextData[{ "You can plot as many functions as you want, but they must all appear in \ the ", StyleBox["list", FontSlant->"Italic"], " that is surrounded by the first set of { }'s. (", StyleBox["Mathematica", FontSlant->"Italic"], " uses { } to surround objects that it regards as ", StyleBox["lists", FontSlant->"Italic"], ".) All the functions will be drawn in black, and ", StyleBox["Mathematica", FontSlant->"Italic"], " may choose a y-range that makes it hard (or impossible) to see all the \ functions if they create vastly different y-values." }], "Text"], Cell[TextData[{ "The ", StyleBox["{x, start, end}", FontSlant->"Italic"], " argument is critical. Without it, ", StyleBox["Mathematica", FontSlant->"Italic"], " will not know what part of the function you want to look at. If you \ forget it (or if you forget to tell ", StyleBox["Mathematica", FontSlant->"Italic"], " the variable name\[LongDash]usually ", StyleBox["x", FontSlant->"Italic"], ") then ", StyleBox["Mathematica", FontSlant->"Italic"], " will not be able to create a plot. " }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Useful options for Plot", "Section"], Cell[TextData[{ "There are many, many options for the ", StyleBox["Plot", FontSlant->"Italic"], " command. Some of them are used to make very fancy plots that convey lots \ of information; others are used to force ", StyleBox["Mathematica", FontSlant->"Italic"], " to draw the plot the way you want it drawn, even though ", StyleBox["Mathematica", FontSlant->"Italic"], " thinks that your way creates an \"ugly\" plot. " }], "Text"], Cell[TextData[{ "The options are all added at the end of the ", StyleBox["Plot", FontSlant->"Italic"], " command, but ", StyleBox["inside", FontSlant->"Italic"], " the closing ]. In other words, a more elaborate ", StyleBox["Plot", FontSlant->"Italic"], " template is: ", StyleBox["Plot[function, {x, start, end}, option1, option2];", FontSlant->"Italic"], " The options can be listed in any order, but they must be separated from \ each other by commas." }], "Text"], Cell[TextData[{ "The four most important options are ", StyleBox["PlotRange", FontSlant->"Italic"], ", ", StyleBox["AxesOrigin", FontSlant->"Italic"], ", ", StyleBox["AspectRatio", FontSlant->"Italic"], ",", StyleBox[" ", FontSlant->"Italic"], "and ", StyleBox["PlotStyle. ", FontSlant->"Italic"], "These options are discussed in this handout." }], "Text"], Cell[CellGroupData[{ Cell["PlotRange", "Subsection"], Cell[TextData[{ "Sometimes ", StyleBox["Mathematica", FontSlant->"Italic"], " doesn't show all the y-values. For example, consider this plot of ", Cell[BoxData[ \(TraditionalForm\`x\^3\)]], "over -1 \[LessEqual] ", StyleBox["x", FontSlant->"Italic"], " \[LessEqual] 8:" }], "Text"], Cell[BoxData[ \(\(Plot[x^3, \ {x, \ \(-1\), \ 8}]; \)\)], "Input"], Cell[TextData[{ "To force ", StyleBox["Mathematica", FontSlant->"Italic"], " to show us the entire plot, we can use the option ", StyleBox["PlotRange->All", FontSlant->"Italic"], ". The -> is formed by typing a minus sign (-) followed by a greater than \ sign (>). Both these keys are on the standard keyboard and don't require any \ special keyboard sequences or palette buttons. Here's the plot showing the \ entire graph:" }], "Text"], Cell[BoxData[ \(\(Plot[x^3, \ {x, \ \(-1\), \ 8}, \ PlotRange -> All]; \)\)], "Input"], Cell[TextData[{ "Of course, neither of these graphs shows the behavior of the function \ around ", StyleBox["x", FontSlant->"Italic"], " = 0 very well. If we really want to see that, we can specify a ", StyleBox["PlotRange", FontSlant->"Italic"], " that tells ", StyleBox["Mathematica", FontSlant->"Italic"], " to only plot the part of the function between chosen ", StyleBox["y", FontSlant->"Italic"], "-values. The syntax is ", StyleBox["PlotRange->{bottom, top}", FontSlant->"Italic"], " (Note there is NO \"y\" in this list!). Here's the part of the plot \ that lies between ", StyleBox["y", FontSlant->"Italic"], " = -2 and ", StyleBox["y", FontSlant->"Italic"], " = 4:" }], "Text"], Cell[BoxData[ \(\(Plot[x^3, \ {x, \ \(-1\), \ 8}, \ PlotRange -> {\(-2\), \ 4}]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["AxesOrigin", "Subsection"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " places the \"axes\" for a plot at a place that it decides is relevant: " }], "Text"], Cell[BoxData[ \(\(Plot[x^2\ + \ 10, \ {x, \ \(-2\), \ 2}]; \)\)], "Input"], Cell[TextData[{ "The \"x-axis\" in this plot is NOT at ", StyleBox["y", FontSlant->"Italic"], "=0; it is at ", StyleBox["y", FontSlant->"Italic"], " = 10. Most of the time, ", StyleBox["Mathematica'", FontSlant->"Italic"], "s placement of the axes is not a problem (as long as you read the scales), \ but sometimes we want or need a picture with the axes at a special place\ \[LongDash]most typically at the origin, (0,0). We can make ", StyleBox["Mathematica", FontSlant->"Italic"], " draw the axes where we want them by using the ", StyleBox["AxesOrigin", FontSlant->"Italic"], " option. The snytax is ", StyleBox["AxesOrigin->{x-value, y-value}", FontSlant->"Italic"], " Note the { }'s around the point instead of ( ). Here's the same \ function as above with the axes for the plot drawn in the handwritten \ \"standard\" place: " }], "Text"], Cell[BoxData[ \(\(Plot[x^2\ + \ 10, \ {x, \ \(-2\), \ 2}, \ AxesOrigin -> {0, 0}]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["AspectRatio", "Subsection"], Cell[TextData[{ "As you may have noticed, ", StyleBox["Mathematica", FontSlant->"Italic"], " often uses different scales in the ", StyleBox["x", FontSlant->"Italic"], " and ", StyleBox["y", FontSlant->"Italic"], " directions to make the plot look pretty. Most of the time this is not a \ problem, but sometimes it is a nuisance. For example, we know that if we \ graph ", Cell[BoxData[ \(TraditionalForm\`y\ = \ \@\(1\ - x\^2\)\)]], " over the range 0 \[LessEqual] ", StyleBox["x", FontSlant->"Italic"], " \[LessEqual] 1, we should see a quarter circle. But when we ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to draw such a plot:" }], "Text"], Cell[BoxData[ \(\(Plot[Sqrt[1 - x^2], \ {x, \ 0, \ 1}]; \)\)], "Input"], Cell[TextData[{ "the plot does not look as expected. The reason why is simple: ", StyleBox["Mathematica", FontSlant->"Italic"], " is using larger units in the ", StyleBox["x", FontSlant->"Italic"], " direction than in the ", StyleBox["y", FontSlant->"Italic"], " direction. What we want here is a \"true-scale\" plot\[LongDash]one in \ which the units in both directions are the same. To make ", StyleBox["Mathematica", FontSlant->"Italic"], " draw a true-scale plot, we use the option ", StyleBox["AspectRatio->Automatic", FontSlant->"Italic"], ":" }], "Text"], Cell[BoxData[ \(\(Plot[Sqrt[1 - x^2], \ {x, \ 0, \ 1}, \ AspectRatio -> Automatic]; \)\)], "Input"], Cell["Now the plot looks as we expected.", "Text"], Cell[TextData[{ "The reason true scale plots are not the default is simple: Most plots are \ very difficult to parse in a true-scale plot. Consider ", Cell[BoxData[ \(TraditionalForm\`y\ = \ x\^3\)]], " over 0 \[LessEqual] ", StyleBox["x", FontSlant->"Italic"], " \[LessEqual] 3 using a true-scale plot:" }], "Text"], Cell[BoxData[ \(\(Plot[x^3, \ {x, \ 0, \ 3}, \ AspectRatio -> Automatic]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["PlotStyle", "Subsection"], Cell[TextData[{ "The PlotStyle option is used to both make plots \"pretty\" and to make it \ easier for the reader to pick out the information that the author is \ attempting to convey with the plot. For example, when several functions are \ plotted together, it can be difficult to tell them apart. Different ", StyleBox["PlotStyle", FontSlant->"Italic"], "'s can be used to distinguish the plots from each other. Moreover, it is \ possible to combine several ", StyleBox["PlotStyle", FontSlant->"Italic"], "'s for one function to create, say, a plot that is made up of Thick Green \ Dashes instead of the plain-jane thin black curve. " }], "Text", PageBreakWithin->False], Cell[TextData[{ "The two most useful ", StyleBox["PlotStyle'", FontSlant->"Italic"], "s are ", StyleBox["Thickness", FontSlant->"Italic"], " (which tells ", StyleBox["Mathematica", FontSlant->"Italic"], " how thick to draw the curve) and ", StyleBox["Color", FontSlant->"Italic"], " (which tells ", StyleBox["Mathematica", FontSlant->"Italic"], " what color to use). ", StyleBox[ "Both of these options are a bit tricky to learn, and if you are content \ with plain-jane plots, that is fine with me!", FontSlant->"Italic"] }], "Text"], Cell[CellGroupData[{ Cell["Thickness", "Subsubsection"], Cell[TextData[{ "Thickness is used in the following way: ", StyleBox["PlotStyle->{{Thickness[0.02]}}", FontSlant->"Italic"], " The use of double {{ }} is optional (i.e. you can get away with single { \ }), but useful for when we start combining options together. ", StyleBox["Thickness", FontSlant->"Italic"], " is a function, and that's why there are [ ]'s around the number. The \ number itself can be any small number\[LongDash]keep it less than .05 for \ practical purposes. The larger the number, the thicker the plot. Compare:" }], "Text"], Cell[BoxData[ \(\(Plot[Sin[x], \ {x, \ 0, \ \[Pi]}, \ PlotStyle -> {{Thickness[0.02]}}]; \)\)], "Input"], Cell["to", "Text"], Cell[BoxData[ \(\(Plot[Sin[x], \ {x, \ 0, \ \[Pi]}, \ PlotStyle -> {{Thickness[0.05]}}]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Color", "Subsubsection"], Cell[TextData[{ "Color is useful in plots. While colors can be created using raw ", StyleBox["Mathematica", FontSlant->"Italic"], " code, a much easier way is to read in a ", StyleBox["Colors", FontSlant->"Italic"], " package. To do this, you ", StyleBox["must", FontSlant->"Italic"], " type\n\t\t", StyleBox["<"Courier", FontWeight->"Bold"], " \nexactly as shown into an input cell and activate it ", StyleBox["before", FontSlant->"Italic"], " you use color names. The ", StyleBox["<<", FontFamily->"Courier", FontWeight->"Bold"], " is just two greater than signs in a row. The ", StyleBox["`", FontFamily->"Courier", FontWeight->"Bold"], "that appears both ", StyleBox["before", FontSlant->"Italic"], " and ", StyleBox["after", FontSlant->"Italic"], " the word ", StyleBox["Colors", FontFamily->"Courier", FontWeight->"Bold"], " is called an ", StyleBox["opening single quote", FontSlant->"Italic"], ". This character is in the upper left corner of the main keyboard just \ above the ", StyleBox["tab", FontWeight->"Bold"], " key. " }], "Text"], Cell[TextData[{ "The cell with ", StyleBox["<"Courier", FontWeight->"Bold"], " in it will ", StyleBox["not", FontSlant->"Italic"], " produce any visible output when it has been activated, and you only need \ to enter this command once in a given ", StyleBox["Mathematica", FontSlant->"Italic"], " session. If you ", StyleBox["quit", FontSlant->"Italic"], " ", StyleBox["Mathematica", FontSlant->"Italic"], " and then (later) re-open the notebook, this cell ", StyleBox["must", FontSlant->"Italic"], " be activated ", StyleBox["before", FontSlant->"Italic"], " any of the plots that require color are activated. In some of the \ textbook notebooks, the ", StyleBox["<"Courier", FontWeight->"Bold"], " command has been put into an initialization cell and in some of them it \ hasn't. It doesn't hurt to activate this command twice in a ", StyleBox["Mathematica", FontSlant->"Italic"], " session, so get into the habit of using this command manually if you plan \ to use color. (A good place to put it is right at the top of the notebook so \ you don't forget to activate when you open the notebook in a different ", StyleBox["Mathematica", FontSlant->"Italic"], " session.) Activate the following input cell if you are reading this \ notebook on-line." }], "Text"], Cell[BoxData[ \(<< Graphics`Colors`\)], "Input"], Cell[TextData[{ "This command has now loaded a very large list of colors into ", StyleBox["Mathematica. ", FontSlant->"Italic"], "The important thing is that we can now refer to these colors by name \ inside the PlotStyle option. The syntax is pretty simple: ", StyleBox["PlotStyle->{{ColorName}}", FontSlant->"Italic"], " makes ", StyleBox["Mathematica", FontSlant->"Italic"], " draw the function in the color ", StyleBox["ColorName", FontSlant->"Italic"], ". Here's an example:" }], "Text"], Cell[BoxData[ \(\(Plot[Cos[x], {x, \ 0, \ Pi}, \ PlotStyle -> {{Red}}]; \)\)], "Input"], Cell["\<\ The list of colors that you can use is very extensive. A complete \ list is included in the Appendix of this document.\ \>", "Text"] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "More about PlotStyle\[LongDash]the finer points of pretty graphics"], "Section"], Cell[CellGroupData[{ Cell["More than one PlotStyle for a given function", "Subsection"], Cell[TextData[{ "If you want to make a thicker, colored picture of a function, the two \ PlotStyles go in one list. The syntax is:\n\t\t", StyleBox["PlotStyle->{{Thickness[0.02], ColorName}}", FontSlant->"Italic"], "\nSo this cell makes a thick, dark green plot of Sin[2 ", StyleBox["x", FontSlant->"Italic"], " + 4]:" }], "Text"], Cell[BoxData[ \(\(Plot[Sin[2\ x\ + \ 4], \ {x, \ 0, \ 2 \[Pi]}, \ \n \t\ \ \ \ \ \ \ \ \ PlotStyle -> {{Thickness[0.02], DarkGreen}}]; \)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Different PlotStyle's for different functions", "Subsection"], Cell[TextData[{ "If you want to plot different functions on the same set of axes, using \ different ", StyleBox["PlotStyle", FontSlant->"Italic"], "'s makes is easier to tell the functions apart. The syntax is:\n\t", StyleBox["PlotStyle->{{function1's style},{function2's style}}", FontSlant->"Italic"], "\nIf you have more than two functions, just keep listing each function's ", StyleBox["PlotStyle", FontSlant->"Italic"], " in an appropriate set of { }'s. Here's an example:" }], "Text"], Cell[BoxData[ \(\(Plot[{Sin[2\ x\ + \ 4], x\^2\/9, \ Cos[x], \ 5\/\(x\ + \ 1\)}, \ {x, \ 0, \ 2 \[Pi]}, \ \n\t\ \ \ \ \ \ \ \ \ PlotStyle -> {{Thickness[0.02], DarkGreen}, \ \n \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ {Thickness[0.01], Orange}, \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ {Purple}, \n \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\ \ \ {Thickness[0.01]}}]; \)\)], "Input", PageBreakWithin->Automatic, GroupPageBreakWithin->Automatic], Cell[TextData[{ "The thick, dark green curve is the first function in our list, ", Cell[BoxData[ \(TraditionalForm\`y\ = \ Sin[2\ x\ + \ 4]\)]], ", the middle-sized, orange curve is the second function ", Cell[BoxData[ \(TraditionalForm\`y\ = \ x\^2\/9\)]], ", the purple curve is the third function, ", Cell[BoxData[ \(TraditionalForm\`y\ = \ Cos[x]\)]], ", and the black, middlesized curve is ", Cell[BoxData[ \(TraditionalForm\`y\ = \ 5\/\(x + 1\)\)]], "." }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "Troubleshooting\[LongDash]Help for when things go wrong"], "Section"], Cell[TextData[{ "You ", StyleBox["must", FontSlant->"Italic"], " remember to specify a range of \"x\" values for the plot. Otherwise, you \ get an error message:" }], "Text", CellDingbat->"\[FilledCircle]"], Cell[BoxData[ \(Plot[x^2]\)], "Input"], Cell["Blank plots and how to fix them.", "Text", CellDingbat->"\[FilledCircle]"], Cell[TextData[{ "Any time you see a string of messages of the sort \n\t", Cell[BoxData[ \(\( < junk > \ is\ not\ a\ machine - size\ real\ number\ at\ x\)\ = constant\)], "Message"], StyleBox["\n", FontFamily->"Courier", FontSize->12, FontColor->RGBColor[0, 0, 1]], "followed by a blank plot, there is a very good chance that the error is \ caused by one of these things: One or more undefined \ parameters\[LongDash]letters that stand for constants; a problem with proper \ capitalization or brackets; a missing underscore in a function definition; or \ mismatched variables.\t" }], "Text", CellDingbat->None], Cell[TextData[StyleBox[ "(If you get this kind of error message, but Mathematica draws a plot anyway, \ chances are the function has a discontinuity in the chosen plot interval and \ Mathematica happened to chose that value as one of its sample points. In \ that case, you can safely ignore these error messages in this class. You \ should, however, look for vertical asymptotes in the graph or consider the \ possiblity that the graph has a \"hole\" in it that you cannot see.)", FontSlant->"Italic"]], "Text"], Cell[TextData[{ StyleBox["Undefined Parameters. ", FontSlant->"Italic"], "The function you are plotting ", StyleBox["cannot", FontSlant->"Italic"], " have undefined parameters in it. In other words, the only letter that is \ \"undefined\" is the variable that appears in the second argument of the ", StyleBox["Plot", FontSlant->"Italic"], " command. For example, asking ", StyleBox["Mathematica", FontSlant->"Italic"], " to plot ", Cell[BoxData[ \(TraditionalForm\`x\^2 + \ b\ x\ + \ c\)]], " where ", StyleBox["b", FontSlant->"Italic"], " and ", StyleBox["c", FontSlant->"Italic"], " have not been given values yields a string of error messages and a blank \ plot:" }], "Text", CellDingbat->"\[EmptySmallCircle]"], Cell[BoxData[ \(Clear[a, \ b, \ c]; \nPlot[x\^2 + \ b*x\ + \ c, \ {x, \ \(-2\), \ 2}]; \)], "Input"], Cell[TextData[{ "But telling ", StyleBox["Mathematica", FontSlant->"Italic"], " values for ", StyleBox["b", FontSlant->"Italic"], " and ", StyleBox["c", FontSlant->"Italic"], " elimates the problem:" }], "Text"], Cell[BoxData[ \(b\ = \ 4; \nc\ = \ \(-10\); \n Plot[x\^2 + \ b*x\ + \ c, \ {x, \ \(-2\), \ 2}]; \)], "Input"], Cell[TextData[{ "Improper capitalization and bracket problems", StyleBox[ ". Mispelling or improperly capitalizing a function name causes ", FontSlant->"Plain"], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[ " to draw a blank plot. So does forgetting to capitalize Pi and E when ", FontSlant->"Plain"], "e", StyleBox[ " or \[Pi] appears in the function. For example, the following is an \ incorrect attempt to plot the function y = ", FontSlant->"Plain"], Cell[BoxData[ \(TraditionalForm\`e\^\(2 x\)\)]], ":", StyleBox[" ", FontSlant->"Plain"] }], "Text", CellDingbat->"\[EmptySmallCircle]", FontSlant->"Italic"], Cell[BoxData[ \(\(Plot[e^\((2\ x)\), \ {x, \ \(-3\), \ 2}]; \)\)], "Input"], Cell[TextData[{ "To fix the problem, change the ", StyleBox["e", FontWeight->"Bold"], " to and ", StyleBox["E", FontWeight->"Bold"], " and reactivate the cell. " }], "Text"], Cell["\<\ Using the wrong kind of brackets for a function will also create an \ empty plot:\ \>", "Text", PageBreakAbove->Automatic], Cell[BoxData[ \(\(Plot[Sin \((x)\), \ {x, 0, \[Pi]}]; \)\)], "Input"], Cell["\<\ You fix the problem by changing the ( ) to [ ] and reactivating the \ cell. \ \>", "Text"], Cell[TextData[{ "Missing underscores.", StyleBox[" When you define a function, the function's variable ", FontSlant->"Plain"], "must", StyleBox[ " have an underscore after it. If you forget this underscore and then use \ the function's name in the ", FontSlant->"Plain"], "Plot", StyleBox[" command, you'll get a blank plot:", FontSlant->"Plain"] }], "Text", CellDingbat->"\[EmptySmallCircle]", PageBreakAbove->True, FontSlant->"Italic"], Cell[BoxData[{ \(Clear[f]\), \(f[x]\ = \ 3\ x^2\ - 2; \nPlot[f[x], {x, \ 0, \ 3}]; \)}], "Input"], Cell[TextData[{ "To fix this problem, add an underscore after the first x on the second \ line of input so that the definition of f[x] reads: \n\t\t\t\t", StyleBox["f[x_] = 3x^2 - 2;", FontWeight->"Bold"], " \nand then reactivate the plot. " }], "Text"], Cell[TextData[{ "Mismatched variables.", StyleBox[ " The variable in the function and the variable in the second part of the \ Plot command (the {variable, start, end} part) must agree. If they don't you \ get a blank plot. This is most apt to happen if you occasionally make plots \ of functions of ", FontSlant->"Plain"], "t", StyleBox[" and forget to change {x, start, end} to {t, start, end}:", FontSlant->"Plain"] }], "Text", CellDingbat->"\[EmptySmallCircle]", FontSlant->"Italic"], Cell[BoxData[ \(\(Plot[t^2, \ {x, \ \(-2\), \ 2}]; \)\)], "Input"], Cell["\<\ Change the {x, -2, 2} to read {t, -2, 2} and reactivate the cell. \ The problems will disappear.\ \>", "Text"], Cell["Problems with color.", "Text", CellDingbat->"\[FilledCircle]"], Cell[TextData[StyleBox[ "(In the on-line version of this notebook, you do NOT need to activate the \ cells in this part of the notebook. If you do so, the error messages will \ disappear.)", FontSlant->"Italic"]], "Text"], Cell[TextData[{ " Problems with color happen whenever you ask ", StyleBox["Mathematica", FontSlant->"Italic"], " to use a ", StyleBox["ColorName", FontSlant->"Italic"], " ", StyleBox["before", FontSlant->"Italic"], " you have activated the command: ", StyleBox["<"Courier", FontWeight->"Bold"], " Here's an example of the kind of error messages you get in this \ situation:" }], "Text", CellDingbat->None], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ \(Plot[x^2, \ {x, \ \(-3\), \ 3}, \ PlotStyle -> {{Red}}]; \), " ", RowBox[{ StyleBox["(*", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox[ \(Do\ Not\ Activate\ this\ cell\ since\ you' ve\ already\ loaded\ the\ Colors\ package\), FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["*)", FontWeight->"Plain"]}]}]], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart 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Ool00`00Oomoo`2>Ool008moo`03001oogoo08ioo`00Sgoo00<007ooOol0SWoo0000\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-3.3151, -0.695724, 0.0231017, 0.056069}}], Cell[BoxData[ \(Graphics::"gprim" \( : \ \) "Unknown \!\(Graphics\) primitive \!\(Red\) encountered."\)], "Message"] }, Open ]], Cell[TextData[{ "Moreover, if you go back and load the ", StyleBox["Colors", FontSlant->"Italic"], " package, ", StyleBox["Mathematica", FontSlant->"Italic"], " will still have problems with the color that you tried to use before the \ ", StyleBox["Colors", FontSlant->"Italic"], " package was loaded:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{\(<< Graphics`Colors`\), RowBox[{ StyleBox["(*", FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox[ \(Do\ Not\ Activate\ this\ cell\ since\ you' ve\ already\ loaded\ the\ Colors\ package\), FontWeight->"Plain"], StyleBox[" ", FontWeight->"Plain"], StyleBox["*)", FontWeight->"Plain"]}]}]], "Input"], Cell[BoxData[ \(Red::"shdw" 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the colors package using the ", StyleBox["<"Courier", FontWeight->"Bold"], " command, you can use any of the following as color names. Pay attention \ to the capitalization since that's important in getting the colors to work \ correctly. " }], "Text"], Cell["\<\ AliceBlue, AlizarinCrimson, Antique, Apricot, Aquamarine, \ AureolineYellow, Azure, Banana, Beige, Bisque, Black, BlanchedAlmond, Blue, \ BlueViolet, Brick, Brown, BrownMadder, BrownOchre, Burlywood, BurntSienna, \ BurntUmber, CadetBlue, CadmiumLemon, CadmiumOrange, CadmiumYellow, Carrot, \ Cerulean, Chartreuse, Chocolate, ChromeOxideGreen, CinnabarGreen, Cobalt, \ CobaltGreen, ColdGray, Coral, CornflowerBlue, Cornsilk, Cyan, CyanWhite, \ DarkGoldenrod, DarkGreen, DarkKhaki, DarkOliveGreen, DarkOrange, DarkOrchid, \ DarkSeaGreen, DarkSlateBlue, DarkSlateGray, DarkTurquoise, DarkViolet, \ DeepCadmiumRed, DeepCobaltViolet, DeepMadderLake, DeepNaplesYellow, \ DeepOchre, DeepPink, DeepSkyBlue, DimGray, DodgerBlue, Eggshell, \ EmeraldGreen, EnglishRed, Firebrick, Floral, ForestGreen, Gainsboro, \ GeraniumLake, Ghost, Gold, Goldenrod, GoldOchreGray, GreenYellow, Honeydew, \ HotPink, IndianRed, Indigo, Ivory, IvoryBlack, Khaki, LampBlack, Lavender, \ LavenderBlush, LawnGreen, LemonChiffon, LightBeige, LightBlue, \ LightCadmiumRed, LightCadmiumYellow, LightCoral, LightGoldenrod, LightGray, \ LightPink, LightSalmon, LightSeaGreen, LightSkyBlue, LightSlateBlue, \ LightSlateGray, LightSteelBlue, LightViridian, LightYellow, LimeGreen, Linen, \ Magenta, ManganeseBlue, Maroon, MarsOrange, MarsYellow, MediumAquamarine, \ MediumBlue, MediumOrchid, MediumPurple, MediumSeaGreen, MediumSlateBlue, \ MediumSpringGreen, MediumTurquoise, MediumVioletRed, Melon, MidnightBlue, \ Mint, MintCream, MistyRose, Moccasin, Navajo, Navy, NavyBlue, Oak, OldLace, \ Olive, OliveDrab, Orange, OrangeRed, Orchid, PaleGoldenrod, PaleGreen, \ PaleTurquoise, PaleVioletRed, PapayaWhip, Peach, PeachPuff, Peacock, \ PermanentGreen, PermanentRedViolet, Peru, Pink, Plum, PowderBlue, \ PrussianBlue, Purple, Raspberry, RawSienna, RawUmber, Red, RoseMadder, \ RosyBrown, RoyalBlue, SaddleBrown, Salmon, SandyBrown, SapGreen, SeaGreen, \ Seashell, Sepia, Sienna, SkyBlue, SlateBlue, SlateGray, Smoke, Snow, \ SpringGreen, SteelBlue, TerreVerte, Thistle, Titanium, Tomato, Turquoise, \ TurquoiseBlue, Ultramarine, UltramarineViolet, VanDykeBrown, VenetianRed, \ Violet, VioletRed WarmGray, Wheat, White, Yellow, YellowBrown, YellowGreen, \ YellowOchre, Zinc\ \>", "Text"], Cell[TextData[ "Many of these colors are very, very pale\[LongDash]they are designed to be \ used in plots with dark backgrounds. If you enjoy playing around with \ colors, try the ones that sound interesting (or strange) to you. If the \ color turns out too pale to see, just edit cell to change the color and \ reactivate."], "Text"] }, Closed]] }, Open ]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 800}, {0, 580}}, WindowSize->{556, 428}, WindowMargins->{{5, Automatic}, {Automatic, 1}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ "The Plot Command"], "Header"]}, {Cell[ TextData[ "The Plot Command"], "Header"], Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PrintingOptions->{"FirstPageHeader"->False, "FacingPages"->True}, StyleDefinitions -> Notebook[{ 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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CounterAssignments->{{"Subsubsection", 0}}, FontFamily->"Times", FontSize->16, 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, CounterIncrements->"Subsubsection", FontFamily->"Times", FontSize->14, 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, 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Open ]], Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. 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ButtonBoxes. 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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, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", FontSize->12, Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{0.6, 1}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], 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]] }], MacintoshSystemPageSetup->"\<\ 00<0004/0B`000002mT8o?mooh<" ] (*********************************************************************** 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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(*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)