(* 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[ 103309, 2303] NotebookOptionsPosition[ 99565, 2188] NotebookOutlinePosition[ 100023, 2207] CellTagsIndexPosition[ 99980, 2204] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Lesson 10 Two-Dimensional Plots (Part II)", "Section", CellChangeTimes->{ 3.4612562964071407`*^9, {3.4614189256292973`*^9, 3.461418929565085*^9}}], Cell[CellGroupData[{ Cell["Axes and Frame Options", "Subsection", CellChangeTimes->{{3.461430530542584*^9, 3.461430537643694*^9}, { 3.461430929722191*^9, 3.4614309370916233`*^9}, {3.461431383632901*^9, 3.4614313896520653`*^9}}], Cell[TextData[{ "There are many options that can be used to control the appearance of the \ axes. The most basic pf these are ", StyleBox["Axes\[Rule]True", "Input"], " and ", StyleBox["Axes", "Input"], StyleBox["\[Rule]", "Input"], StyleBox["False", "Input"], " that switch on and off the axes, ", StyleBox["Frame\[Rule]True", "Input"], " and ", StyleBox["Frame\[Rule]False", "Input"], ", that switch on or off a frame around the graph." }], "Text", CellChangeTimes->{{3.461430552610344*^9, 3.4614305826706333`*^9}, { 3.461430640379756*^9, 3.461430754525219*^9}, {3.461430795831908*^9, 3.461430801593079*^9}, {3.461430874889017*^9, 3.4614308830005093`*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"Axes", "\[Rule]", "False"}]}], "]"}]], "Input", CellChangeTimes->{{3.461430810467395*^9, 3.4614308143202972`*^9}, { 3.461431061570345*^9, 3.4614310635776587`*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"Frame", "\[Rule]", "True"}]}], "]"}]], "Input", CellChangeTimes->{{3.4614307779214067`*^9, 3.461430782743896*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " does not necessarily draw the axes through the origin. In the graph below \ the axes meet at the point (6.0,2.4). ", StyleBox["Mathematica", FontSlant->"Italic"], " is trying to make the best possible graph of the function and to do so is \ choosing a range of x- and y- coordinates that do not include the origin. " }], "Text", CellChangeTimes->{{3.461430963457554*^9, 3.461431039025337*^9}, { 3.461431154268718*^9, 3.461431290196249*^9}, {3.461434328390777*^9, 3.461434342092251*^9}, 3.4614540983997593`*^9}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"3", "+", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "5", ",", "20"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.4614310430483837`*^9, 3.4614310957887173`*^9}, { 3.461431160497908*^9, 3.4614311705096273`*^9}}], Cell[TextData[{ "If it is preferable that the axes intersect at the origin it is necessary \ to tell ", StyleBox["Mathematica", FontSlant->"Italic"], " so using the ", StyleBox["AxesOrigin", "Input"], " option." }], "Text", CellChangeTimes->{{3.461431308558364*^9, 3.461431344032634*^9}, { 3.461431471383747*^9, 3.461431485683251*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"3", "+", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "5", ",", "20"}], "}"}], ",", RowBox[{"AxesOrigin", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "0"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.4614310430483837`*^9, 3.4614310957887173`*^9}, { 3.461431160497908*^9, 3.4614311705096273`*^9}, {3.4614313552424603`*^9, 3.461431367337716*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["PlotLabel, FrameLabel and AxesLabel", "Subsection", CellChangeTimes->{{3.461431521030561*^9, 3.461431522277665*^9}}], Cell[TextData[{ "There are three options that are related to labels. ", StyleBox["PlotLabel", "Input", FontWeight->"Bold"], " gives the plot an overall label, centered at the top of the graph." }], "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"PlotLabel", " ", "->", "\"\\""}]}], "]"}]], "Input"], Cell[TextData[{ StyleBox["FrameLabel", "Input", FontWeight->"Bold"], " and ", StyleBox["AxesLabel", "Input", FontWeight->"Bold"], " can both be used to indicate what quantities are displayed along the two \ axes. However, they differ in the way in which they can be displayed. ", StyleBox["FrameLabel", "Input", FontWeight->"Bold"], StyleBox[" ", FontWeight->"Bold"], "allows the labels to be rotated, and they are displayed below and besides \ the x- and y- axes, respectively. Furthermore, labels can be displayed on all \ four sides of a frame. ", StyleBox["AxesLabel", "Input", FontWeight->"Bold"], StyleBox[", ", FontWeight->"Bold"], "on the other hand, displays the labels at the end of their respective axes \ in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Let's check out the difference. Note that labels have to be strings, \ which are indicated by the double quotation marks." }], "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"PlotLabel", " ", "->", "\"\\""}], ",", " ", RowBox[{"AxesLabel", " ", "->", " ", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]], "Input"], Cell[TextData[{ "One problem with ", StyleBox["AxesLabel", "Input", FontWeight->"Bold"], " is that long labels dramatically change the appearance of the graph, even \ if they are split up into separate lines by using ", StyleBox["\\n", "Input"], " to mark the beginning of a new line." }], "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"PlotLabel", " ", "->", "\"\\""}], ",", " ", RowBox[{"AxesLabel", " ", "->", " ", RowBox[{"{", RowBox[{ "\"\\""}], ",", " ", RowBox[{"Frame", " ", "->", " ", "True"}], ",", "\n", "\t", RowBox[{"FrameLabel", " ", "->", " ", RowBox[{"{", RowBox[{ "\"\\""}], ",", " ", RowBox[{"Frame", " ", "->", " ", "True"}], ",", "\n", "\t", RowBox[{"FrameLabel", " ", "->", " ", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\<\>\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}]}], "]"}]], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Ticks and FrameTicks", "Subsection", CellChangeTimes->{ 3.461418968113398*^9, {3.461434447980584*^9, 3.4614344490337267`*^9}}], Cell[TextData[{ "When ", StyleBox["Mathematica", FontSlant->"Italic"], " draws a plot, it decides where to put ticks. Most of the time you might \ agree with the tick selection, but sometimes (especially for trigonometric \ functions), ", "you", " may want to decide where to put the labels. For example, in the above \ function, the relative maxima and minima occur at odd multiples of \[Pi]/2. \ We can create a list of where the horizontal ticks should be placed:" }], "Text"], Cell[BoxData[ RowBox[{"xticks", " ", "=", " ", RowBox[{"Table", "[", RowBox[{ RowBox[{"i", "*", " ", RowBox[{"Pi", "/", "2"}]}], ",", " ", RowBox[{"{", RowBox[{"i", ",", "1", ",", "11", ",", "2"}], "}"}]}], "]"}]}]], "Input"], Cell[TextData[{ "The specification for tick marks is a list of the form ", StyleBox["{xticks,yticks}", "Input"], ". You can specify ", StyleBox["None", "Input", FontWeight->"Bold"], " to have no tick marks drawn, or ", StyleBox["Automatic", "Input", FontWeight->"Bold"], " to go with ", StyleBox["Mathematica", FontSlant->"Italic"], "'s choice. The following is an example of how it works with ticks on the \ axes when no frame is drawn. If we want to label the horizontal axis with our \ own choice, but are happy with what ", StyleBox["Mathematica", FontSlant->"Italic"], " has choose for ticks on the vertical axis, we would use:" }], "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", "\n", "\t", RowBox[{"Ticks", " ", "->", " ", RowBox[{"{", RowBox[{"xticks", ",", " ", "Automatic"}], "}"}]}]}], "]"}]], "Input"], Cell["\<\ When a frame is drawn, things are just slightly different, as labels for the \ ticks are possible for all four sides of the frame. If only two \ specifications are given, then they are applied repeatedly. \ \>", "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"Frame", " ", "->", " ", "True"}], ",", "\n", "\t", RowBox[{"FrameTicks", " ", "->", " ", RowBox[{"{", RowBox[{"xticks", ",", " ", "Automatic", ",", "None", ",", "None"}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.449192921932534*^9, 3.449192956544029*^9}}], Cell[TextData[{ "Notice that the specification for ", StyleBox["xticks", "Input"], " was used again and that by default no tick specifications are given on the \ right frame. If you do not want to see the tick marks on the top, just \ specify ", StyleBox["None", "Input", FontWeight->"Bold"], "." }], "Text"], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"E", "^", RowBox[{"(", RowBox[{ RowBox[{"-", ".1"}], "x"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "20"}], "}"}], ",", " ", RowBox[{"Frame", " ", "->", " ", "True"}], ",", "\n", "\t", RowBox[{"FrameTicks", " ", "->", " ", RowBox[{"{", RowBox[{ "xticks", ",", " ", "Automatic", ",", " ", "None", ",", " ", "None"}], "}"}]}]}], "]"}]], "Input"] }, Open ]], Cell[CellGroupData[{ Cell["Practice", "Subsection"], Cell[TextData[{ "Find a ", StyleBox["Mathematica", FontSlant->"Italic"], " command to generate the following plot of the sine and cosine functions:" }], "Text"], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[1, 0, 0], Thickness[Large], Dashing[{Small, Small}], LineBox[CompressedData[" 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Open ]], Cell[CellGroupData[{ Cell["Text Style ", "Subsection", CellChangeTimes->{{3.41833900055962*^9, 3.418339004168714*^9}, { 3.418339411836376*^9, 3.418339414226798*^9}, {3.41833950014719*^9, 3.4183395082897987`*^9}, 3.449195537203779*^9, 3.4614190116883307`*^9, { 3.461434876236046*^9, 3.461434904736598*^9}}], Cell[TextData[{ " If you do not like the default font, size and weight of the labels of the \ graph, you can change ", StyleBox["BaseStyle", "Input", FontWeight->"Bold"], ". 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