(*********************************************************************** 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). 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[ 15690, 551]*) (*NotebookOutlinePosition[ 34289, 1232]*) (* CellTagsIndexPosition[ 34245, 1228]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ "Tutorial 11: ", StyleBox["Data", FontSlant->"Italic"] }], "Title", TextAlignment->Left, FontSize->30], Cell["by R. 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Move the axes to the origin. (Use the \ option \"AxesOrigin \[Rule] {0,0}\".) Then make the points a little bigger. \ (Another option: PlotStyle \[Rule] PointSize[.02] or choose a size you \ like.) Then join the points together. (PlotJoined \[Rule] True) Check out \ the options to see if you'd like to do anything else. (Colors?) "], "Text"], Cell[TextData[ "Note that real data will often make \"PlotJoined \[Rule] True\" a lot more \ interesting and useful. Be sure to clear onelist."], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["A table first...", "Section"], Cell[TextData[{ "\tThis example and the resulting graph is a little more interesting since \ there is a pattern to the points. First ", ButtonBox["define", ButtonData:>{"3 define.nb", "definef"}, ButtonStyle->"Hyperlink"], " a function a(n) = sin(n)." }], "Text"], Cell["\<\ Now, name and create a table of ordered pairs (n, a(n)), where n is \ an integer from 1 to 50. (You'll find that numerical values will be helpful \ here.) Not much of pattern? \ \>", "Text"], Cell["Use \"ListPlot\" on your table. Still not much of a pattern?", "Text"], Cell[TextData[ "Increase the integer range to extend from 1 to 300. Plot this. Then add \ another option: AspectRatio \[Rule] 1/3. How's the pattern?"], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Regression", "Section"], Cell["\tLet's begin with some more data.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(somedata\ = \ \ {{ .1, \ 3.1}, \ { .6, \ 3.7}, \ {1.4, \ 3.9}, \ {1.9, \ 3.2}, \ {2.3, \ 2.6}, \ {2.5, \ 2}, \ {2.7, \ 1.8}, \ {3, \ 1.2}, \ {3.1, \ .5}, \ {3.6, \ 0}, \ {4, \ \(- .3\)}, \ {4.2, \ \(- .4\)}, \ {5, \ .2}, \ {5.3, \ \ .8}, \ {5.7, \ 1.4}, \ {6, \ 2.2}}\)], "Input"], Cell[BoxData[ \({{0.1`, 3.1`}, {0.6`, 3.7`}, {1.4`, 3.9`}, {1.9`, 3.2`}, {2.3`, 2.6`}, {2.5`, 2}, {2.7`, 1.8`}, {3, 1.2`}, {3.1`, 0.5`}, {3.6`, 0}, {4, \(-0.3`\)}, {4.2`, \(-0.4`\)}, {5, 0.2`}, {5.3`, 0.8`}, {5.7`, 1.4`}, {6, 2.2`}}\)], "Output"] }, Open ]], Cell["\<\ Use ListPlot to show this, naming the plot \"graphdata\". Make the \ points big enough to see.\ \>", "Text"], Cell["\<\ So how about a cubic? The following command will fit your data as \ well as possible to a polynomial with constant, linear, quadratic, and cubic \ terms, where x is the variable.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(func1\ = \ Fit[somedata, \ {1, \ x, \ x\^2, \ x\^3}, \ x]\)], "Input"], Cell[BoxData[ \(\(\(2.960592070087465`\)\(\[InvisibleSpace]\)\) + 2.222717646649277`\ x - 1.4968031086453248`\ x\^2 + 0.18579577523958568`\ x\^3\)], "Output"] }, Open ]], Cell["\<\ We need to see how reasonable this is. Graph \"func1\" on the \ interval [0, 6], naming the plot \"graph1\".\ \>", "Text"], Cell["\<\ We next want to show the two graphs together. The \"Show\" command \ is necessary to put two graphs which required different commands (Plot and \ ListPlot) together.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Show[graphdata, \ graph1]\)], "Input"], Cell[BoxData[ \(Show::"gcomb" \(\(:\)\(\ \)\) "An error was encountered in combining the graphics objects in \ \!\(Show[\(\(graphdata, graph1\)\)]\)."\)], "Message"], Cell[BoxData[ \(Show[graphdata, graph1]\)], "Output"] }, Open ]], Cell["\<\ Let's look at some trig now. We'll do essentially the same thing, \ using Sin[x] and Cos[x] instead of some polynomial terms. However, the \ constant term still looks reasonable. We'll call this func2.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(func2\ = \ Fit[somedata, \ {1, \ Sin[x], \ Cos[x]}, \ x]\)], "Input"], Cell[BoxData[ \(\(\(1.7713997948476603`\)\(\[InvisibleSpace]\)\) + 1.0316039743654795`\ Cos[x] + 1.9380754902618975`\ Sin[x]\)], "Output"] }, Open ]], Cell["Creat the plot \"graph2\" of func2.", "Text"], Cell["Show the graph of the data and graph2 together. ", "Text"], Cell["\<\ Then show all three graphs together. (Color may be useful here. Go \ back and change graph1 or graph2.) Which is better?\ \>", "Text"] }, Closed]] }, FrontEndVersion->"4.0 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{1016, 668}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ 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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FontSize->9, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->6], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontWeight->"Bold"] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. 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If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1717, 49, 131, 6, 51, "Title"], Cell[1851, 57, 76, 2, 36, "Subtitle"], Cell[CellGroupData[{ Cell[1952, 63, 27, 0, 56, "Section"], Cell[1982, 65, 257, 5, 58, "Text"], Cell[CellGroupData[{ Cell[2264, 74, 181, 3, 63, "Input"], Cell[2448, 79, 140, 2, 70, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2625, 86, 50, 1, 47, "Input"], Cell[2678, 89, 8631, 321, 70, 3508, 253, "GraphicsData", "PostScript", \ "Graphics"], Cell[11312, 412, 130, 3, 70, "Output"] }, Open ]], Cell[11457, 418, 401, 5, 74, "Text"], Cell[11861, 425, 156, 2, 42, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[12054, 432, 35, 0, 36, "Section"], Cell[12092, 434, 278, 7, 42, "Text"], Cell[12373, 443, 202, 4, 42, "Text"], Cell[12578, 449, 77, 0, 26, "Text"], Cell[12658, 451, 164, 2, 42, "Text"] }, Closed]], Cell[CellGroupData[{ Cell[12859, 458, 29, 0, 36, "Section"], Cell[12891, 460, 50, 0, 26, "Text"], Cell[CellGroupData[{ Cell[12966, 464, 337, 5, 111, "Input"], Cell[13306, 471, 277, 4, 70, "Output"] }, Open ]], Cell[13598, 478, 119, 3, 26, "Text"], Cell[13720, 483, 203, 4, 42, "Text"], Cell[CellGroupData[{ Cell[13948, 491, 91, 1, 51, "Input"], Cell[14042, 494, 176, 3, 70, "Output"] }, Open ]], Cell[14233, 500, 133, 3, 42, "Text"], Cell[14369, 505, 190, 4, 42, "Text"], Cell[CellGroupData[{ Cell[14584, 513, 58, 1, 47, "Input"], Cell[14645, 516, 176, 3, 70, "Message"], Cell[14824, 521, 57, 1, 70, "Output"] }, Open ]], Cell[14896, 525, 228, 4, 58, "Text"], Cell[CellGroupData[{ Cell[15149, 533, 90, 1, 47, "Input"], Cell[15242, 536, 149, 2, 70, "Output"] }, Open ]], Cell[15406, 541, 51, 0, 26, "Text"], Cell[15460, 543, 65, 0, 26, "Text"], Cell[15528, 545, 146, 3, 42, "Text"] }, Closed]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)