(************** Content-type: application/mathematica ************** 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[ 7870, 241]*) (*NotebookOutlinePosition[ 8513, 263]*) (* CellTagsIndexPosition[ 8469, 259]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ Go through this entire notebook. Answer all the questions posed. On the You Try It, you MUST insert your own NEW values or functions. Print out your results and attach to a 1-page summary of what you learned \ from this lab.\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Getting Started Plotting Surfaces in 3D ", "Title"], Cell[TextData[StyleBox["Chapter 10, Section 4", FontFamily->"Arial", FontSize->16, FontWeight->"Bold"]], "Text"], Cell[CellGroupData[{ Cell["Introduction", "Section"], Cell[TextData[{ "OBJECTIVE: To learn to use ", StyleBox["Mathematica", FontSlant->"Italic"], " to plot cylinders and quadric surfaces." }], "Text"], Cell[CellGroupData[{ Cell["Technology Guidelines", "Subsection", CellDingbat->"\[LightBulb]"], Cell[TextData[{ StyleBox["NOTE: If you have just finished a module, restart ", CellFrame->True, Background->None], StyleBox["Mathematica", CellFrame->True, FontSlant->"Italic", Background->None], StyleBox[" before executing a new module.\nTO OPEN CELLS, put your cursor \ on the right cell bracket and double click.", CellFrame->True, Background->None], "\nTO STOP AN EXECUTION\n\tSelect the ", StyleBox["Kernel", FontSlant->"Italic"], " pull-down menu and click on ", StyleBox["Abort Evaluation.\n", FontSlant->"Italic"], "ORDER OF EXECUTION\n\tExecute cells in the order given. Do not skip any \ Input cells within a given notebook.\nSAVING NOTEBOOKS\n\tYou can save \ anytime to any directory you choose, and it is wise to save often.\n\t\ However, before you do your final save, delete all your output by selecting \ the \n\t ", StyleBox["Delete All Output", FontSlant->"Italic"], " selection under the ", StyleBox["Kernel", FontSlant->"Italic"], " pull-down menu.\nEXPERIENCING MAJOR PROBLEMS\n\tSave if appropriate, and \ then shut down ", StyleBox["Mathematica", FontSlant->"Italic"], " and start it up again." }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Cylinders and Quadric Surfaces", "Section"], Cell[TextData[{ "When you look at the equations for cylinders or quadric surfaces, notice \ that they are not in the standard form for graphing on most graphing \ calculators or software packages, because you cannot usually solve explicity \ for the ", StyleBox["z", FontSlant->"Italic"], " variable. To get around this, we use a special command called ", StyleBox["ContourPlot3D", FontWeight->"Bold"], " after we first read in a package to enable it to work. In the next \ chapter (Chapter 11), you will learn about contour plots, but, for now, just \ think of this as a command to get the job done." }], "Text"], Cell[BoxData[{ RowBox[{\(Off[General::spell]\), " "}], "\n", \(Off[ General::spell1]\), "\n", RowBox[{"<<", StyleBox[ RowBox[{"Graphics", StyleBox["`", "MB"], "ContourPlot3D", StyleBox["`", "MB"]}]]}]}], "Input"], Cell[TextData[{ "Suppose that you want to plot the cylinder ", Cell[BoxData[ \(y\ = \ x\^2\)]], ". We think of this as ", Cell[BoxData[ \(TraditionalForm\`f(x, y, z) = \(y - x\^2 = 0\)\)]], ", and we ask for a ", StyleBox["ContourPlot3D ", FontWeight->"Bold"], "of this function. The default is to plot only the contour when the \ function specified is 0. Note that we must specify the values of ", StyleBox["x, y,", FontSlant->"Italic"], " and ", StyleBox["z", FontSlant->"Italic"], " overwhich to extend our plot, even though ", StyleBox["z", FontSlant->"Italic"], " does not appear in the function itself." }], "Text"], Cell[BoxData[{ \(Clear[x, y, z, function]\), "\n", \(\(function = y - x\^2;\)\), "\n", \(\(ContourPlot3D[ function, \n\ \ \ {x, \(-3\), 3}, \ {y, \(-2\), 2}, \ {z, \(-4\), 4}, \nAxes -> True, AxesLabel -> {x, y, z}, Boxed -> False];\)\)}], "Input"], Cell["Let's try another cylinder.", "Text"], Cell[BoxData[{ \(\(function = \ y\^2\ - 4\ z\^2\ - 1;\)\), "\n", \(\(ContourPlot3D[\ function, \n\ {x, \(-2\), 2}, \ {y, \(-2\), 2}, \ {z, \(-2\), 2}, Axes -> True, AxesLabel -> {x, y, z}, Boxed -> False];\)\)}], "Input"], Cell[BoxData[ \(TextForm\`Next\ we\ will\ plot\ the\ quadric\ surface, \ z\^2 - 2 x\^2 - 3 y\^2 = \ 0. \)], "Text"], Cell[BoxData[{ \(\(function = z\^2 - 2 x\^2 - 3 y\^2;\)\), "\n", \(\(ContourPlot3D[ function, \n\ \ \ {x, \(-3\), 3}, \ {y, \(-2\), 2}, \ {z, \(-4\), 4}, \n\ \ \ \ \ Axes -> True, AxesLabel -> {x, y, z}, Boxed -> False];\)\)}], "Input"], Cell["Here's an ellipsoid.", "Text"], Cell[BoxData[{ \(\(function = x^2\ + 4 y^2\ + \ z^2\ - 4;\)\), "\n", \(\(ContourPlot3D[\ \ function, \n\ {x, \(-2\), 2}, \ {y, \(-1\), 1}, \ {z, \(-2\), 2}, Axes -> True, AxesLabel -> {x, y, z}, Boxed -> False];\)\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["You Try It", "Section"], Cell[TextData[{ "To plot the cylinders and quadric surfaces, go back to any of the plots \ and alter the functions as you wish. Be sure to use correct terminology. Note \ that some 3-D plots take quite a bit of time to plot. If you find you are \ waiting too long, you can always pull down the Kernel menu and select Abort \ Evaluation. To experiment, replace the function in red with another function \ of ", Cell[BoxData[ \(TraditionalForm\`x, \ y\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`z\)]], ". Be certain to use correct terminology. You might want to see what this \ one looks like first, before putting in a different function. Why isn't this \ a quadric surface?" }], "Text"], Cell[BoxData[ RowBox[{ RowBox[{"function", "=", StyleBox[\(z\^3 - 2 x\^2 + 3 y\^2\), FontColor->RGBColor[1, 0, 0]]}], ";", "\n", \(ContourPlot3D[ function, \n\ \ \ {x, \(-3\), 3}, \ {y, \(-2\), 2}, \ {z, \(-4\), 4}, \n\ \ \ \ \ Axes -> True, AxesLabel -> {x, y, z}, Boxed -> False]\), ";"}]], "Input"] }, Closed]] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 695}}, WindowSize->{496, 537}, WindowMargins->{{0, Automatic}, {Automatic, 0}} ] (******************************************************************* 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. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1705, 50, 255, 5, 107, "Subsubtitle"], Cell[CellGroupData[{ Cell[1985, 59, 57, 0, 170, "Title"], Cell[2045, 61, 118, 3, 37, "Text"], Cell[CellGroupData[{ Cell[2188, 68, 31, 0, 59, "Section"], Cell[2222, 70, 157, 5, 33, "Text"], Cell[CellGroupData[{ Cell[2404, 79, 74, 1, 47, "Subsection"], Cell[2481, 82, 1206, 33, 242, "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[3736, 121, 49, 0, 39, "Section"], Cell[3788, 123, 631, 13, 90, "Text"], Cell[4422, 138, 288, 9, 70, "Input"], Cell[4713, 149, 676, 21, 71, "Text"], Cell[5392, 172, 290, 6, 110, "Input"], Cell[5685, 180, 43, 0, 33, "Text"], Cell[5731, 182, 250, 4, 70, "Input"], Cell[5984, 188, 126, 2, 32, "Text"], Cell[6113, 192, 275, 5, 90, "Input"], Cell[6391, 199, 36, 0, 33, "Text"], Cell[6430, 201, 260, 4, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[6727, 210, 29, 0, 39, "Section"], Cell[6759, 212, 713, 15, 109, "Text"], Cell[7475, 229, 367, 8, 90, "Input"] }, Closed]] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)