(* 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[ 5589334, 91689] NotebookOptionsPosition[ 5587564, 91634] NotebookOutlinePosition[ 5587982, 91651] CellTagsIndexPosition[ 5587939, 91648] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ StyleBox[ RowBox[{"(*", " ", RowBox[{ "Need", " ", "to", " ", "load", " ", "RealTime3D", " ", "package", " ", "in", " ", "order", " ", "to", " ", "rotate", " ", "the", " ", "surface", " ", "plots", " ", "\[IndentingNewLine]", "hidden", " ", "in", " ", "the", " ", "grouped", " ", "cells"}], " ", "*)"}], FontColor->RGBColor[1, 0, 0]]], "Input"], Cell[CellGroupData[{ Cell["\<\ Here are examples for surface plots and their corresponding contour plots. Some things to look for: \t1. Identifying a local maximum and minimum from the contour plot. \t2. Identifying saddle point from the contour plot. \t3. Identifying steepness/flatness of a function from its contour plot. \t4. Identifying common symmetries in contour plot and surface plot.\ \>", "Section", FontSize->18, FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{ RowBox[{"Clear", "[", "f", "]"}], ";"}], " "}], "\[IndentingNewLine]", RowBox[{ StyleBox[ RowBox[{ RowBox[{"f", "[", RowBox[{"x_", ",", "y_"}], "]"}], " ", "=", " ", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], " ", RowBox[{"Sin", "[", "y", "]"}]}]}], FontColor->RGBColor[1, 0, 0]], " ", ";"}], "\[IndentingNewLine]", RowBox[{"g1", " ", "=", " ", RowBox[{"ContourPlot", "[", RowBox[{ RowBox[{"f", "[", RowBox[{"x", ",", "y"}], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", RowBox[{"-", "Pi"}], ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"y", ",", RowBox[{ RowBox[{"-", "2"}], "Pi"}], ",", RowBox[{"2", "Pi"}]}], "}"}], ",", RowBox[{"PlotPoints", "\[Rule]", "50"}], ",", RowBox[{"AspectRatio", "\[Rule]", "Automatic"}]}], "]"}]}], "\[IndentingNewLine]", RowBox[{"g2", " ", "=", " ", RowBox[{"Plot3D", "[", RowBox[{ 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