(* 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[      4712,        167]
NotebookOptionsPosition[      4143,        142]
NotebookOutlinePosition[      4477,        157]
CellTagsIndexPosition[      4434,        154]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Example  1", "Title",
 CellChangeTimes->{{3.455967303412877*^9, 3.455967306677573*^9}}],

Cell[BoxData[
 RowBox[{"Plot3D", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"x", "^", "2"}], "*", "y"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", "0", ",", "1"}], "}"}], ",", 
   RowBox[{"RegionFunction", "\[Rule]", 
    RowBox[{"Function", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", 
      RowBox[{
       RowBox[{"x", "^", "2"}], "<", "y", "<", 
       RowBox[{"Sqrt", "[", "x", "]"}]}]}], "]"}]}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4559656486523027`*^9, 3.455965738679627*^9}, {
  3.4559658011545687`*^9, 3.455965986967208*^9}},
 FontSize->24]
}, Open  ]],

Cell[CellGroupData[{

Cell["Example 2", "Title",
 CellChangeTimes->{{3.4559673269497337`*^9, 3.4559673281752157`*^9}}],

Cell[BoxData[
 RowBox[{"Plot3D", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Cos", "[", "x", "]"}], "*", 
    RowBox[{"Cos", "[", "y", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", 
     RowBox[{"2", "Pi"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", "0", ",", "Pi"}], "}"}], ",", 
   RowBox[{"RegionFunction", "\[Rule]", 
    RowBox[{"Function", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", 
      RowBox[{"y", "<", "x", "<", 
       RowBox[{
        RowBox[{"2", "Pi"}], "-", "y"}]}]}], "]"}]}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4559664351718683`*^9, 3.455966470258646*^9}},
 FontSize->24]
}, Open  ]],

Cell[CellGroupData[{

Cell["Example 3 (#53)", "Title",
 CellChangeTimes->{{3.455967897228142*^9, 3.4559679008457823`*^9}}],

Cell[BoxData[
 RowBox[{"Plot3D", "[", 
  RowBox[{
   RowBox[{"Exp", "[", 
    RowBox[{"-", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"x", "^", "2"}], "+", 
        RowBox[{"y", "^", "2"}]}], ")"}], "^", "2"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", 
     RowBox[{"1", "/", "2"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", "0", ",", 
     RowBox[{"1", "/", "2"}]}], "}"}], ",", 
   RowBox[{"RegionFunction", "\[Rule]", 
    RowBox[{"Function", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"x", ",", "y", ",", "z"}], "}"}], ",", 
      RowBox[{
       RowBox[{
        RowBox[{"x", "^", "2"}], "+", 
        RowBox[{"y", "^", "2"}]}], "<", 
       RowBox[{"1", "/", "4"}]}]}], "]"}]}], ",", 
   RowBox[{"AxesLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"x", ",", "y", ",", "z"}], "}"}]}]}], "]"}]], "Input",
 CellChangeTimes->{{3.4559674281771107`*^9, 3.455967475329729*^9}},
 FontSize->24],

Cell[BoxData[
 RowBox[{"NIntegrate", "[", 
  RowBox[{
   RowBox[{"Exp", "[", 
    RowBox[{"-", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{
        RowBox[{"x", "^", "2"}], "+", 
        RowBox[{"y", "^", "2"}]}], ")"}], "^", "2"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", 
     RowBox[{"1", "/", "2"}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"y", ",", "0", ",", 
     RowBox[{"Sqrt", "[", 
      RowBox[{
       RowBox[{"1", "/", "4"}], "-", 
       RowBox[{"x", "^", "2"}]}], "]"}]}], "}"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.455967829744416*^9, 3.455967883127473*^9}},
 FontSize->24]
}, Open  ]]
},
WindowSize->{640, 652},
WindowMargins->{{4, Automatic}, {Automatic, 4}},
FrontEndVersion->"6.0 for Mac OS X x86 (32-bit) (June 19, 2007)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[590, 23, 93, 1, 76, "Title"],
Cell[686, 26, 784, 22, 160, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[1507, 53, 96, 1, 76, "Title"],
Cell[1606, 56, 784, 23, 160, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2427, 84, 100, 1, 76, "Title"],
Cell[2530, 87, 966, 30, 190, "Input"],
Cell[3499, 119, 628, 20, 100, "Input"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)