(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 7.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[      4654,        165]
NotebookOptionsPosition[      4131,        144]
NotebookOutlinePosition[      4474,        159]
CellTagsIndexPosition[      4431,        156]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
 RowBox[{
  RowBox[{
   RowBox[{"z", "[", "t_", "]"}], ":=", 
   RowBox[{"Exp", "[", 
    FractionBox[
     RowBox[{"-", 
      SuperscriptBox["t", "2"]}], "2"], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"D", "[", 
  RowBox[{
   RowBox[{"z", "[", "t", "]"}], ",", "t"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{
    RowBox[{"z", "[", "t", "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "2"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{
    RowBox[{"z", "[", "t", "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "3"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{
    RowBox[{"z", "[", "t", "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "4"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{
    RowBox[{"z", "[", "t", "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "5"}], "}"}]}], "]"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Simplify", "[", 
  RowBox[{"D", "[", 
   RowBox[{
    RowBox[{"z", "[", "t", "]"}], ",", 
    RowBox[{"{", 
     RowBox[{"t", ",", "6"}], "}"}]}], "]"}], "]"}]}], "Input",
 CellChangeTimes->{{3.488876588302377*^9, 3.488876605271453*^9}, {
  3.4888766688351736`*^9, 3.4888767258675184`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", 
     FractionBox[
      SuperscriptBox["t", "2"], "2"]}]]}], " ", "t"}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["t", "2"], "2"]}]], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "1"}], "+", 
    SuperscriptBox["t", "2"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", 
     FractionBox[
      SuperscriptBox["t", "2"], "2"]}]]}], " ", "t", " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "3"}], "+", 
    SuperscriptBox["t", "2"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["t", "2"], "2"]}]], " ", 
  RowBox[{"(", 
   RowBox[{"3", "-", 
    RowBox[{"6", " ", 
     SuperscriptBox["t", "2"]}], "+", 
    SuperscriptBox["t", "4"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   SuperscriptBox["\[ExponentialE]", 
    RowBox[{"-", 
     FractionBox[
      SuperscriptBox["t", "2"], "2"]}]]}], " ", "t", " ", 
  RowBox[{"(", 
   RowBox[{"15", "-", 
    RowBox[{"10", " ", 
     SuperscriptBox["t", "2"]}], "+", 
    SuperscriptBox["t", "4"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[ExponentialE]", 
   RowBox[{"-", 
    FractionBox[
     SuperscriptBox["t", "2"], "2"]}]], " ", 
  RowBox[{"(", 
   RowBox[{
    RowBox[{"-", "15"}], "+", 
    RowBox[{"45", " ", 
     SuperscriptBox["t", "2"]}], "-", 
    RowBox[{"15", " ", 
     SuperscriptBox["t", "4"]}], "+", 
    SuperscriptBox["t", "6"]}], ")"}]}]], "Output",
 CellChangeTimes->{{3.4888766626788054`*^9, 3.4888767264925303`*^9}}]
}, Open  ]]
},
WindowSize->{616, 750},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 1404, 42, 171, "Input"],
Cell[1974, 66, 249, 7, 42, "Output"],
Cell[2226, 75, 320, 10, 45, "Output"],
Cell[2549, 87, 352, 11, 45, "Output"],
Cell[2904, 100, 362, 11, 45, "Output"],
Cell[3269, 113, 396, 12, 45, "Output"],
Cell[3668, 127, 447, 14, 45, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)