(* 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[     16478,        622]
NotebookOptionsPosition[     12850,        519]
NotebookOutlinePosition[     13251,        536]
CellTagsIndexPosition[     13208,        533]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell["Getting Started, Constants, and Functions", "Title"],

Cell["", "Subsubtitle",
 CellChangeTimes->{{3.454518688515625*^9, 3.454518689375*^9}}],

Cell[TextData[{
 "Getting around - Using ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " as a calculator"
}], "Subsubsection"],

Cell["\<\
To enter an expression, just start typing!  You can enter multiple \
expressions by pressing the \"Enter\" key after each one.  To evaluate \
expressions, press \"Shift+Enter\".  If you don't want to see the output of \
your expression, follow the expression with a semi-colon,  \" ; \"\
\>", "Text"],

Cell[BoxData[{
 RowBox[{"1", "+", "2"}], "\[IndentingNewLine]", 
 RowBox[{"2", "+", "2"}]}], "Input"],

Cell[BoxData[
 RowBox[{
  RowBox[{"3", "^", "2"}], "+", 
  RowBox[{"4", "^", "2"}]}]], "Input"],

Cell["\<\
All functions, commands, and mathematical constants start with a capital \
letter.  Common examples are Sin, Cos, Sqrt, Pi, E, etc.\
\>", "Text"],

Cell[TextData[{
 "All functions and commands use ",
 StyleBox["square brackets",
  FontSlant->"Italic"],
 " ",
 StyleBox["not",
  FontWeight->"Bold"],
 " ",
 StyleBox["parentheses",
  FontSlant->"Italic"],
 ".  Parentheses are used ",
 StyleBox["only",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 " to show order of operations."
}], "Text"],

Cell[BoxData[
 RowBox[{"Sqrt", "[", "9", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Sin", "[", 
  RowBox[{"Pi", "/", "2"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"ArcCos", "[", "0", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Exp", "[", "4", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Exp", "[", 
  RowBox[{"I", "*", "Pi"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Sqrt", "[", "5", "]"}]], "Input"],

Cell[TextData[{
 "Notice in the last expression, we asked ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " what the square root of 5 was.  It responded by telling us that it is the \
square root of 5!  What we really wanted was a numerical approximation to the \
square root of 5.  To do this, use the N[ ] command.  "
}], "Text"],

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"Sqrt", "[", "5", "]"}], "]"}]], "Input"],

Cell["\<\
What if we wanted more digits?  Lets look at the help file for the command N \
[ ]\
\>", "Text"],

Cell[BoxData[
 RowBox[{"?", "N"}]], "Input"],

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{
   RowBox[{"Sqrt", "[", "5", "]"}], ",", "20"}], "]"}]], "Input"],

Cell[TextData[{
 "Lets see if ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " knows Pi to 100 digits!"
}], "Text"],

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"Pi", ",", "100"}], "]"}]], "Input"],

Cell[TextData[{
 "The percent sign in ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " means 'the previous output', and it is sometimes quite handy.  For example,"
}], "Text"],

Cell[BoxData[
 RowBox[{"Sqrt", "[", "924", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"N", "[", 
  RowBox[{"%", ",", "10"}], "]"}]], "Input"],

Cell["Cells", "Subsubsection"],

Cell[TextData[{
 "Information within a ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " notebook is contained in cells.  Different cells have different \
properties.  The default cell type is \"Input\".  When an input cell is \
evaluated, it produces an \"Output\" cell.  This is what the small colored \
In[ ]:= and Out[ ]:= mean on the left side of the notebook.  To create a new \
cell, move the mouse cursor until it becomes horizontal, click, and then \
start typing.  \nCreate a new cell between this line ---------------"
}], "Text"],

Cell["and this line ----------------------------------------------", "Text"],

Cell[TextData[{
 "To create a text cell, (like this one), move the mouse until it becomes \
horizontal, click, then select the menu item:",
 StyleBox[" ",
  FontVariations->{"Underline"->True}],
 StyleBox["Format",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 StyleBox[",",
  FontVariations->{"Underline"->True}],
 " then ",
 StyleBox["Style",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", then ",
 StyleBox["Text",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", then type away!  Try inserting a text cell right after this one.  "
}], "Text"],

Cell[TextData[{
 "To change the type of a cell, click on the blue cell marker on the right of \
the screen, then go to ",
 StyleBox["Format",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", ",
 StyleBox["Style",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", and choose a type."
}], "Text"],

Cell["Defining constants and vectors", "Subsubsection"],

Cell["\<\
To define constants (numbers or vectors) use a single equals sign.\
\>", "Text"],

Cell[BoxData[
 RowBox[{"a", "=", "5"}]], "Input"],

Cell[BoxData[
 RowBox[{"b", "=", "2"}]], "Input"],

Cell[TextData[{
 "Vectors are entered using ",
 StyleBox["curly brackets",
  FontSlant->"Italic"],
 ".  For example, the vector ",
 StyleBox["v",
  FontWeight->"Bold"],
 " = ",
 StyleBox["i ",
  FontWeight->"Bold"],
 "+ 3 ",
 StyleBox["j ",
  FontWeight->"Bold"],
 "- 2 ",
 StyleBox["k ",
  FontWeight->"Bold"],
 "would be entered as"
}], "Text"],

Cell[BoxData[
 RowBox[{"v", "=", 
  RowBox[{"{", 
   RowBox[{"1", ",", "3", ",", 
    RowBox[{"-", "2"}]}], "}"}]}]], "Input"],

Cell["\<\
Once defined, you can use your constants anywhere in the notebook!\
\>", "Text"],

Cell[BoxData[
 RowBox[{"a", "+", "b"}]], "Input"],

Cell[BoxData[
 RowBox[{"a", "*", "v"}]], "Input"],

Cell[BoxData[
 RowBox[{"a", "^", "2"}]], "Input"],

Cell[TextData[{
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " can do dot and cross products for vectors.  It can also find the length of \
a vector by using the command Norm[ ]"
}], "Text"],

Cell[BoxData[
 RowBox[{"u", "=", 
  RowBox[{"{", 
   RowBox[{"2", ",", 
    RowBox[{"-", "1"}], ",", "1"}], "}"}]}]], "Input"],

Cell[BoxData[
 RowBox[{"Dot", "[", 
  RowBox[{"u", ",", "v"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Cross", "[", 
  RowBox[{"u", ",", "v"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Norm", "[", "u", "]"}], "\[IndentingNewLine]"}]], "Input"],

Cell["\<\
To clear a constant so it is again a symbolic variable, use \" = . \".\
\>", "Text"],

Cell[BoxData[
 RowBox[{"a", "=."}]], "Input"],

Cell[BoxData[
 RowBox[{"a", "+", "b"}]], "Input"],

Cell[BoxData[
 RowBox[{"b", "=."}]], "Input"],

Cell[BoxData[
 RowBox[{"a", "+", "b"}]], "Input"],

Cell["\<\
If you want to clear everything you have done from memory, use the command \
Quit\
\>", "Text"],

Cell[BoxData["u"], "Input"],

Cell[BoxData["Quit"], "Input"],

Cell[BoxData["u"], "Input"],

Cell["\<\
Notice how the numbers in the In[ ] and Out[ ]  were reset to 1.\
\>", "Text"],

Cell["Defining functions", "Subsubsection"],

Cell["\<\
To define a function, use an underscore after each argument name on the left \
hand side of the = but not on the right.\
\>", "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "[", "x_", "]"}], "=", 
  RowBox[{
   RowBox[{"x", "^", "2"}], "-", "1"}]}]], "Input"],

Cell["We can now evaluate f for any x value.", "Text"],

Cell[BoxData[
 RowBox[{"f", "[", "5", "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"f", "[", 
  RowBox[{"Sqrt", "[", "9", "]"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"f", "[", 
  RowBox[{"a", "+", "b"}], "]"}]], "Input"],

Cell["\<\
We can define functions of multiple variables in the same way.\
\>", "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{"g", "[", 
   RowBox[{"x_", ",", "y_"}], "]"}], "=", 
  RowBox[{
   RowBox[{"x", "^", "2"}], "+", 
   RowBox[{"y", "^", "2"}], "-", "1"}]}]], "Input"],

Cell[BoxData[
 RowBox[{"g", "[", 
  RowBox[{"0", ",", "0"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"g", "[", 
  RowBox[{"1", ",", "1"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"g", "[", 
  RowBox[{"x", ",", "1"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"g", "[", 
  RowBox[{"2", ",", "y"}], "]"}]], "Input"],

Cell["Working with expressions", "Subsubsection"],

Cell["\<\
There are five commands that are very helpful when you want to simplify \
expressions.  They are Factor[ ] , Expand[ ] , Together[ ] , Apart[ ] , and \
Simplify[ ].\
\>", "Text"],

Cell["\<\
Factor[ ] and Expand[ ] do just what they sound like - they factor or expand \
polynomials.\
\>", "Text"],

Cell[BoxData[
 RowBox[{"Factor", "[", 
  RowBox[{
   RowBox[{"x", "^", "3"}], "-", 
   RowBox[{"7", 
    RowBox[{"x", "^", "2"}]}], "+", 
   RowBox[{"16", "x"}], "-", "12"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Factor", "[", 
  RowBox[{"f", "[", "x", "]"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Expand", "[", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"x", "-", "3"}], ")"}], "^", "2"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Expand", "[", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"x", "-", "1"}], ")"}], "^", "9"}], "]"}]], "Input"],

Cell["\<\
If you want the powers of x in decreasing order, you can add the command \" \
//TraditionalForm \"\
\>", "Text"],

Cell[BoxData[
 RowBox[{
  RowBox[{"Expand", "[", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"x", "-", "1"}], ")"}], "^", "9"}], "]"}], "//", 
  "TraditionalForm"}]], "Input"],

Cell["\<\
The commands Apart[ ] and Together[ ] are helpful when working with fractions.\
\>", "Text"],

Cell[BoxData[
 RowBox[{"Together", "[", 
  RowBox[{
   RowBox[{"a", "/", "b"}], "+", 
   RowBox[{"c", "/", "d"}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"Apart", "[", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"b", "*", "c"}], "+", 
     RowBox[{"a", "*", "d"}]}], ")"}], "/", 
   RowBox[{"(", 
    RowBox[{"b", "*", "d"}], ")"}]}], "]"}]], "Input"],

Cell["\<\
Remember Partial fractions?  What is the Partial Fraction Decomposition of 1 \
/ ( (x-1)(x+1) ) ?\
\>", "Text"],

Cell[BoxData[
 RowBox[{"Apart", "[", 
  RowBox[{"1", "/", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"x", "-", "1"}], ")"}], "*", 
     RowBox[{"(", 
      RowBox[{"x", "+", "1"}], ")"}]}], ")"}]}], "]"}]], "Input"],

Cell["\<\
The last command, Simplify[ ], tries to find the \"Simplest\" form of an \
expression.\
\>", "Text"],

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"x", "^", "2"}], "+", 
     RowBox[{"2", "*", "x", "*", "y"}], "+", 
     RowBox[{"y", "^", "2"}]}], ")"}], "/", 
   RowBox[{"(", 
    RowBox[{"x", "+", "y"}], ")"}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Sin", "[", "x", "]"}], "^", "2"}], "+", 
  RowBox[{
   RowBox[{"Cos", "[", "x", "]"}], "^", "2"}]}]], "Input"],

Cell["\<\
OK, this should be equal to 1, right?  Remember that % means 'previous \
output', and lets use Simplify[ ]\
\>", "Text"],

Cell[BoxData[
 RowBox[{"Simplify", "[", "%", "]"}]], "Input"],

Cell["How do I save?", "Subsubsection"],

Cell[TextData[{
 "Before saving, go to the menu item ",
 StyleBox["Cell",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", then ",
 StyleBox["Delete all output",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", then click OK.  This is ",
 StyleBox["very",
  FontWeight->"Bold"],
 " important, especially if your ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 " notebook has graphs.  Doing this will delete the graphs and other output, \
but it will leave all of your commands.  This ",
 StyleBox["greatly",
  FontWeight->"Bold"],
 " reduces the size of the file.  If you submit homework for class without \
doing this first, it will not be accepted\[LongDash]if it is too large, it \
won't even enter the colorado.edu system\[LongDash]and you will be asked to \
submit again."
}], "Text",
 CellChangeTimes->{{3.452861876496085*^9, 3.452861890413157*^9}, {
  3.454518803*^9, 3.454518861453125*^9}}],

Cell[TextData[{
 "To save, go to ",
 StyleBox["File",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ", then ",
 StyleBox[" Save as",
  FontWeight->"Bold",
  FontSlant->"Italic",
  FontVariations->{"Underline"->True}],
 ".  If you are in the lab, you should save to the desktop, e-mail the file \
to yourself and your instructor, then delete the file from the desktop."
}], "Text"]
},
ScreenStyleEnvironment->"Working",
WindowSize->{961, 858},
WindowMargins->{{-2, Automatic}, {Automatic, 0}},
ShowSelection->True,
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)",
StyleDefinitions->"DemoText.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[545, 20, 58, 0, 56, "Title"],
Cell[606, 22, 86, 1, 56, "Subsubtitle"],
Cell[695, 25, 133, 5, 44, "Subsubsection"],
Cell[831, 32, 310, 5, 43, "Text"],
Cell[1144, 39, 101, 2, 59, "Input"],
Cell[1248, 43, 95, 3, 38, "Input"],
Cell[1346, 48, 155, 3, 25, "Text"],
Cell[1504, 53, 382, 16, 25, "Text"],
Cell[1889, 71, 57, 1, 38, "Input"],
Cell[1949, 74, 80, 2, 38, "Input"],
Cell[2032, 78, 59, 1, 38, "Input"],
Cell[2094, 81, 56, 1, 38, "Input"],
Cell[2153, 84, 80, 2, 38, "Input"],
Cell[2236, 88, 57, 1, 38, "Input"],
Cell[2296, 91, 336, 7, 43, "Text"],
Cell[2635, 100, 85, 2, 38, "Input"],
Cell[2723, 104, 106, 3, 25, "Text"],
Cell[2832, 109, 44, 1, 38, "Input"],
Cell[2879, 112, 110, 3, 38, "Input"],
Cell[2992, 117, 121, 5, 25, "Text"],
Cell[3116, 124, 80, 2, 38, "Input"],
Cell[3199, 128, 181, 5, 25, "Text"],
Cell[3383, 135, 59, 1, 38, "Input"],
Cell[3445, 138, 78, 2, 38, "Input"],
Cell[3526, 142, 30, 0, 44, "Subsubsection"],
Cell[3559, 144, 546, 10, 91, "Text"],
Cell[4108, 156, 76, 0, 25, "Text"],
Cell[4187, 158, 668, 22, 43, "Text"],
Cell[4858, 182, 373, 13, 25, "Text"],
Cell[5234, 197, 55, 0, 44, "Subsubsection"],
Cell[5292, 199, 90, 2, 25, "Text"],
Cell[5385, 203, 49, 1, 38, "Input"],
Cell[5437, 206, 49, 1, 38, "Input"],
Cell[5489, 209, 346, 17, 25, "Text"],
Cell[5838, 228, 126, 4, 38, "Input"],
Cell[5967, 234, 90, 2, 25, "Text"],
Cell[6060, 238, 49, 1, 38, "Input"],
Cell[6112, 241, 49, 1, 38, "Input"],
Cell[6164, 244, 49, 1, 38, "Input"],
Cell[6216, 247, 195, 5, 25, "Text"],
Cell[6414, 254, 126, 4, 38, "Input"],
Cell[6543, 260, 79, 2, 38, "Input"],
Cell[6625, 264, 81, 2, 38, "Input"],
Cell[6709, 268, 93, 2, 59, "Input"],
Cell[6805, 272, 94, 2, 25, "Text"],
Cell[6902, 276, 45, 1, 38, "Input"],
Cell[6950, 279, 49, 1, 38, "Input"],
Cell[7002, 282, 45, 1, 38, "Input"],
Cell[7050, 285, 49, 1, 38, "Input"],
Cell[7102, 288, 105, 3, 25, "Text"],
Cell[7210, 293, 27, 0, 38, "Input"],
Cell[7240, 295, 30, 0, 38, "Input"],
Cell[7273, 297, 27, 0, 38, "Input"],
Cell[7303, 299, 88, 2, 25, "Text"],
Cell[7394, 303, 43, 0, 44, "Subsubsection"],
Cell[7440, 305, 143, 3, 25, "Text"],
Cell[7586, 310, 125, 4, 38, "Input"],
Cell[7714, 316, 54, 0, 25, "Text"],
Cell[7771, 318, 54, 1, 38, "Input"],
Cell[7828, 321, 85, 2, 38, "Input"],
Cell[7916, 325, 77, 2, 38, "Input"],
Cell[7996, 329, 86, 2, 25, "Text"],
Cell[8085, 333, 184, 6, 38, "Input"],
Cell[8272, 341, 77, 2, 38, "Input"],
Cell[8352, 345, 77, 2, 38, "Input"],
Cell[8432, 349, 77, 2, 38, "Input"],
Cell[8512, 353, 77, 2, 38, "Input"],
Cell[8592, 357, 49, 0, 44, "Subsubsection"],
Cell[8644, 359, 188, 4, 25, "Text"],
Cell[8835, 365, 115, 3, 25, "Text"],
Cell[8953, 370, 191, 6, 38, "Input"],
Cell[9147, 378, 87, 2, 38, "Input"],
Cell[9237, 382, 131, 4, 38, "Input"],
Cell[9371, 388, 131, 4, 38, "Input"],
Cell[9505, 394, 122, 3, 25, "Text"],
Cell[9630, 399, 175, 6, 38, "Input"],
Cell[9808, 407, 102, 2, 25, "Text"],
Cell[9913, 411, 132, 4, 38, "Input"],
Cell[10048, 417, 231, 8, 38, "Input"],
Cell[10282, 427, 121, 3, 25, "Text"],
Cell[10406, 432, 236, 8, 38, "Input"],
Cell[10645, 442, 110, 3, 25, "Text"],
Cell[10758, 447, 280, 9, 38, "Input"],
Cell[11041, 458, 157, 5, 38, "Input"],
Cell[11201, 465, 130, 3, 25, "Text"],
Cell[11334, 470, 61, 1, 38, "Input"],
Cell[11398, 473, 39, 0, 44, "Subsubsection"],
Cell[11440, 475, 983, 27, 61, "Text"],
Cell[12426, 504, 420, 13, 43, "Text"]
}
]
*)

(* End of internal cache information *)