(* 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[ 2374626, 41916] NotebookOptionsPosition[ 2354849, 41265] NotebookOutlinePosition[ 2356449, 41314] CellTagsIndexPosition[ 2356225, 41306] WindowFrame->Normal ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[StyleBox["Examples of Useful Stuff", FontColor->RGBColor[1, 0, 1]]], "Title"], Cell[TextData[StyleBox["Updated for version 6.01 July 07, last modified: 5 \ Feb 08\nPlease let me know if you find an error.... wraggj@cofc.edu", FontColor->RGBColor[0, 0, 1]]], "Subsubtitle", CellChangeTimes->{{3.3945742575629063`*^9, 3.394574275294139*^9}, { 3.394903136392393*^9, 3.394903149648065*^9}, {3.41018918541074*^9, 3.410189190604022*^9}, {3.411222540354761*^9, 3.411222546112529*^9}}], Cell[CellGroupData[{ Cell["Getting Started-Numerical Calculations", "Section", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Just type in a simple mathematical expression, as below, and hit enter. You \ will notice that it takes a while for the answer to appear. That is because \ the kernel doesn't start until you actually ask it to do something. Move the \ input point to any place in the 5+18 below and push enter to see what I \ mean.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"5", "+", "18"}]], "Input", AspectRatioFixed->True], Cell[BoxData["23"], "Output", CellChangeTimes->{{3.394575589663537*^9, 3.394575614202579*^9}}] }, Open ]], Cell["\<\ Notice also that Mathematica includes a numbered sequence of your input and \ its output. If you put the insertion point on the same line again and hit \ enter it will change to input and output [2]. Try it. \ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Try some other simple math. For example raising 3 to the 100th power. \ Having entered it and gotten the answer you can easily go back and change the \ 100 to something else, just like using a word processor. Change the 100 to \ 97 and hit enter. The answer is exact. Your calculator can't do that.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox["3", "100"]], "Input", AspectRatioFixed->True], Cell[BoxData["515377520732011331036461129765621272702107522001"], "Output", CellChangeTimes->{{3.394575594743487*^9, 3.394575618269649*^9}}] }, Open ]], Cell["\<\ Mathematica knows a great many things, for example Pi. If you enter an \ expression with Pi in it, Mathematica knows that it is the special number Pi. \ All special things that Mathematica knows always begin with a CAPITAL \ letter. Since Pi is special Mathematica often keeps it in that form when \ evaluating an expression. See what entering 2 (times) Pi(squared) does:\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"2", " ", SuperscriptBox["Pi", "2"]}]], "Input", AspectRatioFixed->True], Cell[BoxData[ RowBox[{"2", " ", SuperscriptBox["\[Pi]", "2"]}]], "Output", CellChangeTimes->{3.394575622797447*^9}] }, Open ]], Cell["\<\ You can type \[Pi] instead of Pi by entering the key sequence \ \"escape-p-escape\". If you want a number instead of the symbolic output just enter N[%]. The N \ means numerical value, the % means the previous output (this saves you from \ having to retype stuff). The square brackets are important. Every command \ or function begins with a capital letter and the stuff it operates on is \ enclosed in square brackets.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", AspectRatioFixed->True], Cell[BoxData["19.739208802178716`"], "Output", CellChangeTimes->{3.3945756274260273`*^9}] }, Open ]], Cell["Mathematica also knows E and I.", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox["I", "2"]], "Input", AspectRatioFixed->True], Cell[BoxData[ RowBox[{"-", "1"}]], "Output", CellChangeTimes->{3.394575630817556*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox["E", "1"]], "Input", AspectRatioFixed->True], Cell[BoxData["\[ExponentialE]"], "Output", CellChangeTimes->{3.394575632389228*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", "%", "]"}]], "Input", AspectRatioFixed->True], Cell[BoxData["2.718281828459045`"], "Output", CellChangeTimes->{3.394575634269925*^9}] }, Open ]], Cell["\<\ for higher precision just try N[\[ExponentialE]^1, 200] to get the value of E \ to 200 places. The fancy \[ExponentialE] symbol (called a double strike e) \ can be entered by typing \"escape-e-e-escape\". The \[ImaginaryI] , used for \ the square root of -1, is a double-strike i.\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{ SuperscriptBox["\[ExponentialE]", "1"], ",", "200"}], "]"}]], "Input", AspectRatioFixed->True], Cell[BoxData["2.\ 718281828459045235360287471352662497757247093699959574966967627724076630353547\ 594571382178525166427427466391932003059921817413596629043572900334295260595630\ 73813232862794349076323382988075319525101901157383351862`200."], "Output", CellChangeTimes->{3.3945756416362247`*^9}] }, Open ]], Cell["\<\ Some other useful things that Mathematica already knows: Sqrt, Sin, Cos, \ Tan, Integrate....\ \>", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{ SqrtBox[ RowBox[{"\[Pi]", "+", "\[ExponentialE]", "+", RowBox[{"Sin", "[", RowBox[{ RowBox[{"2", " ", "\[Pi]"}], "+", "1"}], "]"}]}]], ",", "50"}], "]"}]], "Input", AspectRatioFixed->True], Cell[BoxData["2.\ 5886957076598892874511147216442083875120118126652926241791046257255`50."], \ "Output", CellChangeTimes->{3.394575645955413*^9}] }, Open ]], Cell["Complex numbers are no problem at all", "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"3", "+", RowBox[{"2", " ", "\[ImaginaryI]"}]}], ")"}], "3"]], "Input", AspectRatioFixed->True], Cell[BoxData[ RowBox[{ RowBox[{"-", "9"}], "+", RowBox[{"46", " ", "\[ImaginaryI]"}]}]], "Output", CellChangeTimes->{3.394575648413039*^9}] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Graphics", "Section", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell["Simple 2-D and 3-D Plots", "Subsection"], Cell[TextData[{ "Mathematica can plot two or three dimensional plots easily. Observe that \ Exp[x] means the same as ", Cell[BoxData[ FormBox[ StyleBox[ SuperscriptBox["E", "x"], Background->GrayLevel[1]], TraditionalForm]]], "and as ", Cell[BoxData[ FormBox[ SuperscriptBox["\[ExponentialE]", "x"], TraditionalForm]]], ". Lists are always enclosed in curly brackets {}, with each item separated \ by a comma. See the list in the following Plot command, in which we specify \ what variable we are plotting and over what range." }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"Sin", "[", SuperscriptBox["\[ExponentialE]", "x"], "]"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "\[Pi]"}], "}"}]}], "]"}]], "Input", AspectRatioFixed->True], Cell[BoxData[ GraphicsBox[{{}, {}, {Hue[0.67, 0.6, 0.6], LineBox[CompressedData[" 1:eJwVmnk41F8bxocxi5QWaZGkJBKKtJA8Jz8VkYpQESEKlSVLyVIqW5IWkkKE VFKyljhRJAnZ930dM/NFlrG/3/cv1+dinnOe+7nPmXNfl41WjgY2/BQK5TOV Qvn/TypeVN69y1lDWyQ+7iSHBdKD+fskHh+DlpM5ayJHWDD9cfv5xkcWIGvp xWsaZ0Hvyou8rEeOkENV5JjPs6Dp0J3CxEe+sLepJ9Bi6RDUWjySiX70AMQF Fq5qKg2BwaW1TZGPYuHuJVs1f9cheDhqlh7x6AMMcKcu5vKGYF/RkUWaV7/B 0NyDLdmCHHDy1LdMdyqBDaq5sakjHDhyRT2ZGVYCb2xc0mjjHJCykiPOfiiB MrnskTM8DtTp0L2Z3BKIvVUyvjDPgf1r8yPPOvyCtomWqp2LubAoR6GSYVsK jXP7RA5s4ULi+GIwMy2D7y8uzXWd4oLP4PTdNM8ySAzubpgx5cKp1oEyelQZ 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