(* 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[ 358192, 6570] NotebookOptionsPosition[ 353366, 6416] NotebookOutlinePosition[ 353964, 6439] CellTagsIndexPosition[ 353921, 6436] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "Why should you use ", StyleBox["Mathematica?", FontSlant->"Italic"] }], "Title", CellChangeTimes->{{3.3907458272729015`*^9, 3.390745835374874*^9}, { 3.390746922311163*^9, 3.3907469286805754`*^9}, {3.390747109577908*^9, 3.390747121535579*^9}, {3.458655898359375*^9, 3.458655898625*^9}}], Cell["Comp 160 Course Module 0", "Subtitle", CellChangeTimes->{{3.390745838950158*^9, 3.3907458395911055`*^9}, 3.3907469187659235`*^9, {3.4586558605625*^9, 3.458655861796875*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " is an environment for solving and presenting many of the computational \ problems that you will encounter while you are here at Rice. Our goal is to \ teach you how to use ", StyleBox["Mathematica", FontSlant->"Italic"], " to do your homework and projects. Initially, we will focus on using ", StyleBox["Mathematica", FontSlant->"Italic"], " as a calculator and then quickly move to using ", StyleBox["Mathematica", FontSlant->"Italic"], " as a document preparation environment. Finally, the majority of the class \ will focus on using ", StyleBox["Mathematica", FontSlant->"Italic"], " to write short programs that use ", StyleBox["Mathematica", FontSlant->"Italic"], "'s own built-in functions to solve interesting computational problems \ relevant to Science and Engineering. This short module will give you an \ overview of some of the interesting features of ", StyleBox["Mathematica.", FontSlant->"Italic"] }], "Text", CellChangeTimes->{{3.39074713226143*^9, 3.3907471691158943`*^9}, { 3.391356277758052*^9, 3.3913565069521875`*^9}, {3.391444377210965*^9, 3.3914444109100933`*^9}, {3.3921223659916983`*^9, 3.392122385065473*^9}}], Cell[CellGroupData[{ Cell["Numerical computation", "Section", CellChangeTimes->{{3.390745863927069*^9, 3.390745869505313*^9}, { 3.390746950833313*^9, 3.390746953347028*^9}, 3.390746986846534*^9}], Cell[TextData[{ "At its core, ", StyleBox["Mathematica", FontSlant->"Italic"], " is essentially the world's most sophisticated calculator. To use this \ calculator, you simply click inside an existing Input cell (the orange box \ below) and hit ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], " to compute the value of the expression appearing in the cell. (", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], " tells ", StyleBox["Mathematica", FontSlant->"Italic"], " to evaluate the cell in which the cursor resides.) For example, try \ evaluating the cell below." }], "Text", CellChangeTimes->{{3.391356529364862*^9, 3.3913567075646544`*^9}, { 3.391357153875318*^9, 3.3913571585120783`*^9}, {3.391357352374705*^9, 3.3913573640517282`*^9}, {3.391444415076167*^9, 3.391444448184435*^9}, { 3.392054151348633*^9, 3.392054151689412*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "+", "1"}]], "Input", CellChangeTimes->{{3.3913584042682304`*^9, 3.3913584064213696`*^9}}], Cell[BoxData["2"], "Output", CellChangeTimes->{3.391358407332698*^9, 3.392054165052638*^9, 3.39212058280304*^9}] }, Open ]], Cell[TextData[{ "This first evaluation may have taken a couple of seconds. The reason for \ this delay is that ", StyleBox["Mathematica", FontSlant->"Italic"], " is loading into the computer's memory a very large piece of code called \ the ", StyleBox["kernel", FontSlant->"Italic"], " that performs basic mathematical computations. Subsequent calculations \ will be much faster. " }], "Text", CellChangeTimes->{{3.391358415444524*^9, 3.391358467720736*^9}, { 3.391358682313585*^9, 3.391358766716634*^9}, 3.392054184719204*^9, { 3.458483023578125*^9, 3.45848302425*^9}}], Cell[TextData[{ "Expressions in ", StyleBox["Mathematica", FontSlant->"Italic"], " can be entered in the standard textual form used in most computing \ languages." }], "Text", CellChangeTimes->{{3.391358415444524*^9, 3.391358467720736*^9}, { 3.391358682313585*^9, 3.391358766716634*^9}, 3.3914444728303657`*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"2", "*", "3"}], " ", "-", RowBox[{"4", "/", "2"}], "+", RowBox[{"3", "^", "2"}]}]], "Input", CellChangeTimes->{{3.391358470544853*^9, 3.3913584779456425`*^9}, { 3.3913585168022904`*^9, 3.3913585367013006`*^9}, {3.391358725967226*^9, 3.391358727229066*^9}}], Cell[BoxData["13"], "Output", CellChangeTimes->{ 3.3913584786967373`*^9, {3.391358525404832*^9, 3.3913585415884256`*^9}, 3.3920542059979057`*^9}] }, Open ]], Cell[TextData[{ "One powerful feature of ", StyleBox["Mathematica", FontSlant->"Italic"], " is that it has literally hundreds of pre-defined mathematical functions \ already defined. For example, let's consider the problem of computing the \ product of the integers from ", Cell[BoxData["1"]], " to ", Cell[BoxData["100"]], ". In standard mathematical terminology, the function ", Cell[BoxData["Factorial"]], " computes this product and is usually written as ", Cell[BoxData[ RowBox[{"100", "!"}]]], ". " }], "Text", CellChangeTimes->{{3.3913584863378773`*^9, 3.391358508880742*^9}, { 3.3913585444926596`*^9, 3.391358654783449*^9}, 3.392054219014258*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"100", "!"}]], "Input", CellChangeTimes->{{3.390746959315849*^9, 3.390746960157092*^9}}], Cell[BoxData[\ "93326215443944152681699238856266700490715968264381621468592963895217599993229\ 915608941463976156518286253697920827223758251185210916864000000000000000000000\ 000"], "Output", CellChangeTimes->{3.390746962210126*^9, 3.39205424713*^9}] }, Open ]], Cell[TextData[{ "Note that the resulting whole number has hundreds of digits. ", StyleBox["Mathematica", FontSlant->"Italic"], " has no restrictions on the size of numbers. Most other languages for \ computing (like Java or Matlab) require special libraries to do something \ like this." }], "Text", CellChangeTimes->{{3.391356715486203*^9, 3.3913567469620905`*^9}, { 3.39135679154709*^9, 3.391356949867902*^9}, 3.39135866166348*^9, { 3.3913601984539223`*^9, 3.391360199926069*^9}, {3.3914444950227194`*^9, 3.3914445101848235`*^9}, {3.392054297951767*^9, 3.392054298443179*^9}, 3.408721500081039*^9, {3.458483308484375*^9, 3.45848344409375*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " also handles real (decimal) numbers exceptionally well. For example, ", StyleBox["Mathematica", FontSlant->"Italic"], " understands about constants such as ", Cell[BoxData["\[Pi]"]], ". ", StyleBox["Mathematica", FontSlant->"Italic"], " can give you the first ", Cell[BoxData["100"]], " digits of ", Cell[BoxData["\[Pi]"]], " by using the function ", Cell[BoxData["N"]], " that computes symbolic constants to their numerical form. Evaluate the \ cell below clicking in the cell and hitting ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], "." }], "Text", CellChangeTimes->{{3.3913570065405226`*^9, 3.3913571733236713`*^9}, { 3.3914445211007376`*^9, 3.391444522823249*^9}, {3.392054344156308*^9, 3.392054373043971*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"N", "[", RowBox[{"\[Pi]", ",", "100"}], "]"}]], "Input", CellChangeTimes->{{3.391357118073123*^9, 3.391357125063314*^9}, { 3.392054403315268*^9, 3.3920544065031023`*^9}}], Cell[BoxData["3.\ 141592653589793238462643383279502884197169399375105820974944592307816406286208\ 9986280348253421170679821480865132823`100."], "Output", CellChangeTimes->{ 3.391444534860798*^9, {3.39205438285156*^9, 3.392054407550509*^9}}] }, Open ]], Cell[TextData[{ "Next, let's compute the first ", Cell[BoxData["1000"]], " digits of ", Cell[BoxData["\[Pi]"]], " by clicking inside the cell and adding a zero to ", Cell[BoxData["100"]], ". Again, hit ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], " and ", StyleBox["Mathematica", FontSlant->"Italic"], " will compute the first ", Cell[BoxData["1000"]], " digits of ", Cell[BoxData["\[Pi]"]], ".", Cell[BoxData[Cell[""]]], " (You'll see how to type symbols like ", Cell[BoxData["\[Pi]"]], " into your own expressions later.)" }], "Text", CellChangeTimes->{{3.3913572450482364`*^9, 3.3913573178844223`*^9}, { 3.45848313125*^9, 3.45848320759375*^9}}], Cell[TextData[{ "Usually, you are interested in entering and evaluating your own \ expressions. To create a new ", Cell[BoxData["Input"]], " cell, you simply place the mouse between two existing cells (a cell is \ roughly a chuck of text) and click. The result should be a horizontal line. \ Now, typing in text will expand the line into an ", Cell[BoxData["Input"]], " cell. As a test, let's compute the square of ", Cell[BoxData[ RowBox[{"5", "!"}]]], ". Create a new cell, enter this expression and hit ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], ". If you have done everything correctly, ", StyleBox["Mathematica", FontSlant->"Italic"], " should return ", Cell[BoxData["14400"]], "." }], "Text", CellChangeTimes->{{3.391357179042008*^9, 3.3913572161360865`*^9}, { 3.391357387515936*^9, 3.3913574681534953`*^9}, {3.3913582955797763`*^9, 3.3913583836381545`*^9}, {3.3913587948075867`*^9, 3.391358890817557*^9}, { 3.3914445504535303`*^9, 3.391444580427228*^9}}], Cell[TextData[{ "To find out the more about the functions that ", StyleBox["Mathematica", FontSlant->"Italic"], " supports, go to the ", Cell[BoxData["Help"]], " menu and select ", Cell[BoxData["Documentation"]], " ", Cell[BoxData["Center"]], ". This action will bring up the main window for ", StyleBox["Mathematica", FontSlant->"Italic"], "'s help system. Explore the entries in this window and locate a link to a \ listing of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s mathematical functions. During the course of this class, you will \ become extremely familiar with the ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], "." }], "Text", CellChangeTimes->{{3.391358902204157*^9, 3.391358908042669*^9}, { 3.391358981159263*^9, 3.391359125750058*^9}, {3.3914445961000767`*^9, 3.3914446276660957`*^9}, 3.3921224028219833`*^9, {3.408721580559203*^9, 3.4087215873354816`*^9}, {3.45848313840625*^9, 3.458483140171875*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Symbolic computation", "Section", CellChangeTimes->{{3.3907458730805964`*^9, 3.3907458785787215`*^9}, { 3.390746969080279*^9, 3.3907469723651333`*^9}}], Cell[TextData[{ "Another feature that makes ", StyleBox["Mathematica", FontSlant->"Italic"], " much more powerful than most languages for computation is ", StyleBox["Mathematica's", FontSlant->"Italic"], " ability to compute with symbolic expressions. For example, in Java or \ Matlab, entering the expression ", Cell[BoxData[ RowBox[{"x", "+", "x"}]]], " will yield an error if the variable ", Cell[BoxData["x"]], " is undefined. In ", StyleBox["Mathematica", FontSlant->"Italic"], ", having undefined variables in expressions is commonplace. For example," }], "Text", CellChangeTimes->{{3.3913591388090963`*^9, 3.391359311120304*^9}, { 3.3913601879385924`*^9, 3.391360189450797*^9}, 3.3914446373702435`*^9, { 3.3920546063386927`*^9, 3.3920546142339363`*^9}, {3.392054653104951*^9, 3.3920546712697144`*^9}, 3.408721658176825*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"x", "+", "x"}]], "Input", CellChangeTimes->{{3.3913593133836036`*^9, 3.39135931385429*^9}}], Cell[BoxData[ RowBox[{"2", " ", "x"}]], "Output", CellChangeTimes->{3.39135931435502*^9, 3.392054678437956*^9}] }, Open ]], Cell[TextData[{ "The basic mode of evaluation in ", StyleBox["Mathematica", FontSlant->"Italic"], " is that of simplification instead of computation. ", StyleBox["Mathematica", FontSlant->"Italic"], " attempts to apply a set of built-in rules to simplify any expression that \ it encounters. If the expression consists only of numerical values, ", StyleBox["Mathematica", FontSlant->"Italic"], " computes the expression and returns the appropriate numerical value. \ However, if the expression contains undefined variables, ", StyleBox["Mathematica", FontSlant->"Italic"], " uses the rules of algebra (and beyond) to simply the input expression. \ For example, ", StyleBox["Mathematica", FontSlant->"Italic"], " can be used to illustrate the binomial expansion of a polynomial" }], "Text", CellChangeTimes->{{3.3913591388090963`*^9, 3.391359490772214*^9}, { 3.391359763159319*^9, 3.391359791500637*^9}, {3.392054712324357*^9, 3.392054782147996*^9}, {3.4087216870279837`*^9, 3.408721708611393*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Expand", "[", SuperscriptBox[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}], "10"], "]"}]], "Input", CellChangeTimes->{{3.3913597302513433`*^9, 3.39135975086139*^9}}], Cell[BoxData[ RowBox[{ SuperscriptBox["a", "10"], "+", RowBox[{"10", " ", SuperscriptBox["a", "9"], " ", "b"}], "+", RowBox[{"45", " ", SuperscriptBox["a", "8"], " ", SuperscriptBox["b", "2"]}], "+", RowBox[{"120", " ", SuperscriptBox["a", "7"], " ", SuperscriptBox["b", "3"]}], "+", RowBox[{"210", " ", SuperscriptBox["a", "6"], " ", SuperscriptBox["b", "4"]}], "+", RowBox[{"252", " ", SuperscriptBox["a", "5"], " ", SuperscriptBox["b", "5"]}], "+", RowBox[{"210", " ", SuperscriptBox["a", "4"], " ", SuperscriptBox["b", "6"]}], "+", RowBox[{"120", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "7"]}], "+", RowBox[{"45", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "8"]}], "+", RowBox[{"10", " ", "a", " ", SuperscriptBox["b", "9"]}], "+", SuperscriptBox["b", "10"]}]], "Output", CellChangeTimes->{3.3913597516325145`*^9, 3.392054801598757*^9}] }, Open ]], Cell[TextData[{ "Essentially, ", StyleBox["Mathematica", FontSlant->"Italic"], " encodes most of basic mathematical knowledge and much of advanced \ mathematical knowledge. For example, ", StyleBox["Mathematica", FontSlant->"Italic"], " understands how to handle real numbers raised to an imaginary power. \ Moreover, it has rules for handling this process exactly as if the values are \ known constants. Here is a famous theorem of Euler." }], "Text", CellChangeTimes->{{3.391359494517674*^9, 3.391359511091837*^9}, { 3.3913595526123686`*^9, 3.391359606561019*^9}, {3.3913597943648124`*^9, 3.391359836175768*^9}, 3.3914446570689616`*^9, 3.392054826989625*^9, { 3.408721740185934*^9, 3.408721740751535*^9}}], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox["\[ExponentialE]", RowBox[{"\[ImaginaryI]", " ", "\[Pi]"}]]], "Input", CellChangeTimes->{{3.391359515067633*^9, 3.3913595422873163`*^9}}], Cell[BoxData[ RowBox[{"-", "1"}]], "Output", CellChangeTimes->{3.3913596451973457`*^9, 3.392054843670274*^9}] }, Open ]], Cell[TextData[{ "Here, ", Cell[BoxData["\[ImaginaryI]"]], " is the imaginary number that is the square root of ", Cell[BoxData[ RowBox[{"-", "1"}]]], " and ", Cell[BoxData["\[ExponentialE]"]], " is the constant ", Cell[BoxData["2.718281828459045`"]], " -- that is, the value of the limit" }], "Text", CellChangeTimes->{{3.3913596110575743`*^9, 3.3913596684312177`*^9}, { 3.3913600266534595`*^9, 3.391360036527855*^9}, {3.392054852443963*^9, 3.392054859785378*^9}, {3.4087219532306957`*^9, 3.408721960786374*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Limit", "[", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", FractionBox["1", "n"]}], ")"}], "n"], ",", RowBox[{"n", "\[Rule]", "\[Infinity]"}]}], "]"}]], "Input", CellChangeTimes->{{3.391360039662425*^9, 3.39136005931107*^9}}], Cell[BoxData["\[ExponentialE]"], "Output", CellChangeTimes->{3.3913600610335813`*^9, 3.392054870641304*^9}] }, Open ]], Cell[TextData[{ "One feature that is very useful for students in basic calculus is ", StyleBox["Mathematica", FontSlant->"Italic"], "'s knowledge of sums and integrals. For example, " }], "Text", CellChangeTimes->{{3.3913614446707463`*^9, 3.3913615072619963`*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"\[Integral]", RowBox[{ RowBox[{"Sin", "[", "x", "]"}], RowBox[{"\[DifferentialD]", "x"}]}]}], "\[IndentingNewLine]", RowBox[{ UnderoverscriptBox["\[Sum]", RowBox[{"i", "=", "0"}], "\[Infinity]"], FractionBox["1", SuperscriptBox["2", "i"]]}]}], "Input", CellChangeTimes->{{3.391361510757092*^9, 3.391361629079591*^9}}], Cell[BoxData[ RowBox[{"-", RowBox[{"Cos", "[", "x", "]"}]}]], "Output", CellChangeTimes->{ 3.391361518288071*^9, {3.3913615863773365`*^9, 3.391361630581781*^9}, 3.392054894348196*^9}], Cell[BoxData["2"], "Output", CellChangeTimes->{ 3.391361518288071*^9, {3.3913615863773365`*^9, 3.391361630581781*^9}, 3.392054895064505*^9}] }, Open ]], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " is an essential tool for people who do lots of calculus." }], "Text", CellChangeTimes->{{3.391361645924148*^9, 3.3913616624181943`*^9}, { 3.408721978442268*^9, 3.408721979677155*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["2D Expression input and typesetting", "Section", CellChangeTimes->{{3.390746036702399*^9, 3.3907460434323444`*^9}, { 3.3907469969714966`*^9, 3.3907470031806726`*^9}, {3.3913603015241857`*^9, 3.3913603029562736`*^9}, {3.391442155081385*^9, 3.3914421613204813`*^9}}], Cell[TextData[{ "As the semester progresses, you will become more and more familiar with the \ various numerical and symbolic capabilities of ", StyleBox["Mathematica", FontSlant->"Italic"], ". Another interesting feature of ", StyleBox["Mathematica", FontSlant->"Italic"], " is its ability to represent mathematical expressions in a visually elegant \ manner beyond the standard 1D textual representation of languages like Java \ or Matlab. For example, to compute ", Cell[BoxData["3"]], " squared, in most languages one would normally enter the expression ", Cell[BoxData[ RowBox[{"3", "^", "2"}]]], ". However, ", StyleBox["Mathematica", FontSlant->"Italic"], " has a ", Cell[BoxData["WYSWYG"]], " (what you see is what you get) interface that allows you to enter the \ expression" }], "Text", CellChangeTimes->{{3.391360089284768*^9, 3.3913603295250072`*^9}, { 3.3913617241281595`*^9, 3.391361750706908*^9}, 3.391444659572612*^9, { 3.392055061907557*^9, 3.3920550621343737`*^9}, {3.408722031683251*^9, 3.408722045649844*^9}}], Cell[CellGroupData[{ Cell[BoxData[ SuperscriptBox["3", "2"]], "Input", CellChangeTimes->{{3.3913603335709057`*^9, 3.39136033434203*^9}}], Cell[BoxData["9"], "Output", CellChangeTimes->{3.3913603352032857`*^9, 3.3920551002974377`*^9}, FontSlant->"Italic"] }, Open ]], Cell[TextData[{ "There are several ways to enter such expressions in ", StyleBox["Mathematica", FontSlant->"Italic"], ". The simplest way for new users is to use a ", StyleBox["palette", FontSlant->"Italic"], " to create this expression. Open the ", Cell[BoxData["Palettes"]], " menu and select ", Cell[BoxData[ RowBox[{"Basic", " ", "Math", " ", "Assistant"}]]], ". This action opens a menu on the right hand side of your screen that \ contains a number of expressions. Clicking on one of these expression, adds \ the expression to your currently selected cell. As an example, create the \ number ", Cell[BoxData["\[Pi]"]], " by clicking on ", Cell[BoxData["\[Pi]"]], " in the palette." }], "Text", CellChangeTimes->{{3.3913603541108503`*^9, 3.3913605443081336`*^9}, { 3.3913616892372932`*^9, 3.391361694995688*^9}, 3.391444664970481*^9, { 3.392055191661448*^9, 3.392055219543627*^9}, 3.4087220765212593`*^9, { 3.460048093078125*^9, 3.4600480991875*^9}}], Cell[TextData[{ "Some of the expressions have pieces that are white or black rectangles. \ These rectangles are called ", StyleBox["placeholders", FontSlant->"Italic"], ". Placeholders are dummy expressions waiting to be replaced by the user \ with their desired contents. As an example, create the expression ", Cell[BoxData[ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Pi]"}]]]], " using the placeholder for exponents. You can move the cursor around \ inside the expression using your mouse or arrow keys." }], "Text", CellChangeTimes->{{3.3913605474927764`*^9, 3.3913607164591074`*^9}, { 3.3914446679047585`*^9, 3.3914446699777813`*^9}, {3.392055273890438*^9, 3.392055284015711*^9}}], Cell[TextData[{ "These expressions can also be created very quickly using keyboard \ shortcuts. For example, you can create an exponent by typing ", Cell[BoxData[ RowBox[{"Crtl", " ", "6"}]]], " inside an existing expression. ", StyleBox["Mathematica ", FontSlant->"Italic"], "will automatically create a place holder at the appropriate location. (See \ the ", Cell[BoxData["Insert"]], " menu and ", Cell[BoxData["Typesetting"]], " submenu for more details.) Constants such as ", Cell[BoxData["\[Pi]"]], " can be created using the ", Cell[BoxData["Escape"]], " key. To enter ", Cell[BoxData["\[Pi]"]], ", simply hit ", Cell[BoxData[ RowBox[{"Escape", " ", "p", " ", "Escape"}]]], ". (For more shortcuts, check out the ", Cell[BoxData[ RowBox[{"Special", " ", "Characters"}]]], " palette, and put your cursor over what you're interested in. As an \ exercise, create ", Cell[BoxData[ SuperscriptBox["\[ExponentialE]", RowBox[{ RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Pi]"}]]]], " again, but this time use only the keyboard." }], "Text", CellChangeTimes->{{3.3913607550653906`*^9, 3.391360784448227*^9}, { 3.3913608303952117`*^9, 3.391361038748965*^9}, {3.391361325376831*^9, 3.3913614107012234`*^9}, {3.392055447591312*^9, 3.3920554486427307`*^9}, { 3.392055537147155*^9, 3.3920555433974752`*^9}, {3.46004847959375*^9, 3.46004847959375*^9}, {3.46004852509375*^9, 3.46004852509375*^9}, { 3.4600489025*^9, 3.4600489025*^9}, {3.460049097328125*^9, 3.460049097328125*^9}, {3.46004913321875*^9, 3.460049149265625*^9}}], Cell[TextData[{ "While these examples may seem trivial, the payoff from good typesetting is \ that more complicated expressions are visually easier to parse. 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", StyleBox["Mathematica", FontSlant->"Italic"], " will automatically rotate the surface in 3D in a natural manner." }], "Text", CellChangeTimes->{{3.3914428516068296`*^9, 3.3914429379927697`*^9}, 3.391444153835312*^9, {3.3920557970196753`*^9, 3.392055804515345*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " also allows the creation of custom 2D graphics in two ways. First, ", StyleBox["Mathematica", FontSlant->"Italic"], " includes a simple, but elegant tool for creating 2D figures. To create a \ figure, you simply select ", Cell[BoxData[ RowBox[{"New", " ", "Graphic"}]]], " from the ", Cell[BoxData["Graphics"]], " menu. ", StyleBox["Mathematica", FontSlant->"Italic"], " will insert a new figure at the cursor. You can add elements to the \ graphic by opening the ", Cell[BoxData[ RowBox[{"Drawing", " ", "Tools"}]]], " palette from the ", Cell[BoxData["Graphics"]], " menu. 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Often, the solutions to \ problems that you will work on are not simply static entities, but things \ that change dynamically. ", StyleBox["Mathematica", FontSlant->"Italic"], " incorporates the capabilities to produce dynamic output. In particular, ", StyleBox["Mathematica", FontSlant->"Italic"], " contains functions that allow the user to create a simple interface where \ a variable associated with an expression can be manipulated dynamically by \ the user. 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