(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 21411, 767]*) (*NotebookOutlinePosition[ 22529, 802]*) (* CellTagsIndexPosition[ 22485, 798]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "L2 Introduction to ", StyleBox["Mathematica", FontSlant->"Italic"], " (Part II)" }], "Subtitle", FontSize->16, FontWeight->"Bold"], Cell[TextData[{ StyleBox["This "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[" lesson will continue the introduction to basic features of "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[". We will discuss how to"] }], "Text", TextAlignment->Left], Cell[TextData[ "\[FilledSmallCircle] use editorial features, \n\[FilledSmallCircle] enter \ mathematical expressions via palettes, and\n\[FilledSmallCircle] the \ different uses of parentheses, square brackets and curly braces. \n\n"], "Text", CellMargins->{{37, Inherited}, {Inherited, Inherited}}, TextAlignment->AlignmentMarker], Cell[CellGroupData[{ Cell["Editorial Features", "Section"], Cell[CellGroupData[{ Cell["The Different Types of Cells", "Subsection"], Cell[TextData[{ "As you have already seen, whenever you type anything into a notebook, a \ cell bracket appears at the right side of the screen. By default, any new \ cell is an ", StyleBox["Input", FontWeight->"Bold"], " cell. You can check on the type of cell, as well as change the type, by \ using the ", StyleBox["Format", FontWeight->"Bold"], " menu. To see how it works, type any sentence into your notebook." }], "Text"], Cell[BoxData[ \(This\ is\ a\ test\)], "Input"], Cell[TextData[{ "You will notice that the font is Courier bold. This is the deafult for \ Input cells. To change the cell to a ", StyleBox["text", FontWeight->"Bold"], " cell, click on the cell bracket, which will now be highlighted. Select ", StyleBox["Format \[Rule] Style \[Rule] Text ", FontWeight->"Bold"], "(shortcut \[ControlKey] -7 (Windows) or \[CloverLeaf]-7 (Mac)). Now your \ sentence should look like this:" }], "Text"], Cell["This is a test", "Text"], Cell[TextData[{ "Likewise, by selecting the cell bracket and choosing the respective style \ from the ", StyleBox["Format ", FontWeight->"Bold"], "menu, you can make the content of a cell a title, a section, etc." }], "Text"], Cell[TextData[{ "One reason you would want to make any cells containing comments and \ explanations into text cells is to avoid having ", StyleBox["Mathematica", FontSlant->"Italic"], " try to evaluate these cells when, for example, using ", StyleBox["Kernel \[Rule] Evaluation \[Rule] Evaluate Notebook", FontWeight->"Bold"], ".", StyleBox[" ", FontWeight->"Bold"], "(We will see later when this selection is useful.) Here is an example of \ what happens if you do not do this:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Silvia\ Heubach\)], "Input"], Cell[BoxData[ \(Heubach\ Silvia\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Mathematica ", FontSlant->"Italic"], "thinks that you have two variables, named ", StyleBox["Silvia", FontWeight->"Bold"], " and ", StyleBox["Heubach", FontWeight->"Bold"], ", which are to be multiplied (", StyleBox["Mathematica", FontSlant->"Italic"], " orders the variables in a product in alphabetical order). Therefore, \ always separate text and input in different cells, and make the cells \ containing text into one of the styles 1 - 8." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Other Editorial Features", "Subsection"], Cell[TextData[{ StyleBox[ "Now that you know how to add text to your computations, you may want to \ know how to get different fonts or different faces (bold, italic, etc.). \ These options can also be found in the "], StyleBox["Format", FontWeight->"Bold"], StyleBox[ " menu. For example, if we want to make the previous sentence bold faced in \ a different type of font and also much bigger, we can select the appropriate \ menu choices. Here is the original (text) sentence:"] }], "Text"], Cell["This is a test", "Text"], Cell[TextData[{ StyleBox[ "To make it bold faced, click on the bracket to select the cell, or \ highlight the text itself. Now select "], StyleBox["Format \[Rule] Face \[Rule] Bold", FontWeight->"Bold"], StyleBox[". This results in:"] }], "Text"], Cell[TextData[StyleBox["This is a test"]], "Text", FontWeight->"Bold"], Cell[TextData[{ StyleBox[ "Let's choose a different font. Again, click on the cell bracket, then \ choose "], StyleBox["Format \[Rule] Font \[Rule] Edda ", FontWeight->"Bold"], StyleBox["(or your favorite font). Now the text looks like this:"] }], "Text"], Cell[TextData[StyleBox["This is a test"]], "Text", FontFamily->"Edda", FontWeight->"Bold"], Cell[TextData[{ StyleBox["We can make it bigger, by selecting "], StyleBox["Format \[Rule] Size \[Rule] 24 Point.", FontWeight->"Bold"], StyleBox[" "] }], "Text"], Cell["This is a test", "Text", FontFamily->"Edda", FontSize->24, FontWeight->"Bold"], Cell[TextData[{ "We can even make it a different color (blue) by choosing ", StyleBox["Format \[Rule] Text Color \[Rule] Blue.", FontWeight->"Bold"], " " }], "Text"], Cell["This is a test", "Text", FontFamily->"Edda", FontSize->24, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]] }, Open ]], Cell[CellGroupData[{ Cell["Cutting, Pasting, and Deleting Cells", "Subsection"], Cell[TextData[{ "Sometimes when working with ", StyleBox["Mathematica", FontSlant->"Italic"], ", you may want to rearrange the order of cells, copy cells, or get rid of \ them (for example, incorrect computations). Any of these tasks can be \ accomplished in the same manner as in any word processing program. For \ example, to copy the text cell that was modified above, first select the cell \ by clicking on its bracket (or highlight the part of the content that you'd \ like to copy). Then choose ", StyleBox["Edit \[Rule] Copy ", FontWeight->"Bold"], "and move the cursor to the place in the notebook where you would like to \ place a copy of the cell. Click at that location, then use ", StyleBox["Edit \[Rule] Paste", FontWeight->"Bold"], ". As always, you may instead use the shortcuts indicated in the menu. To \ delete a cell or part of a cell, use ", StyleBox["Edit \[Rule] Cut ", FontWeight->"Bold"], "(or the \[DeleteKey] key) after having selected the cell or highlighted \ the selection." }], "Text"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Built-in Palettes", "Section"], Cell[CellGroupData[{ Cell["Entering Mathematical Expressions via Palettes", "Subsection"], Cell[TextData[{ "One of the new features of ", StyleBox["Mathematica", FontSlant->"Italic"], " 3.0 are palettes, which (among other things) allow for entering complex \ mathematical expressions in the same way as in the equation editor of MS Word \ or similar programs. To access this feature, select ", StyleBox["File \[Rule] Palettes \[Rule] BasicInput", FontWeight->"Bold"], ". This will open a palette which has templates for entering exponents, \ fractions, roots, etc., as well as special operators and frequently used \ Greek symbols. If you cannot find what you need in this palette, try ", StyleBox["File \[Rule] Palettes \[Rule] CompleteCharacters", FontWeight->"Bold"], ". \n\nTo put a template into your notebook, move the cursor to wherever \ you'd like the template to be pasted. Click the mouse, then click on the \ template of your choice. If you want to put the template into a new cell, \ make sure that you first create a horizontal line. \n\nAs an example of the \ process, we will enter the following expression:\n\n\t\t\t \ ", Cell[BoxData[ FormBox[ RowBox[{" ", StyleBox[\(\(x\^4 + 2 x\^3 - 2 x\^2 - 4 x\)\/\(x\^3 - 2 x\)\), FontSize->16]}], TraditionalForm]]] }], "Text"], Cell[TextData[StyleBox["Start by pasting the fraction template:"]], "Text"], Cell[BoxData[ \(\[Placeholder]\/\[Placeholder]\)], "Input"], Cell[TextData[{ "A black placeholder (does not show in the printed version, only in the \ notebook) indicates the location where the next keyboard input will be \ placed. To enter ", Cell[BoxData[ \(TraditionalForm\`x\^4\)]], " you'll need a superscript template. Click on the corresponding template, \ then type ", StyleBox["x", FontSlant->"Italic"], ". " }], "Text"], Cell[BoxData[ \(x\^\[Placeholder]\/\[Placeholder]\)], "Input"], Cell[TextData[ "Use the \[TabKey] key to move to the next place holder and type 4."], "Text"], Cell[BoxData[ \(x\^4\/\[Placeholder]\)], "Input"], Cell[TextData[{ "Now use the right arrow key until you see the cursor to the right of the \ expression ", Cell[BoxData[ \(TraditionalForm\`x\^4\)]], ". Enter + 2 and another superscript template." }], "Text"], Cell[BoxData[ \(\(x\^4 + 2 \[Placeholder]\^\[Placeholder]\)\/\[Placeholder]\)], "Input"], Cell["\<\ Repeat the previous steps until you have completely entered the \ numerator.\ \>", "Text"], Cell[BoxData[ \(\(x\^4 + 2 x\^3 - 2 x\^2 - 4 x\)\/\[Placeholder]\)], "Input"], Cell[TextData[ "Next use the \[TabKey] key to move to the place holder for the denominator, \ then enter the denominator in the same fashion as the numerator."], "Text"], Cell[BoxData[ \(\(x\^4 + 2 x\^3 - 2 x\^2 - 4 x\)\/\(x\^3 - 2 x\)\)], "Input"], Cell[TextData[{ StyleBox["This expression can now be used as input for "], StyleBox["Mathematica.", FontSlant->"Italic"], StyleBox[ " For example, you can move the cursor to the front of the expression and \ click the mouse, then type "], StyleBox["Simplify[ ", FontWeight->"Bold"], StyleBox[ "(remember to start with a capital letter and to use a square bracket)."] }], "Text"], Cell[BoxData[ \(\(Simplify[\(x\^4 + 2 x\^3 - 2 x\^2 - 4 x\)\/\(x\^3 - 2 x\)\)\)], "Input"], Cell[TextData[{ "Move the cursor to the end of the expression and click the mouse, then \ type ", StyleBox["]", FontWeight->"Bold"], ". Evaluate the cell to see the fraction in simplified form" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Simplify[\(x\^4 + 2 x\^3 - 2 x\^2 - 4 x\)\/\(x\^3 - 2 x\)]\)], "Input"], Cell[BoxData[ \(2 + x\)], "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Parentheses, Square Brackets, and Curly Braces", "Section"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " distinguishes between parentheses, square brackets and curly braces, each \ of which is used for a specific task:" }], "Text"], Cell[TextData[{ StyleBox[ "Parentheses - used for grouping terms to influence the order of \ evaluation. \nSquare Brackets - used to enclose the argument of built-in (and \ package) "], StyleBox["Mathematica", FontSlant->"Italic"], StyleBox[ " functions\nCurly Braces - used for indicating lists and matrices."] }], "Text", CellMargins->{{39, Inherited}, {Inherited, Inherited}}, TextAlignment->AlignmentMarker], Cell[CellGroupData[{ Cell["Parentheses versus Square Brackets", "Subsection"], Cell[TextData[{ "One common mistake made by new users of ", StyleBox["Mathematica", FontSlant->"Italic"], " involves the incorrect use of parentheses. In ", StyleBox["Mathematica", FontSlant->"Italic"], ", function arguments are enclosed in ", StyleBox["square brackets", FontWeight->"Bold"], ", not in parentheses. The latter are reserved specifically for the \ grouping of terms. The reason for this distinction is that computers cannot \ interpret context. When reading a mathematics book, it is usually clear from \ the context whether the parentheses are used for functions or for grouping \ terms. Here is an example that shows the ambiguity that could arise without \ context. Look at the expression" }], "Text", TextAlignment->Left], Cell[TextData[{ StyleBox["f ", FontSlant->"Italic"], "(", StyleBox["x+", FontSlant->"Italic"], "1)", StyleBox["\t", FontSlant->"Italic"] }], "Text", TextAlignment->Center], Cell[TextData[{ "There are two different interpretations: \n1) The function ", StyleBox["f", FontSlant->"Italic"], " is evaluated at input value ", StyleBox["x+", FontSlant->"Italic"], "1,\n2) The variable ", StyleBox["f", FontSlant->"Italic"], " is multiplied by the term ", StyleBox["x+", FontSlant->"Italic"], "1. \n\nWithout context, a computer cannot decide which of the two \ interpretations is the correct one. Using square brackets to enclose function \ arguments removes the ambiguity. Thus, in ", StyleBox["Mathematica", FontSlant->"Italic"], ", the first interpretation would be written as\n\t\t\t\t\t\t ", StyleBox["f", FontSlant->"Italic"], "[", StyleBox["x+", FontSlant->"Italic"], "1]\nand the second one as \n\t\t\t\t\t ", StyleBox["f ", FontSlant->"Italic"], "(", StyleBox["x+", FontSlant->"Italic"], "1)", StyleBox[".", FontSlant->"Italic"] }], "Text", TextAlignment->Left] }, Open ]], Cell[CellGroupData[{ Cell["Curly Braces", "Subsection"], Cell[TextData[{ "Curly braces are used for lists in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Lists play an important role in ", StyleBox["Mathematica", FontSlant->"Italic"], ", as operations such as multiplication, division, and even applying \ certain functions can be done for the whole list at once in the same way it \ can be done with a single number or variable. For example, to compute \ input-output pairs for the function ", StyleBox["f(x)=", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`x\^2\)]], ", you can proceed as follows:\n\nCreate a list of input values and give it \ a name." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(x\ = \ {\(-2\), \(-1\), 0, 1, 2, 3, 4}\)], "Input"], Cell[BoxData[ \({\(-2\), \(-1\), 0, 1, 2, 3, 4}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox[ "The above list could also have been created by the built-in function "], StyleBox["Range", FontWeight->"Bold"], StyleBox["."] }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(?Range\)\)], "Input"], Cell[BoxData[ \("Range[imax] generates the list {1, 2, ... , imax}. Range[imin, imax] \ generates the list {imin, ... , imax}. Range[imin, imax, di] uses step \ di."\)], "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Range[\(-2\), 4]\)], "Input"], Cell[BoxData[ \({\(-2\), \(-1\), 0, 1, 2, 3, 4}\)], "Output"] }, Open ]], Cell[TextData[{ "To create the corresponding output values for our function ", StyleBox["f(x)=", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`\(\(x\^2, \)\ \)\)]], " just type the ", StyleBox["right hand side of the functional equation", FontWeight->"Bold"], ". " }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\ x^2\)\)], "Input"], Cell[BoxData[ \({4, 1, 0, 1, 4, 9, 16}\)], "Output"] }, Open ]], Cell[TextData[{ "As an example of how we can apply a funcion to a list, let's look at the \ function ", StyleBox["f(x)=", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`\@x\)]], ". Create a list of input values, all of which are non-negative. The \ command below creates a list of values from 0 to 5 in steps of 0.5. If we do \ not need the previous list, we can name the new list also x. Otherwise, use a \ new name, say t." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(t = Range[0, 5, .5]\)], "Input"], Cell[BoxData[ \({0, 0.5`, 1.`, 1.5`, 2.`, 2.5`, 3.`, 3.5`, 4.`, 4.5`, 5.`}\)], "Output"] }, Open ]], Cell["The output values are given by ", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Sqrt[t]\)], "Input"], Cell[BoxData[ \({0, 0.70710678118654755`, 1.`, 1.22474487139158894`, 1.4142135623730951`, 1.58113883008418953`, 1.73205080756887692`, 1.87082869338697062`, 2.`, 2.12132034355964238`, 2.2360679774997898`} \)], "Output"] }, Open ]], Cell[TextData[{ "Here we have replaced the independent variable in the right hand side of \ the functional expression by the name of our list of input values. Instead of \ typing ", StyleBox["Sqrt", FontWeight->"Bold"], ", you can use the square root template from the palette." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\@t\)], "Input"], Cell[BoxData[ \({0, 0.70710678118654755`, 1.`, 1.22474487139158894`, 1.4142135623730951`, 1.58113883008418953`, 1.73205080756887692`, 1.87082869338697062`, 2.`, 2.12132034355964238`, 2.2360679774997898`} \)], "Output"] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Assignment", "Section"], Cell["\<\ For the write-up of this assignment, use the format given below, \ i.e., give each problem its designation (Problem 1, etc.) in subsection \ style.\ \>", "Text"], Cell[CellGroupData[{ Cell["Problem 1", "Subsection"], Cell[TextData[{ "Enter the following expressions into a notebook using an appropriate \ palette and make the cell a text cell.\na) ", Cell[BoxData[ \(TraditionalForm\`\@\(\((2 + x)\)\^3\)\%5\)]], "\n\nb) ", Cell[BoxData[ FormBox[ StyleBox[\(\(\[Alpha] + \[Beta] + \[Gamma]\)\/180\), FontSize->16], TraditionalForm]]], " (increase the size of the font for the fraction)\n" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Problem 2", "Subsection"], Cell["\<\ Reproduce a sentence of your choice in the indicated style. As each \ part has a different style, you need to have different cells for each of the \ parts a) - c). a) text\ \>", "Text"], Cell[TextData[{ "b) ", StyleBox["bold faced, size 18pt", FontSize->18, FontWeight->"Bold"] }], "Text"], Cell[TextData[{ "c)", StyleBox[" ", FontFamily->"Lucida Handwriting"], StyleBox["Lucida Handwriting (or other script style)", FontFamily->"Lucida Handwriting", FontColor->RGBColor[0, 0, 1]], ", in blue" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Problem 3", "Subsection"], Cell[TextData[{ "Create a list of integers from 0 to 10 and name it ", StyleBox["x", FontWeight->"Bold"], ". Compute the corresponding output values for the functions\n\na)", StyleBox[" ", FontSize->14], StyleBox["f", FontSize->14, FontSlant->"Italic"], StyleBox["(", FontSize->14], StyleBox["x", FontSize->14, FontSlant->"Italic"], StyleBox[")", FontSize->14], StyleBox[" = ", FontSize->14, FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`x\/5\)], FontSize->14], StyleBox[" - 3", FontSize->14], Cell[BoxData[ \(TraditionalForm\`x\^3\)], FontSize->14], "\n", StyleBox[" ", FontSize->9], "\nb) ", StyleBox["f", FontSize->14, FontSlant->"Italic"], StyleBox["(", FontSize->14], StyleBox["x", FontSize->14, FontSlant->"Italic"], StyleBox[")", FontSize->14], StyleBox[" = ", FontSize->14, FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`\@\((x + 2)\)\)], FontSize->14], "\n", StyleBox[" ", FontSize->9], "\nc) ", StyleBox["f", FontSize->14, FontSlant->"Italic"], StyleBox["(", FontSize->14], StyleBox["x", FontSize->14, FontSlant->"Italic"], StyleBox[")", FontSize->14], StyleBox[" = 3 ", FontSize->14, FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`e\^\(2 x\)\)], FontSize->14], " (remember that ", StyleBox["e ", FontSlant->"Italic"], "is the built-in constant E)" }], "Text"] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 800}, {0, 544}}, WindowToolbars->"RulerBar", WindowSize->{566, 385}, WindowMargins->{{30, Automatic}, {Automatic, 5}}, PrintingCopies->1, PrintingStartingPageNumber->7, PrintingPageRange->{4, 10}, PageHeaders->{{Cell[ TextData[ "M-", { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ "Silvia Heubach"], "Header"]}, {Cell[ TextData[ "Introduction to Modeling"], "Header"], Inherited, Cell[ TextData[ "M-", { CounterBox[ "Page"]}], "PageNumber"]}}, PrintingOptions->{"FacingPages"->True} ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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