(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. The data for the notebook starts with the line containing 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 7548, 329]*) (*NotebookOutlinePosition[ 26489, 1024]*) (* CellTagsIndexPosition[ 26359, 1016]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ "Tutorial 3: ", StyleBox["Defining", FontSlant->"Italic"] }], "Title", TextAlignment->Left, FontSize->30], Cell["by R. Dover, IMSA", "Subtitle", TextAlignment->Left, FontSize->14], Cell[CellGroupData[{ Cell["Substituting", "Section"], Cell[TextData[{ "\tIt is quite easy to substitute numbers or expressions into variables. \ First, let's create an expression and call it \"poly.\" (Note the space \ between the x and y in the middle term. The space indicates multiplication \ of the two variables x and y as opposed to our name \"poly\" which is one \ variable with a 4-letter name. Spaces are frequently used in ", StyleBox["Mathematica", FontSlant->"Italic"], " simply to help make the mathematical expressions easier to read. In this \ case, it is necessary.)" }], "Text", CellTags->"spacemult"], Cell[CellGroupData[{ Cell[BoxData[ \(poly\ = \ x\^3 + \ 4 x\ y\ + \ 5 y\^2\)], "Input"], Cell[BoxData[ \(x\^3 + 4\ x\ y + 5\ y\^2\)], "Output"] }, Open ]], Cell["\<\ To make a substitution, we use the not-so-obvious notation \"/.\" \ along with an arrow (from the palette or created by a \"-\" and a \">\"). \ \ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(poly\ /. x\ \[Rule] \ 2\)], "Input"], Cell[BoxData[ \(8 + 8\ y + 5\ y\^2\)], "Output"] }, Open ]], Cell[TextData[{ "Now substitute y = 5 into poly. ", StyleBox["Mathematica", FontSlant->"Italic"], " does not store these values." }], "Text"], Cell["\<\ To substitute x = 3 and y = -1 simultaneously, we use curly braces \ to create a list of values.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(poly\ /. {x\ -> \ 3, \ y\ -> \ \(-1\)}\)], "Input"], Cell[BoxData[ \(20\)], "Output"] }, Open ]], Cell["Substitute x = a and y = b simultaneously.", "Text"], Cell[TextData[{ "Now substitute ", Cell[BoxData[ \(TraditionalForm\`\(x\^2 + 2\ \)\)]], "for x and ", Cell[BoxData[ \(TraditionalForm\`y\^3 - 2 y\)]], " for y." }], "Text"], Cell[TextData[{ "When we are finished using ", StyleBox[" poly", FontWeight->"Bold"], ", it is important to clear it from ", StyleBox["Mathematica", FontSlant->"Italic"], "'s memory. You may wish to re-use the name later. Also, you don't want \ the program to assume something you had forgotten about. (This happens \ particularly often with functions. f tends to be a very popular choice!)" }], "Text"], Cell[BoxData[ \(Clear[poly]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Defining functions", "Section", CellTags->"definef"], Cell[TextData[{ "\tHere again, ", StyleBox["Mathematica", FontSlant->"Italic"], " has some special notation with the underline and the colon. (There is no \ space between : and =.) This is to show a \"delayed assignment.\" Watch it \ carefully. 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