(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. 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[ 21494, 651]*) (*NotebookOutlinePosition[ 30471, 868]*) (* CellTagsIndexPosition[ 28761, 827]*) (*WindowFrame->Normal*) Notebook[{ Cell["Mathematical Tools for Materials Scientists and Engineers", "Title"], Cell[CellGroupData[{ Cell["Learning to use Mathematica as a tool.", "Section"], Cell[TextData[{ "Mathematica is a tool for exploring mathematics and solving problems that \ can be posed as a mathematical problem. Mathematica's coverage of \ mathematics and its applications is both very wide and very deep. The depth \ of Mathematica is such that years must be invested before it can wielded \ masterfully. However, students must begin to use Mathematica immediately. \ This means that you must use this tool before you can master it. Don't \ worry\[LongDash]you can't master this tool unless you use it!\n\nThere are \ several software programs like Mathematica (Maple, Matlab, Macsyma, to \ mention a few). These programs allow you to solve equations, perform \ mathematical operations, and visualize mathematics and data. Each one has it \ benefits. Mathematica, perhaps, has a steep learning curve because it \ integrates so many aspects of mathematics. Nevertheless, I believe that your \ intellectual and time investment in learning Mathematica will be have very \ profitable returns on both your future intellect and your future time.\n\n\ Finally, just as there are many good ways to solve a mathematics problem, \ there are many different ways to solve a particular problem using ", StyleBox["Mathematica. ", FontSlant->"Italic"], "Some methods are perhaps more elegant than others; some methods are \ perhaps more clever than others\[LongDash]these judgements are subjective. \ What is important, in the end, is 1) that the solution method works, 2) the \ method and solution can be communicated to others, and 3) the solution or the \ knowledged obtained is a valuable as the time spent acquiring it." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Starting up Mathematica", "Subtitle"], Cell[TextData[{ "First you must locate or obtain Mathematica and permission to use it.\n \ \n As an MIT student, you have an Athena account from which you can run \ Mathematica. There are a number of\nways to open and run a Mathematica \ session. Of course,you must first login, and then one method would be to:\n\t\ 1. open a shell\n\t2. Add the ", StyleBox["Mathematica", FontSlant->"Italic"], " locker by typing: ", StyleBox["add math", FontFamily->"Courier", FontWeight->"Bold"], "\n\t 2. At the shell prompt, type ", StyleBox["mathematica", FontFamily->"Courier", FontWeight->"Bold"], ". (An interface to mathematica's software (properly known as \ Mathematica's kernel) called the Front End will open as well as menus and \ palettes).\n\t 3. Solve problems by defining symbols, performing mathematical \ operations, employing Mathematica's functions,defining your own functions, \ and graphically displaying results.\n \n Also, as an MIT student, you \ are entitled to download a copy and license for $30 so that you can run \ Mathematica on your own computer. Instructions can be found at this URL: \ http://itinfo.mit.edu/article.php?id=6842\n The colors on your sceen may \ not appear to be the same as what is presented in the lectures. I use my own \ style sheet, you may download my style sheet from ", ButtonBox["here.", ButtonData:>{ URL[ "http://pruffle.mit.edu/~ccarter/3.016/"], None}, ButtonStyle->"Hyperlink"], " Information on where to put the style sheet can be found below. Let's \ get started with some simple ", StyleBox["Mathematica", FontSlant->"Italic"], " commands.\n If you are reading this in the ", StyleBox["Mathematica", FontSlant->"Italic"], " FrontEnd, then you can go ahead and familiarize yourself with some basics \ by executing the following lines which are ", StyleBox["Mathematica", FontSlant->"Italic"], " Input. Typically, ", StyleBox["Mathematica", FontSlant->"Italic"], "'s FrontEnd asks ", StyleBox["Mathematica", FontSlant->"Italic"], "'s Kernal to do its job of evaluating by hitting \[ShiftKey]\[LongDash]\ \[EnterKey] while the mouse in an \"Input Cell.\" Input Cells can be \ identified with the ", StyleBox[" ", FontWeight->"Bold", FontColor->RGBColor[1, 0, 0]], StyleBox["\[LeftDownTeeVector]-", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["thingy at the right.", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontColor->RGBColor[0, 0, 1], FontVariations->{"CompatibilityType"->0}], StyleBox["One can evaluate one or more cells by selecting their ", FontVariations->{"CompatibilityType"->0}], StyleBox[" ", FontColor->RGBColor[0, 0, 1], FontVariations->{"CompatibilityType"->0}], StyleBox["\[LeftDownTeeVector]-", FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox["thingies and hitting ", FontVariations->{"CompatibilityType"->0}], "\[ShiftKey]\[LongDash]\[EnterKey].\n\n Try executing the cells below. \ Try to guess what the output might be or represent\[LongDash]and observe \ carefully whether ", StyleBox["Mathematica", FontSlant->"Italic"], " is doing what you would anticipate. 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Spelling warnings can be disabled by typing ", StyleBox["Off[General::spell1]", "MR"], ". However, prudence and experience show that undiscovered typos can be \ even more annoying.\n \n 2. Typing ", StyleBox["?ExpIntegralEi", FontFamily->"Courier"], " returned information about the symbol ", StyleBox["ExpIntegralEi. ", FontFamily->"Courier"], "Typing", StyleBox[" ??FunctionName ", FontFamily->"Courier"], "gives even more information\[LongDash]try", StyleBox[" ??Plot. ", FontFamily->"Courier"], "Wildcards can also by used as demonstrated below." }], "Text", CellTags->{"mmtag:02:help", "mmtag:02:Help_Browser"}], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(?*Exp*\)\)\)], "Input"], Cell[TextData[{ "Each of the above is linked to Mathematica's Help Browser.\n\n3. Typing \ Options[Plot] returned a list of options that can be adjusted by the user \ until the result (in this case the appearance) of the plot is satisfactory.\n\ \n", StyleBox["Mathematica", FontSlant->"Italic"], "'s Help Browser is a very useful tool and will probably become a primary \ resource for students. It contains good tutorials and demonstrations that \ can be copied and pasted. It has very good and concise descriptions of \ mathematics; in fact, exploring the Help Browser is a good way to explore \ mathematics as well as ", StyleBox["Mathematica", FontSlant->"Italic"], ". For instance , the discussion of \"Combinatorial Functions\" under ", StyleBox["Mathematical Functions \[RightPointer] Combinitorial", FontVariations->{"Underline"->True}], " has summarizes some useful information about counting and parttioning of \ sets. 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