(************** 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[ 276182, 6505]*) (*NotebookOutlinePosition[ 278113, 6562]*) (* CellTagsIndexPosition[ 277847, 6552]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Minimal Mathematica", "Title"], Cell[TextData[{ "This handout is about the program called ", StyleBox["Mathematica", FontSlant->"Italic"], ", which is a high-level symbolic manipulation program that can do a great \ many interesting things. Precisely because it is so powerful, ", StyleBox["Mathematica", FontSlant->"Italic"], " isn't easy to use. This handout tries to teach you just enough about the \ program to get you going, but no more than that. Consult the friendly help \ file if you need to know more.\n\n", StyleBox["Mathematica", FontSlant->"Italic"], " can be used to write articles and to do mathematics. In fact, this \ handout is being written inside ", StyleBox["Mathematica", FontSlant->"Italic"], ". But the main things we want to do with it are going to be (a) plotting \ and graphing, and (b) simple algebra." }], "Text", CellMargins->{{18, Inherited}, {Inherited, Inherited}}], Cell[CellGroupData[{ Cell["Getting Started", "Section"], Cell[TextData[{ "The first thing you need to do is to find the program. ", StyleBox["Mathematica", FontSlant->"Italic"], " has been installed in several machines on campus. It should be available \ in the computer lab on the fourth floor of Mudd (Mudd 416) and in the Olin \ computer lab (Olin 324). These copies work with a \"key server,\" which is a \ program on the central server that controls how many copies are in use at a \ given time. Colby only has a license to use a limited number of copies. In \ practice, this means four things:\n\n-- you can get a copy of ", StyleBox["Mathematica", FontSlant->"Italic"], " from the Colby server and install it on your machine (see the ITS web \ pages for instructions),\n\n-- that copy, however, will only run if you are \ on campus and the keyserver has a key you can use;\n\n-- if you try to use ", StyleBox["Mathematica", FontSlant->"Italic"], " and get a message saying that there are too many copies in use, you have \ to wait until fewer people are using the program; and \n\n-- if you are done \ using the program, shut it down so that others can use it!" }], "Text", TextAlignment->Left], Cell[TextData[{ "When you start up ", StyleBox["Mathematica", FontSlant->"Italic"], " you get a blank screen called a \"notebook.\" Once you start typing, you \ will see some weird markings on the right of the screen. ", StyleBox["Mathematica", FontSlant->"Italic"], " notebooks are composed of \"cells,\" which are indicated by square \ brackets at the right. Cells can have subcells, and different cells have \ different functions. This cell, into which I am typing right now, is \ formatted as a text cell. Since you mostly will be computing stuff, you can \ probably just use the default, which is that every cell is an input cell. \ (You don't see cell markings on this printout, but you will if you look at \ this notebook online.)\n\nSo let's just type something into the first cell. \ Let's ask the program to compute a large power. You do this in the obvious \ way, except for one detail. So type in 37! and ", StyleBox["then hit the Enter (not the Return) key", FontWeight->"Bold"], ". (If you're on a laptop, Shift+Enter will also work. I'm not sure how it \ works on the Mac, sorry.)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(37^34\)], "Input"], Cell[BoxData[ \(208381240119593773598371865160915107617069000520604889\)], "Output"] }, Open ]], Cell[TextData[{ "Notice that ", StyleBox["Mathematica", FontSlant->"Italic"], " numbers your input as In[1], and numbers the output cell correspondingly. \ At this point, you can use ", StyleBox["Mathematica", FontSlant->"Italic"], " as a calculator (but a slightly weird calculator)." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(3 + \((44*3^2)\)/313\)], "Input"], Cell[BoxData[ \(1335\/313\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \(4.26517571884984`\)], "Output"] }, Open ]], Cell[TextData[{ "Notice that by default ", StyleBox["Mathematica", FontSlant->"Italic"], " tries to give you exact answers. The N function tells it to give a \ numerical value; % always refers to the latest output. I could also have \ written it as N[Out[2]]. \n\nHow about variables? ", StyleBox["Mathematica", FontSlant->"Italic"], " is happy to use them. It treats any word (without spaces in it) as a \ variable, unless it already knows what that word means. So if you write" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(33 foo^2\ + \ 4 foo - 2\)], "Input"], Cell[BoxData[ \(\(-2\) + 4\ foo + 33\ foo\^2\)], "Output"] }, Open ]], Cell["\<\ it will happily treat \"foo\" as a variable. That means that if you want f \ times o times o, you need to add spaces:\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f\ o\ o\)], "Input"], Cell[BoxData[ \(f\ o\^2\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " understands that two juxtaposition means multiplication, but you can use \ * too if you want:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f*o*o\)], "Input"], Cell[BoxData[ \(f\ o\^2\)], "Output"] }, Open ]], Cell[TextData[{ "Now comes an important thing. In everyday use, we use parentheses with \ several different meanings, depending on context. When we write f(x+1) there \ is usually no doubt about whether we mean the variable f times the polynomial \ x+1 or the function f evaluated at x+1. Computer programs aren't that smart. \ So, in ", StyleBox["Mathematica", FontSlant->"Italic"], ", round parentheses always mean grouping. Square brackets always mean \ function evaluation. So:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(f \((x + 1)\)\)], "Input"], Cell[BoxData[ \(f\ \((1 + x)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%]\)], "Input"], Cell[BoxData[ \(f + f\ x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[x + 1]\)], "Input"], Cell[BoxData[ \(f[1 + x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Expand[%]\)], "Input"], Cell[BoxData[ \(f[1 + x]\)], "Output"] }, Open ]], Cell[TextData[{ "Of course, ", StyleBox["Mathematica", FontSlant->"Italic"], " doesn't know which function \"f\" is, so it can't expand the last \ expression." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Built-In Functions", "Section"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " comes with several sorts of built-in functions. Some are like the buttons \ in your calculator: sine, cosine, exponential, etc. Some are like the \ Simplify function above: they do things to expressions. There are, of course, \ thousands of these; use the Help pages. One basic thing to know, however: all \ built-in functions have names that start with a capital letter. So \"sin\" \ either is a new variable or a new function; Sin is the sine function." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Sin[x]\)], "Input"], Cell[BoxData[ \(Sin[x]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Sin[2]\)], "Input"], Cell[BoxData[ \(Sin[2]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(N[%]\)], "Input"], Cell[BoxData[ \(0.9092974268256817`\)], "Output"] }, Open ]], Cell[TextData[{ "If you write sin[2], ", StyleBox["Mathematica", FontSlant->"Italic"], " will warn you that it looks very much like a function it already knows:" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(sin[2]\)], "Input"], Cell[BoxData[ RowBox[{\(General::"spell1"\), \(\(:\)\(\ \)\), "\<\"Possible spelling \ error: new symbol name \\\"\\!\\(sin\\)\\\" is similar to existing symbol \ \\\"\\!\\(Sin\\)\\\". \\!\\(\\*ButtonBox[\\\"More\[Ellipsis]\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ 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