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"\nMath 2374 - University of Minnesota\nhttp://www.math.umn.edu/math2374\n\
Questions to: rogness@math.umn.edu"
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"This semester you will spend a significant amount of time working on the \
computers. We've written a number of labs which should help illustrate many \
of the concepts we'll talk about. Sometimes we'll use the computer to draw \
pretty pictures, which the computer is extremely good at, so you can \
understand a certain idea. Other times we'll give you an interesting problem \
to work on which includes some long and technical computations, and would \
therefore be difficult to do by hand; with the computer doing the number \
crunching (and sometimes even the calculus) for you, you can concentrate on \
understanding the ideas and not worrying about evaluating an ugly integral \
which requires three integration by parts, trigonometry substitutions, and an \
extra u-substitution for good measure.\n\nMost of the time you'll be using ",
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", the program you're using to view this notebook right now. Because this \
is an Institute of Technology course, and nearly all of our students are \
enrolled in the IT, we'll assume a basic level of computer knowledge. \
Although we use Linux, which is quite different from Windows or Macintosh \
computers, the interface in ",
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" is very similar to most other applications you can run on any modern \
system. We won't assume you have a working knowledge of Linux, but once \
you're using ",
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" or a web browser, we expect that you will be comfortable working with \
pull-down menus, windows with scroll bars, etc. If you're worried about this \
you should talk to your TA and we'll try to help you improve your computer \
skills. For now all you have to do is read.\n\nAs you move on, you'll find \
there are commands in the lab for you to run. It would also be useful to \
open another notebook while you read the lab so that you can do your own work \
there. (Go to the File menu and choose \"New\" to do this.)\n\nThere are \
also a number of exercises for you to work on in the labs. To help you \
distinguish these from rhetorical questions, or things that we just want you \
to do on your own, we've formatted the labs so that \"official\" exercises \
are always in a box with a reddish background. (On some computers the \
background is more pink than red.) Here's an example:"
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Cell["\<\
Note that you won't always have to turn in every exercise, although \
it would be a good idea to work on all of them. Your TA will tell you at an \
appropriate time which solutions you need to hand in for each lab.
Usually we'll work on a different lab each week, but in general you'll only \
have to turn something in every two weeks. If you look on the syllabus \
you'll notice that most of the labs are in two pieces, as in \"Lab 2A\" and \
\"Lab 2B.\" This means you should hand in the exercises from these two labs \
together in one report. These lab assignments will be due the week after you \
work on them. For example, the exercises in labs 2A and 2B will be due in \
lab the next week, when you'll start working on lab 3. Your TA will \
generally remind you when labs are due, but if you have any questions you \
should ask.
There's another type of colored box that you'll see as well:\
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\>", "Text",
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In fact, here's the first \"real\" gray box, with an important \
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lecture material very carefully. Sometimes they might leave out certain \
concepts with the knowledge that they will be covered in the labs. In other \
words, these labs are one of the ways you will learn the material in this \
course.\n\nYou should also note that the lab assignments make up a \
significant part of your grade, so you should not take them lightly. Many of \
you probably never had to read your calculus book. At most, you may have \
glanced through the examples to find out how to do a certain homework \
problem. (Lest you think I'm accusing you, let me admit right now that I and \
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some cases this might mean re-reading a paragraph a number of times before it \
makes sense.\n\nYour solutions to lab exercises will be written up much more \
carefully than normal homework assignments. This isn't a writing-intensive \
course, so you don't have to turn in ten pages per problem, but we do expect \
clear writing, reasonable mathematical justification for your work, pictures, \
and so on. A good rule of thumb is that your solution should be a like a \
detailed textbook example. Your TA will show you examples of what we expect \
before you hand in your first lab assignment."
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anything there. That's because the other sections in this lab are ",
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pictures. Cells can also be grouped together in sections, which is done by \
having a big bracket which includes all of the cells. You should see a long \
blue line to the right of all these cells; this is the \"section bracket.\"\n\
\nIf you were to double click on it, this Introduction would collapse. \
(Don't do this quite yet!) All you would see is the cell with the title of \
the section, the little blue bracket for that cell, and then another blue \
bracket to the right. This second bracket would have a little arrow on the \
bottom. Any time you see this arrow on a cell it means there are cells below \
which have been collapsed and are hidden from view. To get them back, you \
just double click on the outer bracket (the one with the arrow on it). Try \
collapsing this Introduction section, and then open it back up again. If you \
can't get it back, ask your TA for help.\n\nUsually when you open a lab, all \
of the sections (including the Introduction) will be collapsed. This lets \
you see sort of a \"Table of Contents\" so you know what you'll be doing. We \
left the introduction to this lab open so that you wouldn't open the first \
lab and not know what to do.\n\nOne last note before you start working: a few \
semesters ago we spent a lot of time revising these labs, and we'd really \
appreciate feedback from you. If you think a lab really helped you \
understand a topic, let us know. If you think a lab is boring and dull, and \
needs to be changed, tell us. (And you don't have to wait until the end of \
the semester to give us these comments.) We have lots of ideas about what \
should be done in the labs, but the final measure of success is whether or \
not you learn from them, so your opinion really does matter!\n\nNow you can \
go on to the actual lab. Remember, double click on the outer bracket of a \
section or sub-section to expand it."
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You can use variables and assign values to them. For reasons that \
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If you want to multiply variables be very careful to remember the * \
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Evaluate this next cell to see what happens if you forget the \
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just returns the variable itself.\n\nIf you're done using variables you can \
erase them from memory using the ",
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"In order to do anything really interesting, we need to use functions. \
Functions which are part of ",
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their arguments. For example, here's the square root function:"
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shown here:"
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",
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the first few weeks of the course, it's very common for people to call us to \
their computer and say, \"This isn't working,\" and the problem is that they \
typed ",
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free to ask us for help. Especially during these first few weeks, however, \
you will usually save yourself (and us) some time by carefully \
double-checking your brackets and capitalization; that's very likely the \
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"There is one very important resource for you, called the Help Browser. \
You can find it under the Help menu above. If you want to know how to do \
something you should check there first. Sometimes the help files are a \
little hard to understand, especially if you don't have much experience with \
",
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browser and see if you can figure out how to get ",
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x. (Suggestion: search for \"absolute value.\") Check your work by \
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help browser include examples, which can be very instructive. To see these \
example you have to click on the little triangle next to the words \"Further \
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don't have to worry about a conflict with something that is already defined.\n\
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You can input numbers or symbols -- or even whole expressions -- into a \
function:"
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Cell[BoxData[
\(TraditionalForm\`v\&\[RightVector]\)]],
"\[CenterDot]",
Cell[BoxData[
\(TraditionalForm\`u\&\[RightVector]\)]],
". (The dot product is written as a period.) Make sure the output here \
makes sense to you. Note that we've used semicolons after the definition \
of",
Cell[BoxData[
\(TraditionalForm\`v\&\[RightVector]\)]],
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Cell[BoxData[
\(TraditionalForm\`u\&\[RightVector]\)]],
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Cell[BoxData[{
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\(2 v\), "\[IndentingNewLine]",
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Cell[TextData[{
"Three-dimensional vectors are possible, and in fact we can make a vector \
with as many dimensions as we like. Here is a three dimensional vector, and \
two nine dimensional vectors as well. To see that ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" actually treats these as vectors, you should insert a command into this \
cell to compute ",
Cell[BoxData[
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"."
}], "Text"],
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Cell[TextData[{
StyleBox["Review of Brackets in ",
FontWeight->"Bold"],
StyleBox["Mathematica",
FontWeight->"Bold",
FontSlant->"Italic"],
"\n\nRemember, using the wrong kind of brackets is the number one cause of \
problems for most students. To help you keep them straight, let's review:\n\n\
",
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FontWeight->"Bold"],
" : used to enter mathematical expressions, e.g. (x+1)^2, or 1/(x-2).\n\n",
StyleBox["[ and ]",
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" : used with functions, e.g. f[x_] = x^2, or Sin[x].\n\n",
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FontWeight->"Bold"],
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Cell[CellGroupData[{
Cell["Loading New Commands", "Subsection"],
Cell[TextData[{
StyleBox["Mathematica",
FontSlant->"Italic"],
" has so many commands that most computers would slow to a crawl if \
everything were automatically loaded. To make things a little faster, many \
commands in ",
StyleBox["Mathematica",
FontSlant->"Italic"],
" are contained in \"packages.\" Occasionally this semester we're going to \
use some of these commands. Rather than have you learn the complexities of \
loading packages, we've assembled everything into one notebook, called \
\"math2374.nb,\" which your TA should have directed you to download into your \
home directory. If you haven't downloaded math2374.nb from the course web \
page yet, you should do so now.\n\nThe math2374.nb file contains commands \
which automatically load every command we'll need this semester. You should \
follow these steps to load them:\n\n(1) Open math2374.nb in ",
StyleBox["Mathematica",
FontSlant->"Italic"],
". Do this now by choosing \"Open\" under the File menu.\n(2) Click on the \
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everything works, a gray box will appear with a confirmation message. At \
this point you can close math2374.nb if you like, to avoid cluttering up your \
mailbox. Don't bother saving the changes; the only change is the appearance \
of the box, and you probably don't want to save multiple copies of that \
anyway!\n\nFrom now on, you should follow the steps above ",
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FontWeight->"Bold"],
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move on."
}], "Text"]
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FontSlant->"Italic"],
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FontSlant->"Italic"],
". Today we're going to learn two of them, and you will be introduced to \
others in the rest of lab 1 and in lab 2.\n\nIf we have a function y=f(x), \
the easiest way to graph it is with the ",
StyleBox["Plot",
FontWeight->"Bold"],
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FontWeight->"Bold"],
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StyleBox["]",
FontWeight->"Bold"],
". Note that expressions such as {x, xmin, xmax} will be very common this \
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StyleBox["Plot",
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Cell[TextData[{
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use the ",
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Cell[CellGroupData[{
Cell[TextData[StyleBox["Options",
FontWeight->"Bold"]], "Subsubsection"],
Cell[TextData[{
"Occasionally you will want to use optional arguments when drawing graphs. \
Options generally come at the end of a command and have the form \"OptionName\
\[RightArrow]Setting.\" [You can type the \[RightArrow] as (hyphen)(greater \
than), \[Dash]\[Succeeds]]. For example, the option Axes\[RightArrow]False \
will prevent ",
StyleBox["Mathematica",
FontSlant->"Italic"],
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StyleBox["Plot",
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StyleBox["Show",
FontWeight->"Bold"],
". Try adding it to the ",
StyleBox["Show",
FontWeight->"Bold"],
" command above and re-evaluating it. (You need to add a comma after \
\"plot2\" before you can add the option.) Did the axes disappear?\n\nYou'll \
learn more options in Lab 1B next week."
}], "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell["Plotting Implicit Functions", "Subsubsection"],
Cell[TextData[{
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StyleBox["Plot",
FontWeight->"Bold"],
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an equation such as ",
Cell[BoxData[
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FontSlant->"Italic"],
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Cell[BoxData[
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StyleBox["Plot",
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StyleBox["Plot",
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StyleBox["Plot",
FontWeight->"Bold"],
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the function into the ",
StyleBox["ImplicitPlot",
FontWeight->"Bold"],
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}], "Text"],
Cell[BoxData[
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Cell[CellGroupData[{
Cell["Saving Notebooks", "Subsection"],
Cell[TextData[{
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\"Save\" or \"Save As.\" ",
StyleBox["Please note",
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of disk space and, if you save notebooks with graphics, they will quickly get \
to be so large that you will use up your disk quota and be barred from using \
the computer. This is especially true in later labs, where we will create \
animations. If you save a notebook with an animation, it will take up \
several megabytes of disk space.\n\nSo, before you save a notebook, you \
should always go to the Kernel menu and choose \"Delete All output.\" This \
will leave all of your commands intact, but delete all of the answers and \
graphics from ",
StyleBox["Mathematica",
FontSlant->"Italic"],
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}], "Text"]
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Cell[CellGroupData[{
Cell[TextData[StyleBox["Single Variable Calculus with Mathematica",
FontSize->16]], "Section"],
Cell[TextData[{
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less the same as what you learned to do last year with functions of one \
variable. In the last part of this introduction we'll show you how to use ",
StyleBox["Mathematica",
FontSlant->"Italic"],
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Cell[CellGroupData[{
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Cell[TextData[{
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calculus. We won't focus on them very much this year, but in a few weeks \
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definition. ",
StyleBox["Mathematica",
FontSlant->"Italic"],
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StyleBox["Limit",
FontWeight->"Bold"],
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plot was, anyway.) I made minor modifications in January 2004 to reflect the \
changes in lab exercises and the use of math2374.nb\n\nThis lab is copyright \
2002, 2004 by Jonathan Rogness (rogness@math.umn.edu) and is protected by the \
Creative Commons Attribution-NonCommercial-ShareAlike License. You can find \
more information on this license at \
http://creativecommons.org/licenses/by-nc-sa/1.0/\n\nAlthough it's not \
specifically required by the license, I'd appreciate it if you let me know if \
you use parts of our labs, just so I can keep track of it. Please send me \
any questions or comments!"
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