(*********************************************************************** 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[ 62176, 1915]*) (*NotebookOutlinePosition[ 64092, 1970]*) (* CellTagsIndexPosition[ 64048, 1966]*) (*WindowFrame->Normal*) Notebook[{ Cell["Wright State Calculus Laboratory Project", "Subsubtitle"], Cell[CellGroupData[{ Cell["Calculus Laboratory Information", "Title"], Cell[CellGroupData[{ Cell["About This Notebook", "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell["\<\ Version 8.0, 8/1/2000. Written by Richard Mercer, Copyright 2000.\ \ \>", "Text", Evaluatable->False, AspectRatioFixed->True] }, Closed]], Cell[CellGroupData[{ Cell["General Information", "Subtitle"], Cell[CellGroupData[{ Cell["Welcome to the Calculus Lab!", "Section"], Cell["\<\ The Calculus laboratory is located in room 270 of the \ Mathematical and Microbiological Sciences building (MM). Your class will be \ meeting in this room on certain days of the week. (Some classes will meet in \ room 170 instead.) You will work in pairs or groups on each week\ \[CloseCurlyQuote]s laboratory assignment and submit a report the following \ week.\ \>", "Text"], Cell[TextData[{ " In 270 MM we have 20 Macintosh computers running ", StyleBox["Mathematica\[Trademark]", FontSlant->"Italic"], " software. ", StyleBox["Mathematica", FontSlant->"Italic"], " can perform just about any mathematical computation, and display 2- and \ 3-dimensional color graphics. ", StyleBox["Mathematica", FontSlant->"Italic"], " works with ", StyleBox["notebooks", FontSlant->"Italic"], ", files which are like sections of a textbook in that they can contain \ text and graphics to explain the material, as well as input (commands) and \ output (results). You can change the commands that are there, or enter your \ own commands, and execute them to see the results; this is how you will work \ the assignments. So ", StyleBox["Mathematica", FontSlant->"Italic"], " notebooks are an ", StyleBox["interactive", FontSlant->"Italic"], " textbook." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Why does Calculus have a laboratory?", "Section"], Cell[TextData[{ " We use a laboratory approach because it is part of what we believe to \ be a better way to teach mathematics. In traditional calculus courses, all or \ nearly all of the time is spent in a lecture format, where the instructor is \ the center of attention. Of course you will still have lectures. But in the \ laboratory, you will be participating instead of listening. ", StyleBox["You", FontSlant->"Italic"], ", not your instructor, will be the focus of attention. This alone should \ make the course more interesting. You will have the opportunity to try things \ for yourself, draw your own conclusions, and work at your own pace." }], "Text"], Cell[TextData[{ " There will be more emphasis on ", StyleBox["communicating", FontSlant->"Italic"], " mathematics. Because you will work in pairs or groups, you will spend a \ lot of time discussing what you are doing. In your lab reports you will do \ more writing than is traditionally expected in mathematics courses (usually \ none!). You will have to think more about mathematics because you will have \ to decide ", StyleBox["what", FontSlant->"Italic"], " you want to do before you can ask the computer to do it. Computers make \ it possible to use geometric and numerical approaches to the material that \ are not practical with a textbook, paper and pencil." }], "Text"], Cell["\<\ Whether you are majoring in Engineering, Science, Mathematics \ or Secondary Education, you will be expected to use computers as mathematical \ assistants in your future career, and in many of your other courses before \ graduation.\ \>", "Text"], Cell[TextData[{ " Don\[CloseCurlyQuote]t forget that the computer is just a tool and you \ are the master. You are here to learn and do ", StyleBox["mathematics", FontSlant->"Italic"], ", and the computer is useful only when it can help you do that. Don\ \[CloseCurlyQuote]t be afraid to leave the computers aside at times and work \ with pencil and paper at the center tables. When you are using the computer, \ make sure you understand what the computer is doing, and what you are doing. \ If you go through the labs without thinking about what you are doing or \ talking to anyone about it, you won\[CloseCurlyQuote]t get as much out of \ them as you should." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Calculus Lab FAQ", "Section"], Cell[CellGroupData[{ Cell[TextData[{ "What if I\[CloseCurlyQuote]ve never used a Macintosh or ", StyleBox["Mathematica", FontSlant->"Italic"], " software?" }], "Subsection"], Cell["\<\ The first laboratory session will be devoted to getting used to the \ computers and the software. No experience is necessary, and no programming \ will be required.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["How can I get help with the computers?", "Subsection"], Cell[TextData[ "Your instructor and a student assistant will be available to help during \ scheduled laboratory classes. A student assistant will be available to help \ during open lab hours. Don\[CloseCurlyQuote]t be shy about asking for help!"], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Is there a web site for the calculus lab?", "Subsection"], Cell[TextData[{ "Yes! It\[CloseCurlyQuote]s at ", ButtonBox["http://www.math.wright.edu/Calculus/Lab/", ButtonData:>{ URL[ "http://www.math.wright.edu/Calculus/Lab/"], None}, ButtonStyle->"Hyperlink"], ". There you will find (hopefully!) up-to-date information concerning the \ Calculus Laboratory." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["When can I use the lab?", "Subsection"], Cell["\<\ In addition to laboratory classes, (when your class meets in the \ laboratory instead of a classroom), you can use the lab during open lab \ hours. If you did not finish a laboratory assignment during class, you can \ come during open lab hours to finish it. You can also come in to use the lab \ to help with other homework. Open lab hours will be posted in the laboratory \ a few days after the beginning of classes, and will be also be available on \ the web site.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell[TextData[ "What if we don\[CloseCurlyQuote]t have time to finish the assignment during \ class?"], "Subsection"], Cell[TextData[ "That is the main reason for having open lab hours. We know that some people \ work slower than others, and slower is often better. We \ don\[CloseCurlyQuote]t want you to feel rushed \[Dash] it does no good to \ rush through a lab if you don\[CloseCurlyQuote]t understand what you are \ doing. Please think about what you are doing, ask questions, and take the \ opportunity to try out your own ideas. If necessary you can finish during \ open lab hours. You should expect to have to spend some time in open lab \ during the quarter."], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Can I save my work? Can I print my results?", "Subsection"], Cell["\<\ You can save your work to your account or to a Zip disk. You can \ print your results on the laser printer in the lab.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Should I write my laboratory report during class?", "Subsection"], Cell["\<\ Scheduled laboratory classes usually provide enough time for most \ students to complete the exercises. You should not expect to also be able to \ write your report during class time in the laboratory. Work the problems, and \ prepare and print a notebook with the results of your work. You can prepare \ your report either at home or in the lab, but if you prepare it in the lab \ you should expect to spend extra time outside class.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Can I choose my lab partner?", "Subsection"], Cell["\<\ In general yes, although some instructors may assign lab \ partners.\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Is attendance required at laboratory classes?", "Subsection"], Cell["\<\ Ask your instructor about the attendance policy in your section. \ But regardless of the policy, if you do not attend, you lose an opportunity \ to learn from others, and you deny others an opportunity to learn from you.\ \ \>", "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[StyleBox["calcE", FontSlant->"Italic"]], "Section"], Cell[TextData[{ "A special \[OpenCurlyDoubleQuote]package\[CloseCurlyDoubleQuote]called ", StyleBox["calcE", FontSlant->"Italic"], " is loaded automatically when ", StyleBox["Mathematica", FontSlant->"Italic"], " is started. It customizes ", StyleBox["Mathematica", FontSlant->"Italic"], " for use in teaching Calculus. It provides better graphics and more \ flexible syntax than \[OpenCurlyDoubleQuote]plain\[CloseCurlyDoubleQuote] ", StyleBox["Mathematica", FontSlant->"Italic"], ", and it contains specialized routines used in the Calculus notebooks. " }], "Text"], Cell[TextData[{ "Most commands in the notebooks will not work without the ", StyleBox["calcE", FontSlant->"Italic"], " package!" }], "DisplayText"] }, Closed]], Cell[CellGroupData[{ Cell["Working at Home", "Section"], Cell["\<\ In order to use the Calculus Lab notebooks at home, you need the \ following:\ \>", "Text"], Cell["\<\ (1)\tA computer. To be comfortable you should have a Pentium-class \ processor, Windows 95 or MacOS 8.0 or later, and at plenty of memory and hard \ disk space.\ \>", "Text"], Cell[TextData[{ "(2)\t", StyleBox["Mathematica", FontSlant->"Italic"], " software, version 3.0. There is a student version available for about \ $150 (which is a remarkably good deal). If you do not find it in a bookstore, \ you can order it direct from Wolfram Research, Inc. at 1-800-965-3726 or \ through their web site at ", ButtonBox["http://store.wolfram.com/catalog/student/", ButtonData:>{ URL[ "http://store.wolfram.com/catalog/student/"], None}, ButtonStyle->"Hyperlink"], ". You must verify your student status before the product will be shipped. \ The student version contains all computational features of the professional \ version." }], "Text"], Cell[TextData[{ "(3)\tThe ", StyleBox["calcE", FontSlant->"Italic"], " package described above. Wright State students may purchase a copy from \ Dr. Mercer for a nominal cost of $10." }], "Text"], Cell["(4)\tThe Calculus Lab notebooks themselves, which are free. ", "Text"], Cell[TextData[{ "The notebooks can be obtained directly from the calculus lab. However you \ should ", StyleBox["not", FontSlant->"Italic"], " copy them directly off the server. Instead, open the remote folder \ \[OpenCurlyDoubleQuote]Software for ALL Users\[CloseCurlyDoubleQuote]. Open \ the \[OpenCurlyDoubleQuote]Calculus\[CloseCurlyDoubleQuote] folder inside \ that, and you\[CloseCurlyQuote]ll see a folder called \ \[OpenCurlyDoubleQuote]Take Me Home!\[CloseCurlyDoubleQuote] which contains \ compressed files of notebooks for each course, in Windows or Mac format. Just \ copy the one(s) you want onto a floppy disk (IBM or Mac). If you have Web \ access, you can download the notebooks from ", ButtonBox["http://www.math.wright.edu/Calculus/Lab/Download/", ButtonData:>{ URL[ "http://www.math.wright.edu/Calculus/Lab/Download/"], None}, ButtonStyle->"Hyperlink"], "." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Working on Campus", "Section"], Cell[TextData[{ "The calculus materials may be available at some CATS-operated labs open 24 \ hours, 7 days a week. Check the ", ButtonBox["Web site", ButtonData:>{ URL[ "http://www.math.wright.edu/Calculus/Lab/"], None}, ButtonStyle->"Hyperlink"], " for the latest information." }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Laboratory Program Director", "Section"], Cell[TextData[{ "Dr. Richard Mercer is in charge of the Calculus Laboratory, and is the \ author of the calculus notebooks and the developer of ", StyleBox["calcE", FontSlant->"Italic"], ". You should contact him with any questions, problems, emergencies, etc. \ concerning the administration of the computer lab, the notebooks, or ", StyleBox["calcE", FontSlant->"Italic"], ". In particular any typos or mistakes in the notebooks should be forwarded \ to him in written form, preferably by email. " }], "Text"], Cell[TextData[{ "Contact information:\nOffice: 261 MM, 937-775-2191\nEmail: ", ButtonBox["richard.mercer@wright.edu", ButtonData:>{ URL[ "mailto:richard.mercer@wright.edu"], None}, Active->True, ButtonStyle->"Hyperlink"], "\nWeb: ", ButtonBox["http://www.math.wright.edu/People/Richard_Mercer/", ButtonData:>{ URL[ "http://www.math.wright.edu/People/Richard_Mercer/"], None}, ButtonStyle->"Hyperlink"] }], "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Writing Lab Reports", "Subtitle"], Cell["\<\ Lab reports expect more in the way of writing than you may be \ used to in mathematics. They should be treated the same as lab reports in any \ other laboratory science. You should state the problem, explain your \ procedure, give your results, and draw conclusions.\ \>", "Text"], Cell[TextData[{ " It is usually ", StyleBox["not", FontSlant->"Italic"], " enough to just give the answer. It is ", StyleBox["never", FontSlant->"Italic"], " enough to just print what Mathematica did. 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We backed up this \ conclusion with a formal evaluation:" }], "Text"], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ StyleBox[ UnderscriptBox["lim", RowBox[{ StyleBox["x", UnderscriptBoxOptions->{LimitsPositioning->False}], "\[Rule]", "0"}]], UnderscriptBoxOptions->{LimitsPositioning->False}], StyleBox[ FractionBox[ RowBox[{"tan", RowBox[{"(", StyleBox["x", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}], ")"}]}], StyleBox["x", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]], "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]}], StyleBox["=", "DisplayFormula", FontColor->GrayLevel[0]], RowBox[{ RowBox[{ StyleBox[ UnderscriptBox["lim", RowBox[{ StyleBox["x", UnderscriptBoxOptions->{LimitsPositioning->False}], "\[Rule]", "0"}]], UnderscriptBoxOptions->{LimitsPositioning->False}], StyleBox[ FractionBox[ FractionBox[ RowBox[{"sin", RowBox[{"(", "x", ")"}]}], RowBox[{"cos", RowBox[{"(", "x", ")"}]}]], StyleBox["x", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]], "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]}], StyleBox["=", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}], RowBox[{ RowBox[{ StyleBox[ UnderscriptBox["lim", RowBox[{ StyleBox["x", UnderscriptBoxOptions->{LimitsPositioning->False}], "\[Rule]", "0"}]], UnderscriptBoxOptions->{LimitsPositioning->False}], StyleBox[ FractionBox[ RowBox[{"sin", RowBox[{"(", "x", ")"}]}], RowBox[{ StyleBox["x", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}], " ", "cos", RowBox[{"(", "x", ")"}]}]], "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]}], StyleBox["=", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}], RowBox[{ RowBox[{ StyleBox[ UnderscriptBox["lim", RowBox[{ StyleBox["x", UnderscriptBoxOptions->{LimitsPositioning->False}], "\[Rule]", "0"}]], UnderscriptBoxOptions->{LimitsPositioning->False}], RowBox[{ StyleBox[ FractionBox[ RowBox[{"sin", RowBox[{"(", "x", ")"}]}], StyleBox["x", "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}]], "DisplayFormula", UnderscriptBoxOptions->{LimitsPositioning->False}], RowBox[{ StyleBox[ UnderscriptBox["lim", RowBox[{ StyleBox["x", UnderscriptBoxOptions->{ LimitsPositioning->False}], "\[Rule]", "0"}]], UnderscriptBoxOptions->{LimitsPositioning->False}], StyleBox[ FractionBox[ StyleBox["1", "DisplayFormula", UnderscriptBoxOptions->{ LimitsPositioning->False}], RowBox[{" ", RowBox[{"cos", RowBox[{"(", "x", ")"}]}]}]], "DisplayFormula"]}]}]}], StyleBox["=", "DisplayFormula"], RowBox[{ RowBox[{ RowBox[{"(", StyleBox["1", "DisplayFormula"], StyleBox[")", "DisplayFormula"]}], StyleBox[ RowBox[{"(", "1", ")"}], "DisplayFormula"]}], StyleBox["=", "DisplayFormula"], StyleBox["1", "DisplayFormula"]}]}]}]}]}], TextForm]]]], "DisplayFormula"], Cell["\<\ To check that Mathematica agreed with us, we used the built-in \ Limit command.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Limit", "[", RowBox[{ RowBox[{ RowBox[{"Tan", "[", "x", "]"}], "/", "x"}], ",", RowBox[{"x", "->", "0"}]}], "]"}], FontFamily->"Courier", FontWeight->"Bold"]], "Input"], Cell[BoxData["1"], "Output"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Discussion of Solution", "Subsection"], Cell["\<\ This is admittedly a highly idealized example; it is unlikely that \ you would include in any single problem all the elements shown here. (But you \ should get a really good score if you did!) \ \>", "Text"], Cell["\<\ This problem emphasizes approaching a problem in several different \ ways. It shows graphing and numerical calculations (using the computer) and \ algebraic calculation (paper and pencil). Finally the computer is used to \ check the answer by a direct command. Not all problems will benefit from \ using more than one approach, but many will. You should use alternate methods \ of solution whenever you see the opportunity, even if the problem does not \ explicitly ask you to. \ \>", "Text"] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["About the Problems", "Section"], Cell[CellGroupData[{ Cell["Icons", "Subsection"], Cell["\<\ The icons in front the problems tell you something about the \ nature of the problem. This is an attempt to be helpful, but some problems \ may have been overlooked and may not have the proper icon.\ \>", "Text"], Cell[TextData[StyleBox["L99.1", FontWeight->"Bold"]], "Text", CellDingbat->"\[FilledSquare]"], Cell["\<\ Most problems have an icon of a filled square in front of the \ problem number. This means that the problem requires technology in some way. \ In many cases a graphing calculator would be adequate if you are working \ outside the lab.\ \>", "Text"], Cell[TextData[StyleBox["L99.2", FontWeight->"Bold"]], "Text", CellDingbat->"\[EmptySquare]"], Cell["\<\ Many problems have an icon of an empty square in front of the \ problem number. This means that the problem does not require technology. It\ \[CloseCurlyQuote]s a pencil and paper problem that could be done anywhere. \ You may want to postpone working such problems until you are finished with \ the ones that do require the computer, though it\[CloseCurlyQuote]s often \ good to discuss these problems with your lab partner.\ \>", "Text"], Cell[TextData[StyleBox["L99.2", FontWeight->"Bold"]], "Text", CellDingbat->"\[FivePointedStar]"], Cell[TextData[{ " A few problems have an icon of a star in front of the problem number. \ This means that the problem requires the specific combination of ", StyleBox["Mathematica", FontSlant->"Italic"], " and ", StyleBox["calcE", FontSlant->"Italic"], ", and you are very unlikely to be able to do the problem properly \ otherwise. " }], "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Summary Problems", "Subsection"], Cell["\<\ At the end of each problem set is a Summary problem that asks \ you to write a paragraph or two about the lab. 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