(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 144889, 3284] NotebookOptionsPosition[ 137633, 3055] NotebookOutlinePosition[ 138241, 3078] CellTagsIndexPosition[ 138198, 3075] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ "Getting started in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Title", CellChangeTimes->{{3.3907458272729015`*^9, 3.390745835374874*^9}}], Cell["Comp 160 Course Module 1", "Subtitle", CellChangeTimes->{{3.390745838950158*^9, 3.3907458395911055`*^9}, { 3.45865592271875*^9, 3.45865592521875*^9}}], Cell[CellGroupData[{ Cell[TextData[{ "Survival skills for ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.390745863927069*^9, 3.390745869505313*^9}, { 3.391450281328409*^9, 3.3914502846332273`*^9}, {3.391450529920825*^9, 3.3914505340368257`*^9}}], Cell[TextData[{ "This module begins our process of learning to use ", StyleBox["Mathematica", FontSlant->"Italic"], " as tool for solving and presenting solutions to problems that arise in \ Science and Engineering. ", StyleBox["Mathematica", FontSlant->"Italic"], " consists of two main parts; a front-end and a kernel. The front-end is a \ set of windows that allows the user to view ", StyleBox["Mathematica", FontSlant->"Italic"], " files, called ", StyleBox["notebooks", FontSlant->"Italic"], ", and manipulate the contents of these notebooks. The kernel is a set of \ core mathematical functions that ", StyleBox["Mathematica", FontSlant->"Italic"], " uses to compute the value of expressions that appear in ", StyleBox["Mathematica", FontSlant->"Italic"], " notebooks. Across the top of the screen is a thin, but wide window that \ contains a number of pull-down menus. These windows can be used to " }], "Text", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449190678382*^9}, {3.3914532787482624`*^9, 3.3914533146506033`*^9}, {3.392206947179152*^9, 3.3922070032906322`*^9}, { 3.3922070368143263`*^9, 3.3922070429147882`*^9}}], Cell[TextData[{ "Open and save notebooks (", Cell[BoxData["File"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449241832958*^9}, 3.3914492901033306`*^9, { 3.460126432703125*^9, 3.460126435609375*^9}}], Cell[TextData[{ "Edit the contents of a notebook (", Cell[BoxData["Edit"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449241832958*^9}, {3.3914492901033306`*^9, 3.39144929600193*^9}, {3.3914493472266088`*^9, 3.3914493578721285`*^9}}], Cell[TextData[{ "Format the contents of a notebook (", Cell[BoxData["Format"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449241832958*^9}, {3.3914492901033306`*^9, 3.3914493012696095`*^9}, 3.3914528806478834`*^9}], Cell[TextData[{ "Organize and manipulates cells, the building blocks of a notebook (", Cell[BoxData["Cell"]], "). " }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449241832958*^9}, {3.3914492901033306`*^9, 3.3914493025214343`*^9}}], Cell[TextData[{ "Create graphics for the notebook (", Cell[BoxData["Graphics"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.3914493053655806`*^9}}], Cell[TextData[{ "Control evaluation of expressions in the notebook (", Cell[BoxData["Evaluation"]], "). " }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.3914493073685007`*^9}, {3.392207121085526*^9, 3.392207126334177*^9}}], Cell[TextData[{ "Open palette design to simplify common tasks (", Cell[BoxData["Palettes"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.3914493094615526`*^9}, {3.392207133990933*^9, 3.39220713735007*^9}}], Cell[TextData[{ "Manage the layout of multiple notebooks on the screen (", Cell[BoxData["Window"]], ")," }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449311304239*^9}}], Cell[TextData[{ "Provide helpful information about ", StyleBox["Mathematica ", FontSlant->"Italic"], "(", Cell[BoxData["Help"]], ")." }], "Text", CellDingbat->"\[FilledSquare]", CellChangeTimes->{{3.3914485261095257`*^9, 3.391448738829644*^9}, { 3.391449167865123*^9, 3.391449338073264*^9}, 3.3914528864463367`*^9}], Cell[TextData[{ "Instead of exploring each of these menus in detail, we will focus on a few \ key survival skills for ", StyleBox["Mathematica", FontSlant->"Italic"], " which can be accessed through these menus." }], "Text", CellChangeTimes->{{3.3905860398613024`*^9, 3.3905860615424786`*^9}, { 3.391448681425957*^9, 3.391448682207096*^9}, {3.3914493169024*^9, 3.3914493172829547`*^9}, {3.39144937762092*^9, 3.391449434083235*^9}, { 3.3914523109273033`*^9, 3.391452311718457*^9}, {3.392207150935748*^9, 3.392207170419806*^9}, {3.458484433015625*^9, 3.45848443540625*^9}}], Cell[TextData[{ "These notebooks were created using ", StyleBox["Mathematica", FontSlant->"Italic"], " version 7, the same version as on the Owlnet PCs. If you use ", StyleBox["Mathematica", FontSlant->"Italic"], " version 6, you'll encounter some differences in the interface, such as the \ palettes and ", StyleBox["Documentation Center", FontFamily->"Courier New"], ", but all the equations should still work." }], "Text", CellChangeTimes->{{3.4584853021875*^9, 3.458485465125*^9}, { 3.458485532546875*^9, 3.458485682109375*^9}, 3.4584857945625*^9, { 3.458487199015625*^9, 3.458487226890625*^9}, {3.460126449171875*^9, 3.460126451390625*^9}}], Cell[CellGroupData[{ Cell["Saving your work", "Subsection", CellChangeTimes->{{3.39144945623553*^9, 3.3914494650984507`*^9}}], Cell[TextData[{ "Perhaps the most critical task is saving your work. The ", Cell[BoxData["File"]], " menu has several options for saving a ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook. ", Cell[BoxData["Save"]], " will simply save the notebook into its current location. For notebooks \ first opened via a download from the web, the notebook usually resides in a \ temporary directory local to the machine on which you are currently working. \ Since you will switch machines between classes, this location is not a safe \ place to store your work. Instead, use ", Cell[BoxData[ RowBox[{"Save", " ", "As"}]]], " to save your work to the directory ", Cell[BoxData[ RowBox[{"My", " ", "Documents"}]]], ". For the PCs in Symonds II Lab, ", Cell[BoxData[ RowBox[{"My", " ", "Documents"}]]], " is automatically linked to your Owlnet directory. In the interest of good \ organization, I suggest that you create a ", Cell[BoxData["Comp160"]], " directory in ", Cell[BoxData[ RowBox[{"My", " ", "Documents"}]]], " where you will save all of your notebooks. " }], "Text", CellChangeTimes->{{3.3905860398613024`*^9, 3.3905860615424786`*^9}, { 3.391448681425957*^9, 3.391448682207096*^9}, {3.3914493169024*^9, 3.3914493172829547`*^9}, {3.39144937762092*^9, 3.3914497869877243`*^9}, { 3.391449817171728*^9, 3.391449840896316*^9}, 3.3914529006870975`*^9, { 3.392207280676815*^9, 3.392207281480912*^9}, {3.45925962196875*^9, 3.45925962196875*^9}, {3.459260297890625*^9, 3.459260298625*^9}}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell[TextData[{ "In this and subsequent notebooks, cells in purple signify exercises that \ you are required to do. You will work on these exercises during the \ interactive class, and they are due at the beginning of the next class. As \ your first exercise, create a ", Cell[BoxData[ RowBox[{"Comp", " ", "160"}]]], " directory in ", Cell[BoxData[ RowBox[{"My", " ", "Documents"}]]], " and save this notebook into that directory." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.392207334602003*^9, 3.3922073396376534`*^9}, {3.459259606890625*^9, 3.459259606890625*^9}, { 3.459260726734375*^9, 3.45926079653125*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell["\<\ As another general piece of good advice, I suggest that you save your work \ frequently. Computers (especially running Windows) have a bad habit of \ misbehaving at the most critical time (say after you have done an hour of \ unsaved work). I suggest saving your work at least every 15 minutes.\ \>", "Text", CellChangeTimes->{{3.3914521791952553`*^9, 3.391452289255709*^9}, { 3.392207372758443*^9, 3.3922073739770803`*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Printing your work", "Subsection", CellChangeTimes->{{3.391449887283943*^9, 3.391449890168148*^9}}], Cell[TextData[{ "Another critical task is printing out your notebooks to be turned in for \ grading. Symonds II contains two printers that can be accessed from the ", Cell[BoxData["Print"]], " command in the ", Cell[BoxData["File"]], " menu. You can select either the east or west printer from the list of \ printer names on the small window created by the ", Cell[BoxData["Print"]], " command." }], "Text", CellChangeTimes->{{3.3914503075366173`*^9, 3.391450439859527*^9}, { 3.3918796283038273`*^9, 3.3918796299662504`*^9}}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell["\<\ Print out the first page of this notebook. Be sure to set the appropriate \ page numbers so you don't print the whole notebook.\ \>", "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell["\<\ A printed version of your modules will be due at the beginning of class. \ Since printing out the modules takes a few minutes, either print them out \ beforehand or come to class early enough to print them out before class \ starts. Arriving late to class and then trying to print out your module \ makes me very cranky and prone to start imposing draconian turn-in policies.\ \>", "Text", CellChangeTimes->{{3.391879633881959*^9, 3.391879755759641*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Getting help", "Subsection", CellChangeTimes->{{3.391449870189021*^9, 3.391449871891503*^9}}], Cell[TextData[{ "The ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " that is accessible from the ", Cell[BoxData["Help"]], " menu will become your best friend in this class. Becoming an expert at \ using the ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " will make your life much easier. The main menu for the ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " provides an overview of the capabilities of ", StyleBox["Mathematica", FontSlant->"Italic"], ". Another way to access information about a function is to simply to type \ its name into the blank line at the top of the ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " window and click the ", StyleBox["Mathematica", FontSlant->"Italic"], " icon to the left. The ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " will search for and return links to relevant topics in its library of \ helpful information. " }], "Text", CellChangeTimes->{{3.390586064216323*^9, 3.390586065107605*^9}, { 3.39058653295033*^9, 3.3905865340519133`*^9}, {3.39058678187827*^9, 3.390586786154419*^9}, {3.3905871921782527`*^9, 3.390587197996619*^9}, { 3.391450607513946*^9, 3.3914508469430027`*^9}, {3.392207512877863*^9, 3.3922075133464527`*^9}, {3.4088222319013863`*^9, 3.4088222560179577`*^9}, { 3.408822300635901*^9, 3.4088223020927877`*^9}, {3.458483895625*^9, 3.458483902796875*^9}}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell[TextData[{ "Use the ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " to locate functions that manipulate prime numbers. Locate a function that \ determines whether an integer is prime. Use this function to determine \ whether ", Cell[BoxData[ RowBox[{ SuperscriptBox["2", "31"], "-", "1"}]]], " is prime. " }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, {3.392207789527644*^9, 3.392207789527944*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell[TextData[{ "The ", Cell[BoxData[ RowBox[{"Documentation", " ", "Center"}]]], " contains a number of tutorials on relevant topics in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Instead of rehashing them in our notebooks, I will simply provide a \ hyperlink to the relevant tutorial or explanation. In ", StyleBox["Mathematica", FontSlant->"Italic"], ", hyperlinks are always highlighted in blue. " }], "Text", CellChangeTimes->{{3.3914510238709407`*^9, 3.3914510837081757`*^9}, { 3.391451141342199*^9, 3.3914511980548787`*^9}, {3.3914512374122567`*^9, 3.3914512374423003`*^9}, {3.3914512766294303`*^9, 3.3914513343435698`*^9}, 3.3914514404482574`*^9, {3.3914514715836487`*^9, 3.391451471894101*^9}, { 3.3914515205550423`*^9, 3.3914515907974467`*^9}, {3.3914516233348827`*^9, 3.3914516286326056`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell[TextData[{ "Click on the blue text to visit a tutorial on ", StyleBox[ButtonBox["Integer and Number\[Hyphen]Theoretical Functions", BaseStyle->"Link", ButtonData->"paclet:tutorial/IntegerAndNumberTheoreticalFunctions"], FontColor->RGBColor[0, 0, 1]], "." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Controlling computation in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Subsection", CellChangeTimes->{{3.3914504752010508`*^9, 3.3914504854960594`*^9}}], Cell[TextData[{ "One final skill is learning how to control computations in ", StyleBox["Mathematica", FontSlant->"Italic"], ". As we noted in the previous module, ", StyleBox["Mathematica", FontSlant->"Italic"], " has no notion of an undefined variable. While the idea that computation \ corresponds to simplification of an expression makes ", StyleBox["Mathematica", FontSlant->"Italic"], " an extremely powerful language, this paradigm sometimes causes ", StyleBox["Mathematica", FontSlant->"Italic"], " to strain mightily to simplify or evaluate an expression in which the user \ has unwittingly made a simple mistake such as accidentally inserting an \ undefined variable. " }], "Text", CellChangeTimes->{{3.3905860489243345`*^9, 3.390586054993061*^9}, { 3.3914516729271812`*^9, 3.391451943762024*^9}, {3.3914523916049213`*^9, 3.3914524101319313`*^9}, 3.391452915128151*^9, {3.392208951127565*^9, 3.3922090166469297`*^9}, {3.4088226174937153`*^9, 3.408822622715523*^9}, { 3.408822653886292*^9, 3.408822662502685*^9}}], Cell[TextData[{ "In such cases, ", StyleBox["Mathematica", FontSlant->"Italic"], " may take a long time to find what it thinks is the correct answer to an \ erroneous input expression. If ", StyleBox["Mathematica", FontSlant->"Italic"], " \"hangs\" and fails to return a reasonable answer in a moderate amount of \ time, this situation is often the case. To help deal with this problem, you \ may abort a current evaluation by selecting the ", Cell[BoxData[ RowBox[{"Abort", " ", "Evaluation"}]]], " option from the ", Cell[BoxData["Evaluation"]], " menu. (This command also has the keyboard shortcut ", Cell[BoxData[ RowBox[{"Alt", "+", "."}]]], " .)" }], "Text", CellChangeTimes->{{3.3905860489243345`*^9, 3.390586054993061*^9}, { 3.3914516729271812`*^9, 3.391452091457345*^9}, {3.391452418153626*^9, 3.391452418444049*^9}}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell["\<\ Evaluate the expression below. Abort its evaluation once you realize it will \ never return an answer.\ \>", "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452948626988*^9, 3.3914529584212666`*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell[BoxData[ RowBox[{"While", "[", RowBox[{"True", ",", "1"}], "]"}]], "Input", CellChangeTimes->{{3.391452140378666*^9, 3.3914521452758055`*^9}}], Cell[TextData[{ "Occasionally, ", StyleBox["Mathematica", FontSlant->"Italic"], " may also run slowly due to the presence of lots of complex ", Cell[BoxData["Manipulate"]], " commands. ", StyleBox["Mathematica", FontSlant->"Italic"], " uses much of its computation power dynamically updating the output of \ these ", Cell[BoxData["Manipulate"]], " commands (even if the user is not manipulating the sliders.) If ", StyleBox["Mathematica", FontSlant->"Italic"], " seems to be laggy, you should try disabling ", Cell[BoxData[ RowBox[{"Dynamic", " ", "Updating"}]]], " in the ", Cell[BoxData["Evaluation"]], " menu." }], "Text", CellChangeTimes->{{3.390586340153101*^9, 3.3905863472332816`*^9}, { 3.390586646503611*^9, 3.3905866490372543`*^9}, {3.3914505047641497`*^9, 3.3914505112135525`*^9}, {3.391452164764217*^9, 3.391452169681385*^9}, { 3.391452434767847*^9, 3.3914526206388235`*^9}, 3.391452917882166*^9, { 3.392209125355301*^9, 3.3922091311329613`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell["\<\ Evaluate this expression with dynamic updating turned on. Move the slider. \ Next, disable dynamic updating. Now, what happens when you move the slider? \ Finally, enable dynamic updating once more and move the slider. What happens?\ \>", "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, {3.392209171640656*^9, 3.392209171889008*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"x", "!"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "100", ",", "1"}], "}"}]}], "]"}]], "Input", CellChangeTimes->{{3.391452653927354*^9, 3.3914526649734573`*^9}}], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`x$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[$CellContext`x$$], 0, 100, 1}}, Typeset`size$$ = {14., {0., 15.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`x$347$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`x$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`x$$, $CellContext`x$347$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Factorial[$CellContext`x$$], "Specifications" :> {{$CellContext`x$$, 0, 100, 1}}, "Options" :> {}, "DefaultOptions" :> {}], ImageSizeCache->{501., {92., 103.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{3.391452665764611*^9, 3.3922091943097057`*^9, 3.408822783596272*^9}] }, Open ]] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Numerical calculation in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.3907458730805964`*^9, 3.3907458785787215`*^9}, { 3.3918740526953063`*^9, 3.3918740548184013`*^9}}], Cell[TextData[{ "As mentioned in the previous notebook, ", StyleBox["Mathematica", FontSlant->"Italic"], " at its core is just a very sophisticated calculator. To use this \ calculator, you need to create (or reuse) an ", Cell[BoxData["Input"]], " cell and enter an expression. Hitting ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], " then evaluates the expression in the cell and returns its ", StyleBox["value", FontSlant->"Italic"], " (a simplified version of the expression)." }], "Text", CellChangeTimes->{{3.3905859669364414`*^9, 3.3905859765302367`*^9}, { 3.390586197047325*^9, 3.390586209465181*^9}, {3.3905870778338337`*^9, 3.3905870803474483`*^9}, {3.3918713025259123`*^9, 3.391871318038528*^9}, { 3.391871484861735*^9, 3.3918716058080587`*^9}}], Cell[TextData[{ "Mathematical expressions in ", StyleBox["Mathematica", FontSlant->"Italic"], " can be entered in ", Cell[BoxData["TraditionalForm"]], " that mimics traditional mathematical notation. For example," }], "Text", CellChangeTimes->{{3.3918718655266953`*^9, 3.391871910432162*^9}, 3.392209312614799*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"1", "+", "1"}]], "Input", CellChangeTimes->{{3.3918719124350815`*^9, 3.391871912915783*^9}}], Cell[BoxData["2"], "Output", CellChangeTimes->{3.3918719135667315`*^9, 3.392209323419589*^9}] }, Open ]], Cell[TextData[{ Cell[BoxData["TraditionalForm"]], " is supported by ", StyleBox["Mathematica", FontSlant->"Italic"], " to allow users to enter simple expressions in the way in which they are \ accustomed. Internally, ", StyleBox["Mathematica", FontSlant->"Italic"], " represents all expressions in ", Cell[BoxData["StandardForm"]], ". This form consists of expressions of the form ", Cell[BoxData[ RowBox[{"Function", "[", RowBox[{ SubscriptBox["arg", "1"], ",", SubscriptBox["arg", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["arg", "n"]}], "]"}]]], ". For example, the expression ", Cell[BoxData[ RowBox[{"1", "+", "1"}]]], " in ", Cell[BoxData[ RowBox[{"StandardForm", Cell[""]}]]], " is " }], "Text", CellChangeTimes->{{3.3918719185239587`*^9, 3.3918722915978527`*^9}, { 3.392209387594993*^9, 3.392209388462455*^9}, {3.4088848917730083`*^9, 3.4088849107738867`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Plus", "[", RowBox[{"1", ",", "1"}], "]"}]], "Input", CellChangeTimes->{{3.3918722945020866`*^9, 3.391872296565094*^9}}], Cell[BoxData["2"], "Output", CellChangeTimes->{3.391872296995722*^9, 3.392209401873763*^9}] }, Open ]], Cell[TextData[{ "There are two points to make about ", Cell[BoxData["StandardForm"]], ". First, all ", StyleBox["Mathematica", FontSlant->"Italic"], " function names start with upper case. (To distinguish your functions from \ ", StyleBox["Mathematica", FontSlant->"Italic"], "'s, you should always use lower case.) Second, the parameters to the \ function (the ", Cell[BoxData[ SubscriptBox["arg", "i"]]], ") are contained inside square brackets, not parentheses. Specifically, ", StyleBox["Mathematica", FontSlant->"Italic"], " uses ", Cell[BoxData[ RowBox[{"[", "]"}]]], " for functions and ", Cell[BoxData[ RowBox[{"(", ")"}]]], " for grouping inside expressions. Square brackets and parentheses are ", StyleBox["not", FontSlant->"Italic"], " interchangeable. 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This error is indicated by the red bracket on the \ right-hand side of the cell with a small square labeled with a ", Cell[BoxData["+"]], ". To view the error message associated with ", StyleBox["Mathematica", FontSlant->"Italic"], "'s evaluation, you can click on the ", Cell[BoxData["+"]], " to expand the cell. Confusing the usage of square brackets and \ parentheses is the most common error that a novice ", StyleBox["Mathematica", FontSlant->"Italic"], " user makes. Please remember the difference." }], "Text", CellChangeTimes->{{3.3918725326793184`*^9, 3.3918726728036013`*^9}, { 3.391872743716984*^9, 3.3918727663900385`*^9}, 3.392213460077546*^9}], Cell[TextData[{ "To start learning the basics of evaluating mathematical expressions in ", StyleBox["Mathematica", FontSlant->"Italic"], ", review the ", StyleBox["Mathematica", FontSlant->"Italic"], " tutorials contained in the introduction to ", StyleBox[ButtonBox["Numerical Calculations", BaseStyle->"Link", ButtonData->"paclet:tutorial/NumericalCalculationsOverview"], FontColor->RGBColor[0, 0, 1]], " from the ", StyleBox["Documentation Center", FontFamily->"Courier New"], ". You should spend a couple of minutes working over each of the seven \ short tutorials there and then do the exercises below." }], "Text", CellChangeTimes->{{3.391871615752557*^9, 3.3918716705724773`*^9}, { 3.391871740424312*^9, 3.391871794312875*^9}, {3.3918723694613676`*^9, 3.3918724111421328`*^9}}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell[TextData[{ "Which is larger ", Cell[BoxData[ SuperscriptBox["\[Pi]", "\[ExponentialE]"]]], " or ", Cell[BoxData[ SuperscriptBox["\[ExponentialE]", "\[Pi]"]]], "?" }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918731539049854`*^9}, {3.391873443186721*^9, 3.3918734635163593`*^9}, { 3.391873516293301*^9, 3.3918735876373115`*^9}, {3.3918736406145453`*^9, 3.391873748221422*^9}, {3.3918738283582516`*^9, 3.391873840085348*^9}, { 3.4088850169901342`*^9, 3.408885017281605*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}}], Cell[TextData[{ "Given two numbers ", Cell[BoxData["a"]], " and ", Cell[BoxData["b"]], ", the ", StyleBox["absolute", FontSlant->"Italic"], " error between the two numbers is ", Cell[BoxData[ RowBox[{"|", RowBox[{"a", "-", "b"}], "|"}]]], ". The ", StyleBox["relative", FontSlant->"Italic"], " error between the two number is ", Cell[BoxData[ FractionBox[ RowBox[{"|", RowBox[{"a", "-", "b"}], "|"}], "a"]]], ", assuming that the first number is the true value, and the second number \ is an approximation to it. To 20 decimal places, what are the absolute and \ relative errors between ", Cell[BoxData["\[Pi]"]], " and its approximation ", Cell[BoxData[ FractionBox["22", "7"]]], "?" }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918731539049854`*^9}, {3.391873443186721*^9, 3.3918734635163593`*^9}, { 3.391873516293301*^9, 3.3918735876373115`*^9}, {3.3918736406145453`*^9, 3.391873748221422*^9}, {3.391874371069455*^9, 3.391874371239703*^9}, { 3.40897809496875*^9, 3.408978095171875*^9}, {3.45848391521875*^9, 3.458483934578125*^9}, {3.458483968296875*^9, 3.45848406284375*^9}, { 3.45848414125*^9, 3.458484192171875*^9}, 3.45848429334375*^9, { 3.458484341046875*^9, 3.45848434290625*^9}, {3.458484386921875*^9, 3.458484390296875*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell[TextData[{ "Stirling's formula states that ", Cell[BoxData[ RowBox[{ RowBox[{"Log", "[", RowBox[{"n", "!"}], "]"}], "\[TildeTilde]", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"n", "+", FractionBox["1", "2"]}], ")"}], " ", RowBox[{"Log", "[", "n", "]"}]}], "-", "n", "+", RowBox[{"Log", "[", SqrtBox[ RowBox[{"2", " ", "\[Pi]"}]], "]"}]}]}]]], ". 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Find a value for ", FontColor->RGBColor[0.5, 0, 0.5]], Cell[BoxData["n"]], " such that ", Cell[BoxData[ RowBox[{ SuperscriptBox["2", "n"], "+", "1"}]]], " is divisible by the square of a whole number greater than one." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918731539049854`*^9}, {3.391873443186721*^9, 3.3918734635163593`*^9}, { 3.391873516293301*^9, 3.3918735876373115`*^9}, 3.392213467803707*^9}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "The ", StyleBox["Mathematica", FontSlant->"Italic"], " tutorials often write an expression in the form ", Cell[BoxData[ RowBox[{"arg", " ", "//", " ", "Function"}]]], ". What does the ", Cell[BoxData["//"]], " operator do? Specifically, what is an alternative way to write the \ expression ", Cell[BoxData[ RowBox[{"\[Pi]", "//", "N"}]]], "?" }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, 3.3918748007759113`*^9}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Algebraic computation in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.3918740792139673`*^9, 3.3918740858937054`*^9}, { 3.3918744520174665`*^9, 3.3918744536999197`*^9}}], Cell[TextData[{ "One fundamental feature of ", StyleBox["Mathematica", FontSlant->"Italic"], " that separates it from other languages like Java or Matlab is its ability \ to perform not only numerical calculations, but also algebraic calculations. \ This ability arises because ", StyleBox["Mathematica", FontSlant->"Italic"], " treats a mathematical expression as something to be simplified as opposed \ to something to be evaluated numerically. Thus, ", StyleBox["Mathematica", FontSlant->"Italic"], " is easily able to evaluate " }], "Text", CellChangeTimes->{{3.391874458777322*^9, 3.3918745816965218`*^9}, { 3.392211116061035*^9, 3.392211123830573*^9}, {3.392211153900618*^9, 3.392211233833625*^9}, 3.392213477297399*^9}], Cell[CellGroupData[{ Cell[BoxData[ FractionBox[ RowBox[{"x", "+", "x"}], "x"]], "Input", CellChangeTimes->{{3.391874586533574*^9, 3.391874592081662*^9}}], Cell[BoxData["2"], "Output", CellChangeTimes->{3.391874594114626*^9}] }, Open ]], Cell[TextData[{ "without having a specific value for ", Cell[BoxData["x"]], ". Please spend 20 minutes browsing the tutorials in ", ButtonBox["Algebraic Calculations", BaseStyle->"Link", ButtonData->"paclet:tutorial/AlgebraicCalculationsOverview"], ". You do not need to know this material in depth. Instead, you simply \ need to know where to look to answer the following questions." }], "Text", CellChangeTimes->{{3.3918746041993284`*^9, 3.3918746679923306`*^9}, { 3.3918747379743547`*^9, 3.391874782869807*^9}, 3.392213507885388*^9, 3.458484419640625*^9}], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Expand the expression ", Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}], "10"]]], ". What is the coefficient of ", Cell[BoxData[ RowBox[{ SuperscriptBox["a", "3"], SuperscriptBox["b", "7"]}]]], "? More generally, for ", Cell[BoxData[ SuperscriptBox[ RowBox[{"(", RowBox[{"a", "+", "b"}], ")"}], "n"]]], " do you see a pattern for the coefficients of ", Cell[BoxData[ RowBox[{ SuperscriptBox["a", "i"], SuperscriptBox["b", RowBox[{"n", "-", "i"}]]}]]], "? Investigate the ", StyleBox["Mathematica", FontSlant->"Italic"], " function ", Cell[BoxData["Binomial"]], "." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391874985535267*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Set the variable ", Cell[BoxData["x"]], " to have the value ", Cell[BoxData["1"]], ". Now, simplify the expression ", Cell[BoxData[ FractionBox[ RowBox[{ SuperscriptBox["x", "4"], "-", "1"}], RowBox[{"x", "-", "1"}]]]], ". What is the answer? Next, clear the value of the variable ", Cell[BoxData["x"]], ". Then, evaluate ", Cell[BoxData[ FractionBox[ RowBox[{ SuperscriptBox["x", "4"], "-", "1"}], RowBox[{"x", "-", "1"}]]]], " with ", Cell[BoxData["x"]], " being undefined and then set ", Cell[BoxData[ RowBox[{"x", "=", "1"}]]], ". What is the answer?" }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391875084519573*^9}, { 3.3918752344982233`*^9, 3.3918752448833632`*^9}, {3.3922114912530193`*^9, 3.392211497646697*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Consider the polynomial expression ", Cell[BoxData[ RowBox[{ SuperscriptBox["x", "2"], "-", SuperscriptBox["y", "2"]}]]], " in Cartesian coordinates ", Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "y"}], "}"}]]], ". Transform this expression into polar coordinates ", Cell[BoxData[ RowBox[{"{", RowBox[{"r", ",", "\[Theta]"}], "}"}]]], " using the rules ", Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", RowBox[{"r", " ", RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ",", RowBox[{"y", "\[Rule]", RowBox[{"r", " ", RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}]}], "}"}]]], ". Simplify the resulting expression." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391875084519573*^9}, { 3.3918752344982233`*^9, 3.3918752448833632`*^9}, {3.391875359350241*^9, 3.39187546053776*^9}, {3.391875504041182*^9, 3.391875517941447*^9}}, FontColor->RGBColor[0.5, 0, 0.5]], Cell[TextData[{ "Given its ability to manipulate algebraic expressions, ", StyleBox["Mathematica", FontSlant->"Italic"], " is also well-suited to solving systems of algebraic equations. We will \ leverage this capability often in this class. The bread-and-butter function \ for this task is ", Cell[BoxData["Solve"]], "." }], "Text", CellChangeTimes->{{3.3918759593649855`*^9, 3.3918760350453176`*^9}, { 3.391876161159176*^9, 3.391876305960277*^9}, 3.392211611075569*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"2", "x"}], "+", "1"}], "\[Equal]", "0"}], "]"}]], "Input", CellChangeTimes->{{3.391876307953182*^9, 3.39187631539403*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"x", "\[Rule]", RowBox[{"-", FractionBox["1", "2"]}]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.3918763160149355`*^9}] }, Open ]], Cell[TextData[{ "\nBefore pointing you towards the ", Cell[BoxData[ RowBox[{"Document", " ", "Center"}]]], " for more reading, let me make two points about equations in ", StyleBox["Mathematica", FontSlant->"Italic"], ". First, ", StyleBox["Mathematica", FontSlant->"Italic"], " uses double equals (", Cell[BoxData["\[Equal]"]], ") for equations and single equals ", Cell[BoxData["="]], " for assignment. Confusing the two is another common mistake in ", StyleBox["Mathematica", FontSlant->"Italic"], ". Note what happens if we replace ", Cell[BoxData["\[Equal]"]], " by ", Cell[BoxData["="]], " in the expression above." }], "Text", CellChangeTimes->{{3.3918759593649855`*^9, 3.3918760350453176`*^9}, { 3.391876161159176*^9, 3.3918763766032653`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"2", "x"}], "+", "1"}], "=", "0"}], "]"}]], "Input", CellChangeTimes->{{3.391876307953182*^9, 3.39187631539403*^9}, 3.3918763853359966`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"Set", "::", "\<\"write\"\>"}], ":", " ", "\<\"Tag \\!\\(Plus\\) in \\!\\(1 + \\(\\(2\\\\ x\\)\\)\\) is \ Protected. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\ \\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/General/write\\\", ButtonNote -> \ \\\"Set::write\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.391876386347471*^9}], Cell[BoxData[ RowBox[{ RowBox[{"Solve", "::", "\<\"eqf\"\>"}], ":", " ", "\<\"\\!\\(0\\) is not a well-formed equation. \\!\\(\\*ButtonBox[\\\"\ \[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \ ButtonData:>\\\"paclet:ref/message/Solve/eqf\\\", ButtonNote -> \ \\\"Solve::eqf\\\"]\\)\"\>"}]], "Message", "MSG", CellChangeTimes->{3.391876386607851*^9}], Cell[BoxData[ RowBox[{"Solve", "[", "0", "]"}]], "Output", CellChangeTimes->{3.391876386647909*^9}] }, Open ]], Cell[TextData[{ Cell[BoxData["Solve"]], " (and many more ", StyleBox["Mathematica", FontSlant->"Italic"], ") functions can take not only a single equation as input, but also a ", StyleBox["list", FontSlant->"Italic"], " of equations. Lists in ", StyleBox["Mathematica", FontSlant->"Italic"], " consist of a sequence of expressions, separated by commas and enclosed by \ curly brackets. For example, " }], "Text", CellChangeTimes->{{3.3918764112037086`*^9, 3.391876510828949*^9}, { 3.392211688905538*^9, 3.392211701874744*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Solve", "[", RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"x", "+", "y"}], "\[Equal]", "4"}], ",", RowBox[{ RowBox[{"x", "-", "y"}], "\[Equal]", "0"}]}], "}"}], "]"}]], "Input", CellChangeTimes->{{3.391876514243928*^9, 3.3918765244087467`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"x", "\[Rule]", "2"}], ",", RowBox[{"y", "\[Rule]", "2"}]}], "}"}], "}"}]], "Output", CellChangeTimes->{3.3918765247692723`*^9}] }, Open ]], Cell[TextData[{ "We will learn much, much more about lists in subsequent modules. For now, \ briefly review the following tutorial on ", ButtonBox["Solving Equations ", BaseStyle->"Link", ButtonData->"paclet:tutorial/SolvingEquations"], "and do the following exercises." }], "Text", CellChangeTimes->{{3.3918765332716675`*^9, 3.3918767001749916`*^9}, 3.3922135274425507`*^9}] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Find an exact solution to the four degree equation ", Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"4", SuperscriptBox["x", "4"]}], "+", RowBox[{"3", SuperscriptBox["x", "3"]}], "+", RowBox[{"2", SuperscriptBox["x", "2"]}], "+", "x", "+", "1"}], "\[Equal]", "0"}]]], ". Next, compute numerical solutions to this equation." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391875084519573*^9}, { 3.3918752344982233`*^9, 3.3918752448833632`*^9}, {3.391875359350241*^9, 3.39187546053776*^9}, {3.391875504041182*^9, 3.391875517941447*^9}, { 3.3918767278152876`*^9, 3.391876863723424*^9}, {3.3918768974926553`*^9, 3.391876929399171*^9}, {3.458484701734375*^9, 3.45848470215625*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Use ", StyleBox["Mathematica", FontSlant->"Italic"], " to find the solutions to the quadratic equation ", Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"a", " ", SuperscriptBox["x", "2"]}], "+", RowBox[{"b", " ", "x"}], "+", "c"}], "\[Equal]", "0"}]]], ". (Note the use of spaces here: ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{ StyleBox["b", FontSlant->"Plain"], " ", StyleBox["x", FontSlant->"Plain"]}], FontFamily->"Courier New"], TraditionalForm]]], " is the multiplication of two variables, whereas ", Cell[BoxData[ FormBox[ StyleBox["bx", FontFamily->"Courier New"], TraditionalForm]]], " is a single variable.) Backsubstitute the ", StyleBox["Mathematica", FontSlant->"Italic"], "'s answer into the equation and show the answers are actual solutions to \ the equation." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391875084519573*^9}, { 3.3918752344982233`*^9, 3.3918752448833632`*^9}, {3.391875359350241*^9, 3.39187546053776*^9}, {3.391875504041182*^9, 3.391875517941447*^9}, { 3.3918767278152876`*^9, 3.3918768099850807`*^9}, {3.458486011921875*^9, 3.458486082265625*^9}, {3.458486119265625*^9, 3.458486136515625*^9}, { 3.458486927203125*^9, 3.458486952734375*^9}, {3.458486985875*^9, 3.45848698790625*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]], Cell[CellGroupData[{ Cell["Exercise", "Exercise", CellChangeTimes->{{3.3914498977492*^9, 3.3914499052301064`*^9}, 3.3918748007558823`*^9}], Cell[TextData[{ "Given a line through origin with slope ", Cell[BoxData["m"]], " (equation ", Cell[BoxData[ RowBox[{"y", "\[Equal]", RowBox[{ RowBox[{"m", " ", "x"}], "+", "b"}]}]]], ") and a parabola of the form ", Cell[BoxData[ RowBox[{"y", "\[Equal]", SuperscriptBox["x", "2"]}]]], ", find the coordinates of their intersection point(s) as a function of ", Cell[BoxData["m"]], "." }], "ExerciseText", CellChangeTimes->{{3.3914499126909833`*^9, 3.3914499937491555`*^9}, { 3.3914502962000904`*^9, 3.3914503003160906`*^9}, {3.3914504496538057`*^9, 3.391450456343559*^9}, {3.3914505505909595`*^9, 3.391450580674818*^9}, { 3.3914508734316196`*^9, 3.3914509133498154`*^9}, {3.3914514834809933`*^9, 3.391451509849435*^9}, 3.3914515934413013`*^9, {3.391451658736493*^9, 3.391451659046946*^9}, {3.391452106679537*^9, 3.3914521368234825`*^9}, { 3.391452688337519*^9, 3.3914527949529505`*^9}, 3.3918728001893134`*^9, { 3.3918729449102983`*^9, 3.391872974753806*^9}, {3.391873051425584*^9, 3.3918732023255763`*^9}, {3.3918748007759113`*^9, 3.3918748819642735`*^9}, {3.391874938867231*^9, 3.391875084519573*^9}, { 3.3918752344982233`*^9, 3.3918752448833632`*^9}, {3.391875359350241*^9, 3.39187546053776*^9}, {3.391875504041182*^9, 3.391875517941447*^9}, { 3.3918767278152876`*^9, 3.3918768099850807`*^9}, {3.391876997228057*^9, 3.3918770554829845`*^9}, {3.391877103843488*^9, 3.3918771544873204`*^9}}, FontColor->RGBColor[0.5, 0, 0.5]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Document creation in ", StyleBox["Mathematica", FontSlant->"Italic"] }], "Section", CellChangeTimes->{{3.390746036702399*^9, 3.3907460434323444`*^9}, { 3.3918784140035334`*^9, 3.3918784207834177`*^9}}], Cell[TextData[{ "Up to now, we have focused on ", StyleBox["Mathematica", FontSlant->"Italic"], " as a powerful calculator. However, this is just the start of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s capabilities. ", StyleBox["Mathematica", FontSlant->"Italic"], " also serves as a full-fledged document preparation environment that \ incorporate text, equations, figures and graphics. In this section, we \ discuss some of ", StyleBox["Mathematica", FontSlant->"Italic"], "'s more important features for document preparation." }], "Text", CellChangeTimes->{{3.391877180965923*^9, 3.391877256496036*^9}, { 3.391877426674134*^9, 3.391877450909466*^9}, {3.3922124043020277`*^9, 3.392212433333887*^9}, 3.3922133408883142`*^9, 3.392213408472373*^9}], Cell[CellGroupData[{ Cell["Cells", "Subsection", CellChangeTimes->{{3.3918784806506963`*^9, 3.391878481231543*^9}}], Cell[TextData[{ "A ", StyleBox["Mathematica", FontSlant->"Italic"], " notebook consists of a sequence of ", StyleBox["cells", FontSlant->"Italic"], ". Each cell has a particular style associated with it. To view this \ style, you first select the cell by clicking on the square bracket bounding \ the cell on the right side of the window. Next, select the ", Cell[BoxData["Format"]], " menu and the ", Cell[BoxData["Style"]], " submenu. (Alternatively, right-click on the square bracket and select the \ ", StyleBox["Style", "InlineInput", FontWeight->"Plain"], " submenu.) The resulting drop-down menu lists the possible cell styles for \ the current notebook and has a check mark next to the style associated with \ the selected cell. You may change the style of an existing cell using this \ menu or set the style of a new cell (created by clicking between existing \ cells)." }], "Text", CellChangeTimes->{{3.3905859948265457`*^9, 3.3905860284849443`*^9}, { 3.3918774691861105`*^9, 3.3918777208530087`*^9}, 3.392213358730625*^9, { 3.458484880921875*^9, 3.458484933296875*^9}, 3.458484976328125*^9}], Cell[TextData[{ "In most notebooks there are two important types of cells, ", Cell[BoxData["Input"]], " cells and ", Cell[BoxData["Text"]], " cells. ", Cell[BoxData["Input"]], " cells contain ", StyleBox["Mathematica", FontSlant->"Italic"], " expressions waiting to be evaluated (and are colored in orange in this \ notebook style). Hitting ", Cell[BoxData[ RowBox[{"Shift", "+", "Enter"}]]], " in an ", Cell[BoxData["Input"]], " cell causes ", StyleBox["Mathematica", FontSlant->"Italic"], " to evaluate the contents of the cell and produce a corresponding ", Cell[BoxData["Output"]], " cell. On the other hand, ", Cell[BoxData["Text"]], " cells do not contain expressions that are destined to be evaluated. \ Instead, they contain text and formulas that are meant to be read. " }], "Text", CellChangeTimes->{{3.391877865964563*^9, 3.3918780968812094`*^9}, { 3.392212523294924*^9, 3.392212555302466*^9}}], Cell[TextData[{ "As you progress in this class, I will ask you to add text cells to your \ notebook to answer questions and document your ", StyleBox["Mathematica", FontSlant->"Italic"], " functions. A common beginner mistake is to type text into an ", Cell[BoxData["Input"]], " cell. Since ", StyleBox["Mathematica", FontSlant->"Italic"], " interprets this text as an algebraic expression, the result often looks \ strange." }], "Text", CellChangeTimes->{{3.391877865964563*^9, 3.3918781504593196`*^9}, { 3.3918782246775203`*^9, 3.3918782265001774`*^9}, {3.392212589117529*^9, 3.3922125893119593`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ "As", " ", "you", " ", "progress", " ", "in", " ", "this", " ", "class"}], ",", RowBox[{ "I", " ", "will", " ", "ask", " ", "you", " ", "to", " ", "add", " ", "text", " ", "cells", " ", "to", " ", "your", " ", "notebook", " ", "to", " ", "answer", " ", "questions", " ", "and", " ", "document", " ", RowBox[{ StyleBox[ RowBox[{"your", StyleBox["Mathematica", FontSlant->"Italic"], "functions"}]], ".", "A"}], " ", "common", " ", "beginner", " ", "mistake", " ", "is", " ", "to", " ", "type", " ", "text", " ", "into", " ", RowBox[{"anInputcell", ".", StyleBox[ RowBox[{"Since", StyleBox["Mathematica", FontSlant->"Italic"], "interprets"}]]}], " ", "this", " ", "text", " ", "and", " ", "an", " ", "algebraic", " ", "expression"}], ",", RowBox[{"the", " ", "result", " ", "often", " ", "looks", " ", RowBox[{"strange", "."}]}]}]], "Input", CellChangeTimes->{{3.39187815407459*^9, 3.3918781999614873`*^9}}], Cell[TextData[{ "Another common beginner mistake is to punch all of their text into a single \ ", Cell[BoxData["Text"]], " cell and try to format the text inside the cell. A better method is to \ treat each ", Cell[BoxData["Text"]], " cell as a single paragraph -- observe how each paragraph of this notebook \ has its own bracket at the right. Then, let ", StyleBox["Mathematica", FontSlant->"Italic"], " handle the typesetting using the options in the ", Cell[BoxData["Format"]], " menu." }], "Text", CellChangeTimes->{{3.3918782328193903`*^9, 3.391878257415248*^9}, { 3.3918783082593718`*^9, 3.391878317012132*^9}, {3.391878582138653*^9, 3.3918785967599688`*^9}, {3.391878652611393*^9, 3.391878677217265*^9}, 3.392212641358615*^9, {3.458484628484375*^9, 3.458484674234375*^9}}], Cell[TextData[{ "Some cells such as the \"Document creation in ", StyleBox["Mathematica", FontSlant->"Italic"], "\" cell above act as titles or section heading that cause cells to be \ grouped together hierarchically. If we select this cell and check its style, \ we note its style is ", Cell[BoxData["Section"]], ". All text cells in between two section cells make up the body of this \ section. You can expand and collapse this section of the notebook by double \ clicking on the right bracket associated with the section heading. Adding \ cells for titles and sections makes your notebook look more polished." }], "Text", CellChangeTimes->{{3.3918777265713453`*^9, 3.391877854187393*^9}, { 3.3918780114666862`*^9, 3.3918780127585697`*^9}, {3.3918784970746403`*^9, 3.3918785624699783`*^9}, {3.392212678815942*^9, 3.392212696539652*^9}}], Cell[TextData[{ "For more information on cells and notebooks, you should take a brief look \ at the tutorial ", StyleBox[ButtonBox["Notebooks as Documents", BaseStyle->"Link", ButtonData->"paclet:tutorial/NotebooksAsDocuments"], FontColor->RGBColor[0, 0, 1]], StyleBox[".", FontColor->GrayLevel[0]] }], "Text", CellChangeTimes->{{3.3918773897603183`*^9, 3.3918773900807858`*^9}, { 3.391878604331006*^9, 3.3918786297580757`*^9}, {3.46012652271875*^9, 3.46012659215625*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Editing", "Subsection", CellChangeTimes->{{3.391878636808354*^9, 3.391878637609522*^9}, { 3.460126571328125*^9, 3.460126575109375*^9}}], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " supports all of the standard cut and paste operations common in most \ Windows applications. These operations can be accessed through the ", Cell[BoxData["Edit"]], " menu. One particularly important operation that you should remember is ", Cell[BoxData["Undo"]], ". ", StyleBox["Mathematica", FontSlant->"Italic"], " supports only one round of ", Cell[BoxData["Undo"]], "s. So, if you think that you have made an editing mistake, stop and think \ for a second before blindly proceeding. Then use ", Cell[BoxData["Undo"]], " if you think it is appropriate." }], "Text", CellChangeTimes->{{3.39058645634017*^9, 3.390586465493331*^9}, { 3.3905865379274864`*^9, 3.3905865470405903`*^9}, {3.390587154554152*^9, 3.3905871734713535`*^9}, {3.3918787383864417`*^9, 3.3918788031909184`*^9}, { 3.3918789737696*^9, 3.3918791134732704`*^9}, {3.458483841640625*^9, 3.45848384259375*^9}}], Cell[TextData[{ "Another useful trick involves selecting a portion of a mathematical \ expression (for either copying or deletion). One option is to click and drag \ to select the desired subexpression. One drawback with this approach is that \ matching up square brackets, parentheses and curly brackets can be tricky for \ large expression. A better alternative is to click inside the desired \ expression and repeatedly click. ", StyleBox["Mathematica", FontSlant->"Italic"], " will automatically select larger and larger subexpressions that contains \ the cursor. This approach avoids the problem of balancing parentheses. " }], "Text", CellChangeTimes->{{3.391879115506234*^9, 3.3918791437373915`*^9}, { 3.3918792002297497`*^9, 3.3918793994802313`*^9}, {3.3922127969305077`*^9, 3.392212797628566*^9}}], Cell[TextData[{ "Finally, you will often be asked to evaluate an expression contained in a ", Cell[BoxData["Text"]], " cell. Instead of trying to retype the expression into an ", "Input", " cell by hand, I suggest that you cut and paste the expression into an ", Cell[BoxData["Input"]], " cell. Why? Because retyping the expression often introduces a mistake \ into the expression that will make your life miserable later on when trying \ to understand why your answer is incorrect. Always cut and paste if possible." }], "Text", CellChangeTimes->{{3.3918794261791553`*^9, 3.3918795596337147`*^9}, { 3.392212826618415*^9, 3.392212850768059*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Creating 2D math expressions", "Subsection", CellChangeTimes->{{3.390585998722147*^9, 3.390586006002616*^9}, { 3.3905864043854623`*^9, 3.3905864086816397`*^9}, {3.3918786990891514`*^9, 3.3918787162041025`*^9}, 3.391964674348254*^9}], Cell[TextData[{ "Another feature of ", StyleBox["Mathematica", FontSlant->"Italic"], " is its ability to typeset mathematical expression in a quick and easy to \ use way. For novice users, the easiest way to create 2D math expressions is \ to use the ", Cell[BoxData["BasicMathInput"]], " palette from the ", Cell[BoxData["Palette"]], " menu. This palette contains most of the interesting expressions that you \ might like to create." }], "Text", CellChangeTimes->{{3.391964742818074*^9, 3.391964744590658*^9}, { 3.3919650554939156`*^9, 3.3919651555097256`*^9}, {3.3922128864638844`*^9, 3.392212906166725*^9}}], Cell[TextData[{ "As you become more proficient at using ", StyleBox["Mathematica", FontSlant->"Italic"], ", you will start to become interested in using keyboard shortcuts to create \ most of these expressions. Many of these shortcuts involve using either the \ control key or the escape key. Take a brief look at the tutorials", StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ButtonBox["Editing and Evaluating Two-Dimensional Expressions ", BaseStyle->"Link", ButtonData->"paclet:tutorial/EditingAndEvaluatingTwoDimensionalExpressions"], FontColor->RGBColor[0, 0, 1]], "and", StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox[ButtonBox["Entering Two-Dimensional Input", BaseStyle->"Link", ButtonData->"paclet:tutorial/EnteringTwoDimensionalInput"], FontColor->RGBColor[0, 0, 1]], " for more a detailed description of how these shortcuts work." }], "Text", CellChangeTimes->{{3.391965163911975*^9, 3.3919653222628307`*^9}, { 3.392212931565117*^9, 3.392212932241294*^9}, {3.460126729640625*^9, 3.46012673540625*^9}}], Cell[TextData[{ "An interesting thing to note about typesetting in ", StyleBox["Mathematica", FontSlant->"Italic"], " is that, if done properly, the resulting expression can be evaluated by ", StyleBox["Mathematica", FontSlant->"Italic"], " as input. For example, is ", Cell[BoxData[ RowBox[{"\[Integral]", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}]]], " equal to ", Cell[BoxData[ RowBox[{"Sin", "[", "\[Theta]", "]"}]]], "? We can cut and paste these two expression and enter the operator ", Cell[BoxData["\[Equal]"]], " from the ", Cell[BoxData["BasicMathInput"]], " palette and arrive at" }], "Text", CellChangeTimes->{{3.391965351946105*^9, 3.3919655364450808`*^9}, { 3.391965585196153*^9, 3.3919655936484756`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"\[Integral]", RowBox[{ RowBox[{"Cos", "[", "\[Theta]", "]"}], RowBox[{"\[DifferentialD]", "\[Theta]"}]}]}], "\[Equal]", RowBox[{"Sin", "[", "\[Theta]", "]"}]}]], "Input", CellChangeTimes->{{3.3919655217035894`*^9, 3.3919655418830085`*^9}}], Cell[BoxData["True"], "Output", CellChangeTimes->{{3.3919655263603783`*^9, 3.39196554234368*^9}}] }, Open ]], Cell[TextData[{ "Note that ", StyleBox["Mathematica", FontSlant->"Italic"], " returns ", Cell[BoxData["True"]], ", acknowledging that this is an identity that holds for all ", Cell[BoxData["\[Theta]"]], "." }], "Text", CellChangeTimes->{{3.391965545748644*^9, 3.3919655680611725`*^9}, { 3.3919655988861113`*^9, 3.391965602230988*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["Figure creation", "Subsection", CellChangeTimes->{{3.3905860823323727`*^9, 3.390586086017672*^9}}], Cell["\<\ The final ingredients in any well-done report or presentation are compelling \ 2D and 3D figures. While text can be useful for explaining a concept, \ nothing beats a nice figure. In many of your modules, the bulk of your work \ will be building visual elements that help explain and interpret your answers.\ \>", "Text", CellChangeTimes->{{3.3919656446328044`*^9, 3.3919657364566717`*^9}, 3.392212996554317*^9, {3.408886832206571*^9, 3.408886834029999*^9}}], Cell[TextData[{ "The simplest way to create a 2D figure is to use the ", Cell[BoxData[ RowBox[{"New", " ", "Graphic"}]]], " command in the ", Cell[BoxData["Graphics"]], " menu. To use this feature, place your cursor inside an existing cell (or \ create a new one) and select ", Cell[BoxData[ RowBox[{"New", " ", "Graphic"}]]], ". ", StyleBox["Mathematica", FontSlant->"Italic"], " will insert a resizeable rectangle corresponding to the figure. To add \ content to the figure, select ", Cell[BoxData[ RowBox[{"Drawing", " ", "Tools"}]]], " from the same menu. 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