(* 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[ 1132003, 27454] NotebookOptionsPosition[ 1069044, 25747] NotebookOutlinePosition[ 1070225, 25786] CellTagsIndexPosition[ 1070182, 25783] WindowFrame->Generic ContainsDynamic->False*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["SCCC ", CellFrame->3], StyleBox["Mathematica", CellFrame->3, FontSlant->"Italic"], StyleBox[" Tutorial", CellFrame->3] }], "Text", CellFrame->0.5, CellChangeTimes->{{3.393694500438837*^9, 3.3936945105133233`*^9}, { 3.3937033788464656`*^9, 3.3937033792270126`*^9}, {3.39429114332375*^9, 3.39429115913625*^9}, {3.394326962276875*^9, 3.394326979995625*^9}, 3.394494211651875*^9}, FontFamily->"Comic Sans MS", FontSize->24, Background->RGBColor[0.6666666666666666, 0.8431372549019608, 1.]], Cell[TextData[{ StyleBox["SCCC ", FontSize->9, FontColor->GrayLevel[0.5]], StyleBox["Mathematica", FontSize->9, FontSlant->"Italic", FontColor->GrayLevel[0.5]], StyleBox[" Tutorial, \[Copyright] 2007, Seattle Central Community College \ Math Dept., contact: Mike Pepe at mdpepe@gmail.com\nVersion 1.2/ Winter, \ 2008", FontSize->9, FontColor->GrayLevel[0.5]] }], "Text", Editable->False, Deletable->False, CellChangeTimes->{{3.393694805056856*^9, 3.3936948436723824`*^9}, { 3.393703204405632*^9, 3.3937032115258703`*^9}, {3.393703401819499*^9, 3.393703414627917*^9}, {3.394290864495625*^9, 3.394290886026875*^9}, { 3.394291021995625*^9, 3.394291025714375*^9}, {3.39432690732375*^9, 3.394326941214375*^9}, {3.39432698538625*^9, 3.39432701173*^9}, { 3.3969686842884693`*^9, 3.3969687035697193`*^9}, {3.399040915296875*^9, 3.39904091553125*^9}, {3.399557728890625*^9, 3.399557860234375*^9}, { 3.39955791925*^9, 3.39955792971875*^9}, {3.39955798521875*^9, 3.39955799546875*^9}, {3.399755205875*^9, 3.399755252703125*^9}}, TextAlignment->Right, FontFamily->"Comic Sans MS"], Cell[CellGroupData[{ Cell["\t\t\tIntroduction", "Section", CellFrame->0.5, CellChangeTimes->{{3.3936948695095344`*^9, 3.3936948718929615`*^9}, { 3.3962873666558685`*^9, 3.3962873705222874`*^9}, {3.396319889765625*^9, 3.396319893125*^9}, {3.39637949125*^9, 3.396379498171875*^9}}, FontFamily->"Comic Sans MS", FontSize->16, FontWeight->"Plain", Background->RGBColor[ 0.6901960784313725, 0.8235294117647058, 0.7019607843137254]], Cell[TextData[{ StyleBox["Purpose", FontWeight->"Bold"], "\nThis tutorial has been designed by the Mathematics Department at Seattle \ Central Community College to provide you with a complete, hands-on \ introduction to the basic commands that you will need to use ", StyleBox["Mathematica", FontSlant->"Italic"], " effectively in your math and science classes. The six lessons of the \ tutorial will step you through each topic with many opportunities for you to \ practice and experiment with ", StyleBox["Mathematica", FontSlant->"Italic"], ". It is expected that you will be able to work through the tutorial on \ your own with minimal help in a relatively short time. 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Therefore the tutorial only \ assumes familiarity with mathematics at the Precalculus level." }], "Text", CellChangeTimes->{{3.3936948796040497`*^9, 3.3936949916151133`*^9}, { 3.394290517683125*^9, 3.3942907001675*^9}, {3.3942921521675*^9, 3.394292186089375*^9}, 3.394293931839375*^9, {3.394295257026875*^9, 3.39429529032375*^9}, {3.394540217870625*^9, 3.394540981433125*^9}, { 3.394541033089375*^9, 3.3945410534175*^9}, {3.394541085808125*^9, 3.394541507870625*^9}, {3.394541560276875*^9, 3.39454161182375*^9}, { 3.394541720776875*^9, 3.394541877355*^9}, {3.3945420070425*^9, 3.394542075776875*^9}, 3.39454286748*^9, {3.39454290248*^9, 3.394542991605*^9}, {3.39454302373*^9, 3.39454313713625*^9}, { 3.394543183605*^9, 3.394543184605*^9}, 3.394544243355*^9, { 3.39463656560425*^9, 3.3946365885105*^9}, {3.394636632963625*^9, 3.394636637901125*^9}, {3.39463673279175*^9, 3.394636819151125*^9}, { 3.394636903619875*^9, 3.394637064948*^9}, {3.3948845872053747`*^9, 3.3948845944553747`*^9}, 3.39594427929*^9}, FontFamily->"Comic Sans MS"], Cell[TextData[{ StyleBox["Structure", FontWeight->"Bold"], "\nThe tutorial is divided into six lessons. 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You \ can use either one. In fact, if you use the Enter key that is located at the \ extreme right of the keyboard, next to the numeric keypad, then you do not \ have to press the Shift key at all ; just pressing the Enter key by itself \ works. 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Both produce the same output. 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Change the 5 in the input \ above to 500 and then ", "evaluate", StyleBox[" the revised input.", CellFrame->0.5], StyleBox[" ", FontSize->18, FontColor->RGBColor[0, 0, 1]], "Observe that the output automatically updates to reflect the new input. 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At any point where the cursor is horizontal \ you can click on the screen and just start typing math input. A red input \ cell is automatically created as you type. Try entering and ", "evaluating", " a new input cell by clicking between the end of this paragraph and the \ gray box below when you see the cursor switch to horizontal." }], "Text", CellChangeTimes->{{3.39467128815625*^9, 3.394671599015625*^9}, { 3.3946716343125*^9, 3.394671857328125*^9}, {3.39467195134375*^9, 3.394671952875*^9}, {3.394679459359375*^9, 3.394679463953125*^9}, { 3.39467949471875*^9, 3.394679541765625*^9}, {3.394713494609375*^9, 3.394713774625*^9}, 3.394717603109375*^9, {3.39471763821875*^9, 3.39471764128125*^9}, {3.3948509330178747`*^9, 3.3948510557991247`*^9}, { 3.3948511060334997`*^9, 3.3948512747053747`*^9}, {3.395944601915*^9, 3.39594461404*^9}, {3.395969691461875*^9, 3.39596973025875*^9}, { 3.39620441203125*^9, 3.396204420625*^9}, 3.397678839609375*^9}], Cell[TextData[{ " ", StyleBox[" ", CellFrame->0.5] }], "Text", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.39471316603125*^9, 3.394713219765625*^9}, 3.394713273625*^9, {3.394718610046875*^9, 3.394718628640625*^9}, { 3.3948464664866247`*^9, 3.3948466418147497`*^9}, {3.3948467139241247`*^9, 3.3948468329084997`*^9}, {3.3948468646741247`*^9, 3.3948469197678747`*^9}, {3.3948470984709997`*^9, 3.3948471069084997`*^9}, {3.3948471410647497`*^9, 3.3948471816741247`*^9}, {3.3948472279553747`*^9, 3.3948474031897497`*^9}, {3.3948474402834997`*^9, 3.3948475213772497`*^9}, {3.3948482179397497`*^9, 3.3948484224241247`*^9}, {3.3948485525178747`*^9, 3.3948487169553747`*^9}, {3.3948487739084997`*^9, 3.3948489175959997`*^9}, {3.3948490166116247`*^9, 3.3948490907209997`*^9}, {3.3948491255334997`*^9, 3.3948492081897497`*^9}, {3.3948492476897497`*^9, 3.3948492905334997`*^9}, {3.3948503085647497`*^9, 3.3948503677522497`*^9}, {3.3948504097834997`*^9, 3.3948504300491247`*^9}, {3.3948842795647497`*^9, 3.3948842868147497`*^9}, 3.3948843329084997`*^9, {3.395944420680625*^9, 3.39594456154*^9}, { 3.39594464250875*^9, 3.39594464429*^9}, {3.395944688274375*^9, 3.395944689055625*^9}}, FontFamily->"Comic Sans MS", Background->RGBColor[ 0.8627450980392157, 0.8627450980392157, 0.8705882352941177]], Cell[CellGroupData[{ Cell[TextData[StyleBox["Exercise 1.1 A", FontWeight->"Bold", FontSlant->"Italic", FontVariations->{"Underline"->False}]], "Subsubsubsection", CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295963808125*^9, 3.39429597588625*^9}, { 3.394298058058125*^9, 3.39429806344875*^9}, {3.3942981760425*^9, 3.39429818444875*^9}, {3.39432913019875*^9, 3.394329130558125*^9}, { 3.3948918258303747`*^9, 3.3948918260334997`*^9}}, FontFamily->"Comic Sans MS", FontWeight->"Plain", FontSlant->"Italic", FontVariations->{"Underline"->True}, FontColor->RGBColor[ 0.25882352941176473`, 0.41568627450980394`, 0.5333333333333333]], Cell[TextData[{ "Evaluate the expression ", Cell[BoxData[ FormBox[ StyleBox[ FractionBox[ RowBox[{ SuperscriptBox["3.56", "2"], "+", SuperscriptBox["4.53", "4"]}], "34.87"], FontSize->16], TraditionalForm]]], ". 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Move the mouse from one text cell down to the other and click and \ start typing when the cursor is horizontal. \ \>", "Text", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.3948918484397497`*^9, 3.3948919150959997`*^9}, {3.3948919541897497`*^9, 3.3948919809553747`*^9}, {3.3948920430178747`*^9, 3.3948920865491247`*^9}, {3.3948923263459997`*^9, 3.3948923520491247`*^9}, {3.3948924308772497`*^9, 3.3948924956741247`*^9}, {3.3948925422678747`*^9, 3.3948925841428747`*^9}, {3.3948927500647497`*^9, 3.3948927615178747`*^9}, {3.3948928337522497`*^9, 3.3948928934241247`*^9}, {3.3948929390647497`*^9, 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Using the \"N\" command. \ \>", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, 3.39429576188625*^9, 3.39429581701125*^9, {3.394298169401875*^9, 3.394298172308125*^9}, {3.39433098482375*^9, 3.39433100194875*^9}, 3.3943310409175*^9, {3.39433288198*^9, 3.3943329432925*^9}, 3.39438222157375*^9, 3.3948254773147497`*^9}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ "Calculate ", Cell[BoxData[ FormBox[ SuperscriptBox["34", "19"], TraditionalForm]]], ". Enter the expression ", StyleBox["34^19", FontColor->RGBColor[1, 0, 0]], ", then press", StyleBox[" ", FontColor->RGBColor[0, 0, 1]], StyleBox["\[EnterKey]", FontSize->18, FontColor->GrayLevel[0]], StyleBox[".", FontSize->18, FontColor->RGBColor[0, 0, 1]] }], "Item", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, 3.39429581701125*^9, 3.394295888370625*^9, {3.3949295165491247`*^9, 3.3949295752053747`*^9}}, FontFamily->"Comic Sans MS", Background->GrayLevel[1]], Cell[BoxData[""], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.393703864184347*^9, 3.3937038660970974`*^9}, 3.39429581701125*^9, {3.394306420433125*^9, 3.39430643882375*^9}, { 3.394306525058125*^9, 3.394306532464375*^9}, {3.3943284161675*^9, 3.394328419026875*^9}, 3.3948209990491247`*^9, {3.3948344421741247`*^9, 3.3948345384397497`*^9}, 3.3948470780491247`*^9, 3.3989966755625*^9}], Cell[TextData[{ "Note that ", StyleBox["Mathematica", FontSlant->"Italic"], " produces the ", StyleBox["exact", FontVariations->{"Underline"->True}], " answer here; all thirty digits! ", StyleBox["Mathematica", FontSlant->"Italic"], " will always display the exact value when doing a calculation if it is \ possible to do so. However, if we really just want a ", StyleBox["numerical approximation", FontVariations->{"Underline"->True}], ", then we can use the \"N\" command as shown below. Here \"N\" stands for \ \"numerical\". 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(Note the use of square brackets in the command below. 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To get more digits, we just add a second argument to the command. For \ example, if we want 25 digits we enter ", StyleBox["N[34^19, 25]", FontColor->RGBColor[1, 0, 0]], ". 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Recall that rational numbers are \ always expressible as either terminating decimals (e.g. ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox["3", "4"], "=", ".75"}], TraditionalForm]]], ") ... or repeating, nonterminating decimals (e.g. ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox["1", "3"], "=", RowBox[{".333333", "..."}]}], TraditionalForm]]], "). What can you say about ", Cell[BoxData[ FormBox[ FractionBox["29", "21"], TraditionalForm]]], "?" }], "Text", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.39433039494875*^9, 3.394330404183125*^9}, {3.394330570401875*^9, 3.394330630933125*^9}}, FontFamily->"Comic Sans MS", FontSize->10] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["1.4\tAnother way to apply the N command.", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, 3.39429576188625*^9, 3.39429581701125*^9, {3.394298169401875*^9, 3.394298172308125*^9}, {3.39433098482375*^9, 3.39433100194875*^9}, 3.3943310409175*^9, {3.39433288198*^9, 3.3943329432925*^9}, 3.39438222157375*^9, {3.39463766935425*^9, 3.394637687026125*^9}, 3.3946798719375*^9, 3.394679938671875*^9, {3.394682054734375*^9, 3.39468212115625*^9}, {3.3947129628125*^9, 3.394712975265625*^9}, 3.3948254861584997`*^9, 3.398615821670375*^9}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ "In Section 1.2 you learned about the N command which produces numerical \ approximations. Recall that ", StyleBox["Mathematica", FontSlant->"Italic"], " will produce the exact answer for a calculation whenever possible. This \ sometimes produces surprising results." }], "Text", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.394329438901875*^9, 3.394329489995625*^9}, { 3.394637751932375*^9, 3.3946378107605*^9}, {3.39467995371875*^9, 3.394680037046875*^9}, {3.39468019815625*^9, 3.394680245578125*^9}, { 3.394680310796875*^9, 3.39468032921875*^9}, {3.394680408375*^9, 3.3946804193125*^9}, {3.394680543625*^9, 3.394680583703125*^9}, 3.3949300967522497`*^9, {3.395970550368125*^9, 3.3959705522275*^9}}, FontFamily->"Comic Sans MS"], Cell["Execute the input below.", "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.394329438901875*^9, 3.394329489995625*^9}, { 3.394637751932375*^9, 3.3946378107605*^9}, {3.39467995371875*^9, 3.394680037046875*^9}, {3.39468019815625*^9, 3.394680245578125*^9}, { 3.394680310796875*^9, 3.39468032921875*^9}, {3.394680408375*^9, 3.3946804193125*^9}, {3.394680543625*^9, 3.394680583703125*^9}, { 3.3949300967522497`*^9, 3.3949301075022497`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"987", "^", "17"}], " ", "-", " ", RowBox[{"85", "^", "20"}]}], ")"}], "/", "1452"}]], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.393703864184347*^9, 3.3937038660970974`*^9}, 3.39429581701125*^9, {3.394306420433125*^9, 3.39430643882375*^9}, { 3.394306525058125*^9, 3.394306532464375*^9}, {3.394327552089375*^9, 3.39432755538625*^9}, {3.394539591745625*^9, 3.394539593401875*^9}, { 3.394550663808125*^9, 3.394550671776875*^9}, {3.394637717619875*^9, 3.394637725713625*^9}, {3.3946804275*^9, 3.39468050928125*^9}}], Cell[TextData[{ "Well, there it is, the exact answer! This is the exact, reduced fraction \ which is equal to our input. In cases like this we almost always prefer ", StyleBox["Mathematica", FontSlant->"Italic"], " to give us a numerical approximation. 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Execute this cell.\ \>", "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.394329438901875*^9, 3.394329489995625*^9}, { 3.394637751932375*^9, 3.3946378107605*^9}, {3.39467995371875*^9, 3.394680037046875*^9}, {3.39468019815625*^9, 3.394680245578125*^9}, { 3.394680310796875*^9, 3.39468032921875*^9}, {3.394680408375*^9, 3.3946804193125*^9}, {3.394680543625*^9, 3.394680583703125*^9}, { 3.3946807219375*^9, 3.39468078534375*^9}, {3.39468097109375*^9, 3.394681024*^9}, 3.3946812024375*^9, 3.3946821511875*^9, 3.3947187545*^9, { 3.3949302757209997`*^9, 3.3949303073303747`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"987", "^", "17"}], " ", "-", " ", RowBox[{"85", "^", "20"}]}], ")"}], "/", "1452"}], "]"}]], "Input", CellChangeTimes->{{3.394680676609375*^9, 3.3946806855625*^9}}], Cell["\<\ In the input cell below, we introduce an alternative way to achieve the same \ result. This is called \"postfix\" (as contrasted to \"prefix\") form, since \ here the command follows, rather than precedes, the argument. Note the use of \ the double forward slash \" // \". Execute this cell.\ \>", "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.394329438901875*^9, 3.394329489995625*^9}, { 3.394637751932375*^9, 3.3946378107605*^9}, {3.39467995371875*^9, 3.394680037046875*^9}, {3.39468019815625*^9, 3.394680245578125*^9}, { 3.394680310796875*^9, 3.39468032921875*^9}, {3.394680408375*^9, 3.3946804193125*^9}, {3.394680543625*^9, 3.394680583703125*^9}, { 3.3946807943125*^9, 3.394680948390625*^9}, {3.394681091609375*^9, 3.39468116475*^9}, {3.394681226015625*^9, 3.39468123325*^9}, { 3.394681392921875*^9, 3.394681403890625*^9}, 3.39468153390625*^9, { 3.39468216753125*^9, 3.3946822523125*^9}, {3.394682322640625*^9, 3.39468232603125*^9}, {3.3949303354553747`*^9, 3.3949303493147497`*^9}, { 3.39597059044625*^9, 3.395970618461875*^9}, 3.3976050664375*^9}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"987", "^", "17"}], " ", "-", " ", RowBox[{"85", "^", "20"}]}], ")"}], "/", "1452"}], "//", "N"}]], "Input",\ CellChangeTimes->{{3.394680688546875*^9, 3.39468068909375*^9}, { 3.399480756703125*^9, 3.399480761046875*^9}, {3.399481063015625*^9, 3.399481063734375*^9}}], Cell[TextData[{ StyleBox["Prefix vs. Postfix", CellFrame->{{0.5, 3}, {3, 0.5}}, FontWeight->"Bold"], StyleBox[" \[LineSeparator]Postfix form is often convenient, however it does \ have one significant limitation. ", CellFrame->{{0.5, 3}, {3, 0.5}}], StyleBox["It is not possible to specify options for a command when using the \ postfix form.", CellFrame->{{0.5, 3}, {3, 0.5}}, FontVariations->{"Underline"->True}], StyleBox[" So, for example, if you want \[Pi] displayed with 20 digits then \ you will need to use ", CellFrame->{{0.5, 3}, {3, 0.5}}], Cell[BoxData[ FormBox[ RowBox[{"N", "[", RowBox[{"\[Pi]", ",", "20"}], "]"}], TraditionalForm]]], " . There is no way to use //N and at the same time specify that you want 20 \ digits. 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" }], "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, 3.39429602048*^9, {3.39430616019875*^9, 3.39430616069875*^9}, 3.394330940355*^9, {3.3943323711675*^9, 3.394332447495625*^9}, 3.39438223144875*^9, 3.394681270109375*^9, 3.3948254889553747`*^9, 3.39861582546725*^9}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ StyleBox["In ", CellFrame->0.5], StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox[" we can enter the constant \[Pi] by using the keyboard shortcut ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " p ", StyleBox["\[EscapeKey]", FontSize->14], ". (You will find the ", StyleBox["\[EscapeKey]", FontSize->14], " key at the upper left-hand corner of your keyboard). 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(Observe", StyleBox[" that when you press the ", FontColor->GrayLevel[0]], StyleBox["\[EscapeKey]", FontSize->14, FontColor->GrayLevel[0]], StyleBox[" key it appears as ", FontColor->GrayLevel[0]], StyleBox["\[AliasIndicator] ", FontSize->14, FontColor->GrayLevel[0]], StyleBox[", then you enter p, and when you press the ", FontColor->GrayLevel[0]], StyleBox["\[EscapeKey]", FontSize->14, FontColor->GrayLevel[0]], StyleBox[" key the second time, the \[Pi] symbol magically appears). ", FontColor->GrayLevel[0]] }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.39429499648*^9, 3.394294996808125*^9}, 3.394296047526875*^9, {3.394328943808125*^9, 3.394328982120625*^9}, { 3.394332505120625*^9, 3.394332552245625*^9}, {3.394332632058125*^9, 3.394332705245625*^9}, {3.39433274463625*^9, 3.394332759526875*^9}, 3.394669223796875*^9, {3.39466943271875*^9, 3.3946695245*^9}, { 3.39466956025*^9, 3.394669614421875*^9}, {3.394669669640625*^9, 3.394669749296875*^9}, {3.394669786375*^9, 3.3946698608125*^9}, { 3.394669901671875*^9, 3.394669920640625*^9}, {3.394670036796875*^9, 3.394670225390625*^9}, {3.394670808375*^9, 3.39467089234375*^9}, { 3.394671032921875*^9, 3.394671051109375*^9}, 3.39471891865625*^9, 3.3948951654553747`*^9, {3.3949308997991247`*^9, 3.3949309505959997`*^9}, { 3.3949309868459997`*^9, 3.3949310050647497`*^9}, {3.3949312460022497`*^9, 3.3949312619241247`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.39467022909375*^9, 3.39467023021875*^9}, { 3.3948951845491247`*^9, 3.3948951886428747`*^9}, {3.3949313606897497`*^9, 3.3949313719084997`*^9}, 3.398996709171875*^9}], Cell[TextData[{ "Find the first 1000 digits of \[Pi]. Note the next line is entered ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{"N", "[", RowBox[{ StyleBox[ RowBox[{ StyleBox["\[EscapeKey]", FontSize->14], "p", StyleBox["\[EscapeKey]", FontSize->14]}]], ",", "1000"}], "]"}], FontColor->RGBColor[1, 0, 0]], TraditionalForm]]], "." }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.39429499648*^9, 3.394294996808125*^9}, 3.394296047526875*^9, {3.394328943808125*^9, 3.394328982120625*^9}, { 3.394332505120625*^9, 3.394332552245625*^9}, {3.394332632058125*^9, 3.394332705245625*^9}, {3.39433274463625*^9, 3.394332759526875*^9}, 3.394669223796875*^9, {3.39466943271875*^9, 3.3946695245*^9}, { 3.39466956025*^9, 3.394669614421875*^9}, {3.394669669640625*^9, 3.394669749296875*^9}, {3.394669786375*^9, 3.3946698608125*^9}, { 3.394669901671875*^9, 3.394669963625*^9}, {3.394670232625*^9, 3.394670300609375*^9}, {3.39467037253125*^9, 3.394670386734375*^9}, { 3.3947571588152275`*^9, 3.3947572265496025`*^9}, {3.3949313831897497`*^9, 3.3949313836897497`*^9}, {3.3949314242366247`*^9, 3.3949314450647497`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{"N", "[", RowBox[{"\[Pi]", ",", " ", "1000"}], "]"}]], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.3937029242728205`*^9, 3.393702925063958*^9}, { 3.394328989745625*^9, 3.39432899398*^9}, {3.39433258032375*^9, 3.3943325860425*^9}, {3.394332763776875*^9, 3.394332771026875*^9}, { 3.39467041028125*^9, 3.39467041834375*^9}, {3.398998185734375*^9, 3.398998187*^9}}], Cell[TextData[{ "In ", StyleBox["Mathematica", FontSlant->"Italic"], ", we can enter the ", StyleBox["exponential constant ", FontSlant->"Italic"], "(i.e. the base of the natural logarithm) ", StyleBox[", ", FontSlant->"Italic"], Cell[BoxData[ FormBox[ StyleBox[ RowBox[{" ", "\[ExponentialE]"}], FontSize->14], TraditionalForm]]], " \[TildeTilde] 2.71828 , by ", StyleBox["using the keyboard shortcut ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " ee ", StyleBox["\[EscapeKey]. ", FontSize->14], StyleBox[" ", CellFrame->0.5, FontSize->16], "Note that you must use ", StyleBox["two", FontVariations->{"Underline"->True}], " e's. If you use just ", StyleBox["one", FontVariations->{"Underline"->True}], " e, you will get the symbol ", StyleBox["\[Epsilon]", FontSize->16], " for the Greek letter epsilon. Try entering ", StyleBox["\[ExponentialE]", FontSize->14], " using the keyboard shortcut in the red input cell below. 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" }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.39429499648*^9, 3.394294996808125*^9}, 3.394296047526875*^9, {3.394328943808125*^9, 3.394328982120625*^9}, { 3.394332505120625*^9, 3.394332552245625*^9}, {3.394332632058125*^9, 3.394332705245625*^9}, {3.39433274463625*^9, 3.394332759526875*^9}, 3.394669223796875*^9, {3.39466943271875*^9, 3.3946695245*^9}, { 3.39466956025*^9, 3.394669614421875*^9}, {3.394669669640625*^9, 3.394669749296875*^9}, {3.394669786375*^9, 3.3946698608125*^9}, { 3.394669901671875*^9, 3.394669920640625*^9}, {3.394670036796875*^9, 3.394670225390625*^9}, {3.394670808375*^9, 3.39467089234375*^9}, { 3.394671032921875*^9, 3.394671051109375*^9}, 3.39471891865625*^9, 3.3948951654553747`*^9, {3.3949308997991247`*^9, 3.3949309505959997`*^9}, { 3.3949309868459997`*^9, 3.3949310050647497`*^9}, {3.3949312460022497`*^9, 3.3949312619241247`*^9}, {3.3949314983616247`*^9, 3.3949315043616247`*^9}, 3.395970646836875*^9}, FontFamily->"Comic Sans MS"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.3949332617991247`*^9, 3.3949332632991247`*^9}, 3.398996716234375*^9}], Cell[TextData[{ StyleBox["\[CheckmarkedBox] ", FontSize->24], StyleBox["Mathematica", FontSlant->"Italic"], " has simple shortcuts for the Greek alphabet. Here some common ones that \ you may want to use. " }], "Text", CellChangeTimes->{ 3.3948946998459997`*^9, {3.3948947369241247`*^9, 3.3948947646741247`*^9}, 3.3948953724709997`*^9, {3.3948954172053747`*^9, 3.3948956138147497`*^9}, { 3.3948958081272497`*^9, 3.3948959455803747`*^9}, {3.3948959950178747`*^9, 3.3948961226741247`*^9}, {3.3948961534553747`*^9, 3.3948961568616247`*^9}, 3.3949331721584997`*^9}], Cell[TextData[{ Cell[BoxData[GridBox[{ {"alpha", StyleBox["\[Alpha]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "a", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"beta", StyleBox["\[Beta]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "b", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"gamma", StyleBox["\[Gamma]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "g", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"delta", StyleBox["\[Delta]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "d", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"epsilon", StyleBox["\[Epsilon]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "e", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"theta", StyleBox["\[Theta]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "th", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"kappa", StyleBox["\[Kappa]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "k", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"lambda", StyleBox["\[Lambda]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "l", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"pi", StyleBox["\[Pi]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "p", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]}, {"omega", StyleBox["\[Omega]", FontSize->14, FontWeight->"Bold"], RowBox[{ StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}], " ", "o", " ", StyleBox["\[EscapeKey]", CellFrame->{{0.5, 3}, {3, 0.5}}]}]} }, GridBoxDividers->{ "Columns" -> {{True}}, "ColumnsIndexed" -> {}, "Rows" -> {{True}}, "RowsIndexed" -> {}}]]], " " }], "Text", CellChangeTimes->{ 3.3948946998459997`*^9, {3.3948947369241247`*^9, 3.3948947646741247`*^9}, 3.3948953724709997`*^9, {3.3948954172053747`*^9, 3.3948956138147497`*^9}, { 3.3948958081272497`*^9, 3.3948959455803747`*^9}, {3.3948959950178747`*^9, 3.3948961226741247`*^9}, {3.3948961534553747`*^9, 3.3948961642834997`*^9}, {3.3948963257366247`*^9, 3.3948963503147497`*^9}, {3.396442989623412*^9, 3.396443014008829*^9}}, TextAlignment->Center], Cell[CellGroupData[{ Cell[TextData[StyleBox["Exercise 1.5 A", FontSlant->"Italic"]], "Subsubsubsubsection", CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295963808125*^9, 3.39429597588625*^9}, { 3.394298058058125*^9, 3.39429806344875*^9}, {3.3942981760425*^9, 3.39429818444875*^9}, {3.39432913019875*^9, 3.394329130558125*^9}, 3.39433094598*^9, {3.394332195901875*^9, 3.394332196651875*^9}, { 3.39433307123*^9, 3.39433307457375*^9}, 3.394681272296875*^9, 3.398615840201625*^9}, FontFamily->"Comic Sans MS", FontSize->12, FontSlant->"Italic", FontColor->RGBColor[ 0.25882352941176473`, 0.41568627450980394`, 0.5333333333333333]], Cell[TextData[{ "Multiple choice question.\nWhich of the following will give us the \ exponential constant ", Cell[BoxData[ FormBox[ StyleBox[ RowBox[{" ", "\[ExponentialE]"}], FontSize->14], TraditionalForm]]], " \[TildeTilde] 2.71828 ?\nA. ", StyleBox[" ", CellFrame->0.5], "e", StyleBox["\n", FontSize->14], "B. ", StyleBox[" ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " e ", StyleBox["\[EscapeKey]\n", FontSize->14], "C. ", StyleBox[" ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " ee ", StyleBox["\[EscapeKey]", FontSize->14] }], "Text", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.394331872464375*^9, 3.39433199323*^9}, {3.39433204338625*^9, 3.394332118589375*^9}, { 3.39433220282375*^9, 3.394332227214375*^9}, {3.394333097214375*^9, 3.3943331921675*^9}, {3.3943332470425*^9, 3.39433324738625*^9}, { 3.39433330948*^9, 3.39433339326125*^9}, {3.394333486605*^9, 3.394333716245625*^9}, {3.3948248102678747`*^9, 3.3948249422366247`*^9}, 3.394994769765625*^9}, FontFamily->"Comic Sans MS"], Cell[CellGroupData[{ Cell[TextData[{ StyleBox["Answer to ", FontSize->10], StyleBox["Exercise 1.5A", FontSize->10, FontSlant->"Italic"] }], "Subsubsubsection", CellFrame->None, CellDingbat->None, ShowGroupOpener->True, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.39429295526125*^9, 3.394292955995625*^9}, { 3.39429337701125*^9, 3.394293380964375*^9}, {3.394300655308125*^9, 3.394300657714375*^9}, {3.3943291901675*^9, 3.394329190464375*^9}, { 3.39433372507375*^9, 3.394333725558125*^9}, 3.3946812760625*^9, { 3.3986158673735*^9, 3.398615868170375*^9}}, FontFamily->"Comic Sans MS", FontSize->9, FontColor->RGBColor[ 0.25882352941176473`, 0.41568627450980394`, 0.5333333333333333]], Cell[TextData[{ "A. ", StyleBox[" ", CellFrame->0.5], "e\t\t", StyleBox["\[SadSmiley]", FontSize->24], " WRONG! \tThis is just the letter e. ", StyleBox["\n", FontSize->14], "B. ", StyleBox[" ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " e ", StyleBox["\[EscapeKey]\t ", FontSize->14], StyleBox["\[SadSmiley] ", FontSize->24], "WRONG! ", StyleBox["\t ", FontSize->14], "This gives the Greek letter epsilon ", Cell[BoxData[ FormBox[ StyleBox["\[Epsilon]", FontSize->14], TraditionalForm]]], ".", StyleBox["\n", FontSize->14], "C. ", StyleBox[" ", CellFrame->0.5], StyleBox["\[EscapeKey]", FontSize->14], " ee ", StyleBox["\[EscapeKey] \t ", FontSize->14], StyleBox["\[HappySmiley] ", FontSize->24], StyleBox[" ", FontSize->14], "RIGHT !!" }], "Text", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.394331872464375*^9, 3.39433199323*^9}, {3.39433204338625*^9, 3.394332118589375*^9}, { 3.39433220282375*^9, 3.394332227214375*^9}, {3.394333097214375*^9, 3.3943331921675*^9}, {3.3943332470425*^9, 3.39433324738625*^9}, { 3.39433330948*^9, 3.39433339326125*^9}, {3.394333486605*^9, 3.394333716245625*^9}, {3.3948248102678747`*^9, 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Cell[TextData[{ "Look at the first two thousand digits of ", StyleBox["\[ExponentialE].", FontSize->14], " Given that ", StyleBox["\[ExponentialE]", FontSize->14], StyleBox[" ", FontSize->16], "is an ", StyleBox["irrational number", FontSlant->"Italic"], " what should we expect to see (or not see) when we look at this decimal?" }], "Text", CellFrame->None, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.394331872464375*^9, 3.39433199323*^9}, {3.39433204338625*^9, 3.394332118589375*^9}, { 3.39433220282375*^9, 3.394332227214375*^9}, {3.394333097214375*^9, 3.3943331921675*^9}, {3.3943332470425*^9, 3.39433324738625*^9}, { 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number it is a \ nonrepeating, nonterminating decimal. Therefore we should expect to see a \ decimal that goes on forever with no repeating sequence of digits. \ \>", "Text", CellFrame->None, ShowGroupOpener->True, CellFrameColor->RGBColor[0.6, 0.4, 0.2], CellChangeTimes->{{3.393702970639493*^9, 3.393702974324792*^9}, { 3.3937037957960095`*^9, 3.3937038244071503`*^9}, {3.39429326423*^9, 3.394293304855*^9}, {3.394293613839375*^9, 3.39429364519875*^9}, 3.394295979526875*^9, {3.394296547495625*^9, 3.39429656301125*^9}, { 3.39432914144875*^9, 3.394329177714375*^9}, 3.3943292140425*^9, { 3.39432924576125*^9, 3.394329246355*^9}, {3.39433039494875*^9, 3.394330404183125*^9}, {3.394330570401875*^9, 3.394330630933125*^9}, { 3.39433374998*^9, 3.39433384569875*^9}}, FontFamily->"Comic Sans MS", FontSize->10] }, Closed]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["1.6\tA keyboard shortcut for entering square roots.", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, 3.39429602048*^9, {3.39430616019875*^9, 3.39430616069875*^9}, 3.394330940355*^9, {3.3943323711675*^9, 3.394332447495625*^9}, 3.39438223144875*^9, 3.394681270109375*^9, 3.3948254889553747`*^9, 3.39861582546725*^9, {3.398994843328125*^9, 3.39899486128125*^9}, { 3.399038271984375*^9, 3.399038285578125*^9}}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ "If you need to enter a square root on your calculator you simply press the \ button with the square root symbol ", Cell[BoxData[ FormBox[ SqrtBox[ StyleBox[".", FontColor->GrayLevel[1], Background->RGBColor[0.529198, 0.777737, 1]]], TraditionalForm]]], " . Unfortunately, standard computer keyboards don't have a square root key. \ But ", StyleBox["Mathematica", FontSlant->"Italic"], " does have a special keyboard shortcut which allows you to enter a square \ root symbol. To enter a square root enter ", StyleBox["\[ControlKey]", FontSize->18], StyleBox["\[LeftModified]", FontSize->14], "2", StyleBox["\[RightModified]", FontSize->14], " , (that is, while holding down the Control key, type the number 2).", StyleBox[" ", FontSize->14], " The result is the square root template ", Cell[BoxData[ FormBox[ SqrtBox["\[Placeholder]"], TraditionalForm]]], ". If you now enter a number, while the small entry box is still \ highlighted, it will be placed under the radical. " }], "Text", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.39432903963625*^9, 3.39432913398*^9}, 3.394330745105*^9, {3.39433167838625*^9, 3.394331856839375*^9}, { 3.394384378276875*^9, 3.39438447657375*^9}, {3.394384527620625*^9, 3.394384545355*^9}, {3.3948213615647497`*^9, 3.3948213692834997`*^9}, { 3.3948214312366247`*^9, 3.3948214989397497`*^9}, 3.3949299430334997`*^9, { 3.396701269046875*^9, 3.396701306375*^9}, {3.3967015085*^9, 3.39670151159375*^9}, {3.398995007078125*^9, 3.39899524871875*^9}, { 3.39899528425*^9, 3.39899532740625*^9}, {3.398995418203125*^9, 3.3989954905*^9}, {3.398995524984375*^9, 3.398995601046875*^9}, { 3.398995676046875*^9, 3.39899574159375*^9}, {3.398995814609375*^9, 3.398995837734375*^9}, {3.398995905671875*^9, 3.3989959319375*^9}, 3.399039028578125*^9, 3.3994861400625*^9}, FontFamily->"Comic Sans MS"], Cell[TextData[{ "To enter the expression ", Cell[BoxData[ FormBox[ SqrtBox["49"], TraditionalForm]]], ", enter ", StyleBox["\[ControlKey]", FontSize->18, FontColor->RGBColor[1, 0, 0]], StyleBox["\[LeftModified]", FontSize->14, FontColor->RGBColor[1, 0, 0]], StyleBox["2", FontColor->RGBColor[1, 0, 0]], StyleBox["\[RightModified]", FontSize->14, FontColor->RGBColor[1, 0, 0]], StyleBox[" 49", FontColor->RGBColor[1, 0, 0]], ". Try this below. " }], "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.39432903963625*^9, 3.39432913398*^9}, 3.394330745105*^9, {3.3948214748772497`*^9, 3.3948215051428747`*^9}, { 3.3949300436272497`*^9, 3.3949300441428747`*^9}, 3.39670152134375*^9, { 3.39760455734375*^9, 3.397604567578125*^9}, {3.39899594853125*^9, 3.398995950140625*^9}, 3.398996729125*^9}, FontFamily->"Comic Sans MS"], Cell[BoxData[""], "Input", CellChangeTimes->{{3.398995610421875*^9, 3.39899561171875*^9}, 3.398995666859375*^9, {3.39899570646875*^9, 3.3989957096875*^9}, { 3.398995745671875*^9, 3.39899574659375*^9}, {3.398995936953125*^9, 3.39899593834375*^9}, 3.398996731328125*^9}] }, Closed]], Cell[CellGroupData[{ Cell["1.7\tDecimals in -- decimals out.", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, { 3.39429735526125*^9, 3.394297369683125*^9}, {3.394298164105*^9, 3.39429816569875*^9}, {3.394298228839375*^9, 3.394298243964375*^9}, { 3.394331018105*^9, 3.394331037245625*^9}, {3.394332947151875*^9, 3.394333007464375*^9}, {3.39438129419875*^9, 3.394381313464375*^9}, { 3.394381406370625*^9, 3.39438141351125*^9}, 3.39438223463625*^9, 3.39468128134375*^9, 3.394712981*^9, 3.395107551445136*^9, 3.398615828061*^9, {3.398994865453125*^9, 3.398994866046875*^9}}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox[" employs a useful convention when doing numerical calculations. If \ your input contains any numbers in decimal form then it automatically \ produces an answer in decimal form. This is an alternative way to get a \ numerical approximation without using the \"N\" command. ", CellFrame->0.5] }], "Text", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394381328745625*^9, 3.394381658651875*^9}, 3.3943816970425*^9, {3.394381997495625*^9, 3.394382005401875*^9}, 3.39438211923*^9, 3.3949333238928747`*^9}, FontFamily->"Comic Sans MS"], Cell[TextData[{ StyleBox["Compare the outputs resulting from entering ", CellFrame->0.5], Cell[BoxData[ FormBox[ SqrtBox["90"], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ SqrtBox["90."], TraditionalForm]]], " below. Observe that the mere presence of the decimal point in the second \ radical is enough to change the output form from exact to decimal." }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394381328745625*^9, 3.394381658651875*^9}, 3.3943816970425*^9, {3.39438176663625*^9, 3.3943818911675*^9}, { 3.394382017683125*^9, 3.394382055995625*^9}, {3.3949333289866247`*^9, 3.3949333503616247`*^9}, {3.40037606084375*^9, 3.40037606084375*^9}, { 3.4087507368220263`*^9, 3.4087507570599146`*^9}, {3.4087508516704745`*^9, 3.4087508516704745`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ SqrtBox["90"]], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.393703864184347*^9, 3.3937038660970974`*^9}, 3.39429581701125*^9, {3.394306420433125*^9, 3.39430643882375*^9}, { 3.394327065776875*^9, 3.3943270666675*^9}, {3.394327950589375*^9, 3.39432796294875*^9}, {3.39438167088625*^9, 3.39438167701125*^9}, { 3.394387735605*^9, 3.394387740605*^9}, {3.398999212953125*^9, 3.398999219796875*^9}, {3.408750804459179*^9, 3.4087508094246664`*^9}, { 3.4087508407526665`*^9, 3.4087508447626505`*^9}}], Cell[BoxData[ SqrtBox["90."]], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.393703864184347*^9, 3.3937038660970974`*^9}, 3.39429581701125*^9, {3.394306420433125*^9, 3.39430643882375*^9}, { 3.394327065776875*^9, 3.3943270666675*^9}, {3.394327950589375*^9, 3.39432796294875*^9}, {3.39438167088625*^9, 3.39438168838625*^9}, { 3.3989992436875*^9, 3.39899924928125*^9}, 3.40037606440625*^9, { 3.4087507386390505`*^9, 3.4087507592372103`*^9}, {3.408750818979707*^9, 3.4087508197785707`*^9}, {3.4087508547876105`*^9, 3.4087508568239307`*^9}}],\ Cell[TextData[StyleBox["Here is another example. Note that if any part of the \ input contains a decimal then the output will be displayed in decimal form. 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Here \ are some examples of how it works.\nThe basic syntax is: ", StyleBox["Range[ start, end, increment] ", FontWeight->"Bold"] }], "Text", CellChangeTimes->{{3.395108956195136*^9, 3.395109010804511*^9}, { 3.395109058601386*^9, 3.395109063507636*^9}, {3.3951672149636636`*^9, 3.39516725629747*^9}}], Cell["\<\ Generate a list of numbers starting with 10 ending with 200 in increments of \ 2.\ \>", "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.39432903963625*^9, 3.39432913398*^9}, 3.394330745105*^9, {3.3948214748772497`*^9, 3.3948215051428747`*^9}, { 3.3949300436272497`*^9, 3.3949300441428747`*^9}, {3.395109051820136*^9, 3.395109079726386*^9}, {3.395109118304511*^9, 3.395109137382636*^9}, { 3.395147524632125*^9, 3.3951475481165*^9}, {3.3951475801165*^9, 3.395147582413375*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{"Range", "[", RowBox[{"10", ",", " ", "200", ",", " ", "2"}], "]"}]], "Input", CellChangeTimes->{{3.395109083242011*^9, 3.395109100179511*^9}, { 3.395109140835761*^9, 3.395109141617011*^9}, {3.39514755214775*^9, 3.39514758821025*^9}}], Cell["\<\ Generate a list of numbers starting with 1, ending with 10 in increments of \ .5.\ \>", "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.39432903963625*^9, 3.39432913398*^9}, 3.394330745105*^9, {3.39433167838625*^9, 3.394331856839375*^9}, { 3.394384378276875*^9, 3.39438447657375*^9}, {3.394384527620625*^9, 3.394384545355*^9}, {3.3948213615647497`*^9, 3.3948213692834997`*^9}, { 3.3948214312366247`*^9, 3.3948214989397497`*^9}, {3.3949299430334997`*^9, 3.3949300318616247`*^9}, {3.395147863944625*^9, 3.395147894194625*^9}, 3.395147933382125*^9, {3.3969684987103443`*^9, 3.3969684999134693`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{"Range", "[", RowBox[{"1", ",", " ", "10", ",", " ", "0.5"}], "]"}]], "Input", CellChangeTimes->{{3.395147938725875*^9, 3.39514794808525*^9}, { 3.3951672804244432`*^9, 3.3951672805803027`*^9}}], Cell[TextData[{ "Generate a list of numbers starting with 0, ending with \[Pi] in increments \ of ", Cell[BoxData[ FormBox[ FractionBox["\[Pi]", "16"], TraditionalForm]]], "." }], "Item", CellChangeTimes->{{3.3937028613022738`*^9, 3.393702898035093*^9}, { 3.3937029303715906`*^9, 3.3937029435104833`*^9}, {3.3937041372670207`*^9, 3.3937041684718914`*^9}, {3.393704205815589*^9, 3.393704214608232*^9}, { 3.39428985907375*^9, 3.394289901714375*^9}, 3.394290507526875*^9, { 3.39432716719875*^9, 3.394327207839375*^9}, {3.394327242776875*^9, 3.39432753788625*^9}, {3.3943276322925*^9, 3.394327641933125*^9}, { 3.39432768332375*^9, 3.394327849401875*^9}, {3.394327903308125*^9, 3.394327919589375*^9}, {3.39432903963625*^9, 3.39432913398*^9}, 3.394330745105*^9, {3.39433167838625*^9, 3.394331856839375*^9}, { 3.394384378276875*^9, 3.39438447657375*^9}, {3.394384527620625*^9, 3.394384545355*^9}, {3.3948213615647497`*^9, 3.3948213692834997`*^9}, { 3.3948214312366247`*^9, 3.3948214989397497`*^9}, {3.3949299430334997`*^9, 3.3949300318616247`*^9}, {3.395147863944625*^9, 3.395147920913375*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{"Range", "[", RowBox[{"0", ",", " ", "\[Pi]", ",", " ", RowBox[{"\[Pi]", "/", "16"}]}], "]"}]], "Input", CellChangeTimes->{{3.395147958975875*^9, 3.3951479724915*^9}, { 3.39899954246875*^9, 3.398999549*^9}}], Cell["\<\ If you leave out the increment, it is assumed to be 1 . That is, Range[ a, b] \ is equivalent to Range[a, b, 1] (see below). \ \>", "Text", CellChangeTimes->{{3.395108956195136*^9, 3.395109010804511*^9}, { 3.395109058601386*^9, 3.395109063507636*^9}, {3.395109167554511*^9, 3.395109195710761*^9}, {3.395148016679*^9, 3.3951480632415*^9}, { 3.3951672967896385`*^9, 3.395167302821382*^9}, 3.39637756215625*^9, 3.39714295919375*^9, 3.3971464594125*^9, {3.3994710155625*^9, 3.399471034859375*^9}, {3.399471170671875*^9, 3.399471187984375*^9}, { 3.399471383*^9, 3.399471437234375*^9}}], Cell[BoxData[ RowBox[{"Range", "[", RowBox[{ RowBox[{"-", "2"}], ",", "8"}], "]"}]], "Input", CellChangeTimes->{{3.395148012257125*^9, 3.395148013304*^9}, { 3.395148067304*^9, 3.3951480708665*^9}, {3.399471038640625*^9, 3.39947104309375*^9}, {3.39947111234375*^9, 3.3994711181875*^9}, { 3.39947129403125*^9, 3.39947129840625*^9}}], Cell["\<\ If you want to generate a list of positive integers, starting with 1, up to \ some particular integer, then you can use the shorter form below. That is, \ Range[n] is equivalent to Range[1,n,1] and Range[1,n]. \ \>", "Text", CellChangeTimes->{{3.395108956195136*^9, 3.395109010804511*^9}, { 3.395109058601386*^9, 3.395109063507636*^9}, {3.395109167554511*^9, 3.395109195710761*^9}, {3.395148016679*^9, 3.3951480632415*^9}, { 3.3951672967896385`*^9, 3.395167302821382*^9}, 3.39637756215625*^9, 3.39714295919375*^9, 3.3971464594125*^9, {3.399471149109375*^9, 3.399471157859375*^9}, {3.3994713171875*^9, 3.399471343828125*^9}}], Cell[BoxData[ RowBox[{"Range", "[", "20", "]"}]], "Input", CellChangeTimes->{{3.395148012257125*^9, 3.395148013304*^9}, { 3.395148067304*^9, 3.3951480708665*^9}}], Cell["\<\ If you apply an arithmetic operation to a list and the operation will be \ performed on each element of the list. \ \>", "Text", CellChangeTimes->{{3.395108956195136*^9, 3.395109010804511*^9}, { 3.395109058601386*^9, 3.395109063507636*^9}, {3.395109167554511*^9, 3.395109195710761*^9}, {3.395148016679*^9, 3.3951480632415*^9}, { 3.395148124944625*^9, 3.3951481931165*^9}, {3.395148467944625*^9, 3.395148529132125*^9}, {3.3951673156797495`*^9, 3.3951673838213043`*^9}, { 3.4100356039*^9, 3.400165582484375*^9}}], Cell["Find the square of all the positive integers from 1 to 25. 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The correct ", StyleBox["Mathematica", FontSlant->"Italic"], " syntax in this case is: ", Cell[BoxData[ FormBox[ SuperscriptBox[ RowBox[{"Sin", "[", RowBox[{"\[Pi]", "/", "3"}], "]"}], "2"], TraditionalForm]]], " . Note in particular that you must place the exponent after the argument, \ ", Cell[BoxData[ FormBox[ RowBox[{"[", RowBox[{"\[Pi]", "/", "3"}], "]"}], TraditionalForm]]], ", and not directly after the Sin. So the keystrokes for entering ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["sin", "2"], "(", FractionBox["\[Pi]", "3"], ")"}], TraditionalForm]]], " are: ", StyleBox["Sin[ \[Pi]/3] ", FontColor->RGBColor[1, 0, 0]], StyleBox["^", FontSize->14, FontColor->RGBColor[1, 0, 0]], StyleBox[" 2", FontColor->RGBColor[1, 0, 0]], StyleBox[" . 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They \ are called ", CellFrame->0.5], StyleBox["StandardForm", CellFrame->0.5, FontWeight->"Bold"], StyleBox[" and ", CellFrame->0.5], StyleBox["TraditionalForm", CellFrame->0.5, FontWeight->"Bold"], StyleBox[". The default form is StandardForm. The most noticeable aspect of \ this form is that polynomial expressions are displayed in ", CellFrame->0.5], StyleBox["ascending", CellFrame->0.5, FontSlant->"Italic"], StyleBox[" powers of the variable. So if you enter ", CellFrame->0.5], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"3", "x"}], "+", "5"}], TraditionalForm]]], ", ", StyleBox["Mathematica", FontSlant->"Italic"], " will automatically display it as ", Cell[BoxData[ FormBox[ RowBox[{"5", "+", RowBox[{"3", "x"}], "+", SuperscriptBox["x", "2"]}], TraditionalForm]]], ". Execute the line below to see how this works. 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Note that the command TraditionalForm is \ just one word, no space. 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", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, { 3.39429735526125*^9, 3.394297369683125*^9}, {3.394298164105*^9, 3.39429816569875*^9}, {3.394298228839375*^9, 3.394298243964375*^9}, { 3.394331018105*^9, 3.394331037245625*^9}, {3.394332947151875*^9, 3.394333007464375*^9}, {3.394382216339375*^9, 3.394382217651875*^9}, { 3.394558579964375*^9, 3.394558589651875*^9}, 3.394558786355*^9, { 3.394558849558125*^9, 3.394558855870625*^9}, {3.3945603797925*^9, 3.394560380308125*^9}, 3.3945853551885486`*^9, 3.3948255172366247`*^9, { 3.395150620944625*^9, 3.395150633975875*^9}, {3.395151327319625*^9, 3.39515133358525*^9}, {3.397143062271875*^9, 3.397143068334375*^9}}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[{ StyleBox["If we wish to assign the value 10 to the variable ", CellFrame->0.5], Cell[BoxData[ FormBox["x", TraditionalForm]]], " we just enter ", Cell[BoxData[ FormBox[ RowBox[{"x", "=", "10"}], TraditionalForm]]], ". ", StyleBox["Once the assignment is made it will remain in ", CellFrame->0.5], StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox["'s memory until either there is a reassignment or the variable is \ \"cleared\". ", CellFrame->0.5], "\n", StyleBox["\nLook at the input cell below. Observe", CellFrame->0.5], " that the letter ", Cell[BoxData[ FormBox[ RowBox[{"x", " "}], TraditionalForm]]], "is currently", StyleBox[" ", FontWeight->"Bold"], StyleBox["blue", FontVariations->{"Underline"->True}, FontColor->RGBColor[0, 0, 1]], " . Unassigned variables and functions are always displayed in a color. \ However, as soon as you ", "evaluate", " the cell, the ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " will change to ", StyleBox["black", FontVariations->{"Underline"->True}], ". 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As you \ ", "evaluate", " this command in the next input cell notice how all of the ", Cell[BoxData[ FormBox["x", TraditionalForm]]], "'s (up and down the page) become ", StyleBox["blue", FontVariations->{"Underline"->True}, FontColor->RGBColor[0, 0, 1]], " again. 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This is \ illustrated below.\nFirst let's set ", CellFrame->0.5], Cell[BoxData[ FormBox[ RowBox[{"x", "=", "20"}], TraditionalForm]]], ". Watch as the ", Cell[BoxData[ FormBox["x", TraditionalForm]]], "'s go from ", StyleBox["blue", FontVariations->{"Underline"->True}, FontColor->RGBColor[0, 0, 1]], " to", StyleBox[" black", FontVariations->{"Underline"->True}], " as soon as you ", "evaluate", " the input cell. 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Execute the \ next set of inputs to see how this works. \ \>", "Text", CellChangeTimes->{{3.39714321250625*^9, 3.39714324606875*^9}}], Cell[BoxData[ RowBox[{"a", " ", "=", " ", "1"}]], "Input", CellChangeTimes->{{3.397143252771875*^9, 3.397143254928125*^9}}], Cell[BoxData[ RowBox[{"b", " ", "=", " ", "2"}]], "Input", CellChangeTimes->{{3.397143258209375*^9, 3.397143259709375*^9}}], Cell[BoxData[ RowBox[{"a", " ", "+", " ", "b"}]], "Input", CellChangeTimes->{{3.3971433021*^9, 3.3971433029125*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", RowBox[{"a", ",", " ", "b"}], "]"}]], "Input", CellChangeTimes->{{3.39714327506875*^9, 3.39714327838125*^9}}], Cell[BoxData[ RowBox[{"a", " ", "+", " ", "b"}]], "Input", CellChangeTimes->{{3.397143281084375*^9, 3.397143296115625*^9}}], Cell[TextData[{ StyleBox["\[CheckmarkedBox] ", FontSize->24], "It turns out that the most common error that new users make is to forget \ that they have assigned a value to a variable. ", StyleBox["Mathematica", FontSlant->"Italic"], "'s color coding scheme is designed to help avoid this error. " }], "Text", CellChangeTimes->{ 3.3948946998459997`*^9, {3.3948947369241247`*^9, 3.3948947646741247`*^9}, 3.3948953724709997`*^9, {3.3949355513772497`*^9, 3.3949355561897497`*^9}, { 3.395663837109375*^9, 3.395663860375*^9}, {3.39714340744375*^9, 3.3971434255375*^9}}], Cell[TextData[StyleBox["The ClearNames command.", FontWeight->"Bold", FontVariations->{"Underline"->True}]], "Text", CellChangeTimes->{{3.39714311856875*^9, 3.397143173334375*^9}, { 3.397594171625*^9, 3.397594175359375*^9}, 3.39767846096875*^9, { 3.397678501515625*^9, 3.39767852196875*^9}}], Cell[TextData[{ "The ClearNames command (see the input cell below) allows us, in a single \ step, to clear ", StyleBox["all", FontVariations->{"Underline"->True}], " variable and function names that we have defined during the current \ session. Note that the command has no arguments in the square brackets. 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This gives you a \"clean slate\" from which to work. For \ convenience, we will include a ClearNames command at the start of each of the \ remaining sections of the tutorial. 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", "Subsection", CellFrame->{{0, 0}, {0.5, 0.5}}, CellDingbat->None, ShowGroupOpener->True, CellChangeTimes->{{3.394295677245625*^9, 3.39429567923*^9}, { 3.39429735526125*^9, 3.394297369683125*^9}, {3.394298164105*^9, 3.39429816569875*^9}, {3.394298228839375*^9, 3.394298243964375*^9}, { 3.394331018105*^9, 3.394331037245625*^9}, {3.394332947151875*^9, 3.394333007464375*^9}, {3.394382216339375*^9, 3.394382217651875*^9}, { 3.394558579964375*^9, 3.394558589651875*^9}, {3.394558805370625*^9, 3.394558827589375*^9}, {3.394559854339375*^9, 3.394559947245625*^9}, { 3.39456044357375*^9, 3.394560482058125*^9}, {3.394560527105*^9, 3.39456053523*^9}, 3.3945826383928885`*^9, {3.39472685640625*^9, 3.39472685675*^9}, 3.3947283094375*^9, 3.3948255200803747`*^9}, FontFamily->"Comic Sans MS", FontWeight->"Plain"], Cell[TextData[StyleBox["Please evaluate the following command, before \ continuing with this section.", CellFrame->{{0.5, 3}, {3, 0.5}}]], "Text", CellChangeTimes->{{3.398111918427375*^9, 3.39811191897425*^9}, { 3.398111968364875*^9, 3.39811197066175*^9}}], Cell[BoxData[ RowBox[{"ClearNames", "[", "]"}]], "Input", CellChangeTimes->{{3.397177378053125*^9, 3.39717740694375*^9}, { 3.397177488475*^9, 3.397177493771875*^9}, 3.3972183115262403`*^9, 3.397678461015625*^9}, Background->RGBColor[1., 1., 0.8235294117647058]], Cell[TextData[StyleBox["The principal use of the Expand command is to \ \"multiply out\" products of polynomial expressions. 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To answer this \ question we can use ", CellFrame->0.5], StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox["'s Numerator and Denominator commands. 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With this information we can say that ", Cell[BoxData[ FormBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox["x", "3"], "-", RowBox[{"4", SuperscriptBox["x", "2"]}], "+", "x", "+", "6"}], RowBox[{ SuperscriptBox["x", "2"], "-", "x", "-", "2"}]], "=", RowBox[{"x", "-", "3"}]}], TraditionalForm]]], " if and only if ", Cell[BoxData[ FormBox[ RowBox[{"x", "\[NotEqual]", "2"}], TraditionalForm]]], " and ", Cell[BoxData[ FormBox[ RowBox[{"x", "\[NotEqual]", RowBox[{"-", "1"}]}], TraditionalForm]]], ".", StyleBox[" ", CellFrame->0.5] }], "Text", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394558595683125*^9, 3.39455862623*^9}, { 3.394559954683125*^9, 3.39456003073*^9}, {3.394582655989483*^9, 3.3945826667905807`*^9}, 3.394726372609375*^9, {3.3948253446116247`*^9, 3.3948254323303747`*^9}, {3.3948255937209997`*^9, 3.3948256330803747`*^9}, {3.3948948216584997`*^9, 3.3948949306116247`*^9}, {3.3948950091741247`*^9, 3.3948950307991247`*^9}, {3.3948964296897497`*^9, 3.3948964307366247`*^9}, {3.3948976283459997`*^9, 3.3948976459397497`*^9}, 3.3949096968459997`*^9, {3.3949100880178747`*^9, 3.3949100915959997`*^9}, { 3.3949108524709997`*^9, 3.3949108763459997`*^9}, {3.3949109913616247`*^9, 3.3949110845491247`*^9}, {3.3949115454241247`*^9, 3.3949115840647497`*^9}, {3.3949117437678747`*^9, 3.3949119842209997`*^9}, {3.3949120183303747`*^9, 3.3949120977522497`*^9}, 3.3949122003303747`*^9, {3.3949123302678747`*^9, 3.3949123477991247`*^9}, { 3.3949357205491247`*^9, 3.3949358540491247`*^9}, {3.3949358853616247`*^9, 3.3949359767991247`*^9}, 3.39499482409375*^9}, FontFamily->"Comic Sans MS"], Cell[TextData[{ StyleBox["If ", CellFrame->0.5], StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox[" cannot factor an expression using rational numbers (integers and \ fractions) then it returns the input unchanged. 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They employ the \ full range of trigonometric identities that you encountered in Precalculus. \ \>", "Text", CellChangeTimes->{{3.3948966477678747`*^9, 3.3948967177991247`*^9}, { 3.3948969976741247`*^9, 3.3948970273459997`*^9}, {3.3948971997209997`*^9, 3.3948972315178747`*^9}, 3.3948974469866247`*^9, 3.3948975006116247`*^9, 3.394994830703125*^9}], Cell["\<\ The TrigExpand command expands out trigonometric functions. Here are two \ examples.\ \>", "Text", CellChangeTimes->{{3.3948966477678747`*^9, 3.3948967177991247`*^9}, { 3.3948969976741247`*^9, 3.3948970605491247`*^9}, 3.3948971373303747`*^9}], Cell[BoxData[ RowBox[{"TrigExpand", "[", RowBox[{"Sin", "[", RowBox[{"2", "x"}], "]"}], "]"}]], "Input", CellChangeTimes->{{3.3948967561428747`*^9, 3.3948967779084997`*^9}, { 3.3948972608772497`*^9, 3.3948972722366247`*^9}, 3.398997524015625*^9}], Cell[BoxData[ RowBox[{"TrigExpand", "[", RowBox[{"Cos", "[", RowBox[{"a", " ", "+", " ", "b"}], "]"}], "]"}]], "Input", CellChangeTimes->{ 3.3948966145334997`*^9, {3.3948967271897497`*^9, 3.3948967307991247`*^9}, { 3.3948967851741247`*^9, 3.3948967992366247`*^9}, {3.3971450571*^9, 3.397145059271875*^9}}], Cell["\<\ The TrigFactor command factors trigonometric functions. 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", CellFrame->0.5] }], "Text", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394558595683125*^9, 3.39455862623*^9}, { 3.39455893326125*^9, 3.394559252433125*^9}, {3.39455930573*^9, 3.394559348151875*^9}, {3.394559628855*^9, 3.394559750308125*^9}, { 3.394585106965913*^9, 3.3945852563421364`*^9}, {3.394726272171875*^9, 3.394726293125*^9}, {3.394726974734375*^9, 3.394727195203125*^9}, { 3.394727261859375*^9, 3.394727529140625*^9}, {3.394727669625*^9, 3.394727701890625*^9}, {3.3947511754714775`*^9, 3.3947511760027275`*^9}, { 3.3947569613464775`*^9, 3.3947569840964775`*^9}, {3.3949386256272497`*^9, 3.3949387620803747`*^9}, {3.3949761424241247`*^9, 3.3949761460647497`*^9}}, FontFamily->"Comic Sans MS"], Cell[TextData[{ "Substitute the value 7 for ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " in the expression ", Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"3", "x"}], "-", "4"}], TraditionalForm]]], "." }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394412599901875*^9, 3.394412906026875*^9}, { 3.394413015964375*^9, 3.39441302232375*^9}, {3.3944131440425*^9, 3.39441334723*^9}, {3.39441348523*^9, 3.394413588855*^9}, { 3.394413654151875*^9, 3.394413864995625*^9}, 3.394413917120625*^9, { 3.39441401007375*^9, 3.39441401394875*^9}, {3.394414127745625*^9, 3.39441420307375*^9}, {3.39441429832375*^9, 3.394414332464375*^9}, { 3.394414519401875*^9, 3.3944145405425*^9}, {3.394416142120625*^9, 3.394416222464375*^9}, {3.3949352751272497`*^9, 3.3949352815334997`*^9}, 3.3949353364397497`*^9, {3.3949360767209997`*^9, 3.3949361196116247`*^9}, { 3.3949761627209997`*^9, 3.3949761692053747`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"x", "^", "2"}], " ", "+", " ", RowBox[{"3", "x"}], " ", "-", " ", "4"}], " ", "/.", " ", RowBox[{"x", " ", "->", " ", "7"}]}]], "Input", CellFrame->0.5, CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.393703864184347*^9, 3.3937038660970974`*^9}, 3.39429581701125*^9, {3.394306420433125*^9, 3.39430643882375*^9}, { 3.394327065776875*^9, 3.3943270666675*^9}, {3.394327950589375*^9, 3.39432796294875*^9}, {3.39456057082375*^9, 3.394560626558125*^9}, 3.39472724203125*^9, 3.3947513127527275`*^9, 3.398997534515625*^9}], Cell[TextData[{ StyleBox["Mathematica", CellFrame->0.5, FontSlant->"Italic"], StyleBox[" allows you to substitute many values for a variable in a single \ command. 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Note we use curly brackets { } to \ enter the list of inputs. 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You should get 0.389924 as the output." }], "Item", CellFrame->None, CellFrameColor->Automatic, CellChangeTimes->{{3.3936943905508256`*^9, 3.393694402608163*^9}, { 3.3937038213026867`*^9, 3.3937038217032623`*^9}, {3.394293294308125*^9, 3.394293296401875*^9}, {3.394295727901875*^9, 3.39429572882375*^9}, 3.394297916651875*^9, {3.394558595683125*^9, 3.39455862623*^9}, { 3.39455893326125*^9, 3.394559252433125*^9}, {3.39455930573*^9, 3.394559348151875*^9}, {3.394559628855*^9, 3.394559750308125*^9}, { 3.394585106965913*^9, 3.3945852563421364`*^9}, {3.394726272171875*^9, 3.394726293125*^9}, {3.394726974734375*^9, 3.394727195203125*^9}, { 3.394727261859375*^9, 3.394727585828125*^9}, {3.39472763859375*^9, 3.39472766228125*^9}, {3.39472832696875*^9, 3.3947283315625*^9}, 3.3949361109553747`*^9, {3.3949387796272497`*^9, 3.3949387821897497`*^9}}, FontFamily->"Comic Sans MS"], Cell[BoxData[""], "Input", CellFrameColor->RGBColor[1, 0, 0], CellChangeTimes->{{3.394582466526067*^9, 3.3945824763452463`*^9}, { 3.394727597484375*^9, 3.394727626140625*^9}, 3.3949361379084997`*^9, { 3.3976065615*^9, 3.397606609390625*^9}, 3.3989967591875*^9}], Cell[TextData[{ StyleBox["Evaluate the expression ", CellFrame->0.5], Cell[BoxData[ FormBox[ RowBox[{ SuperscriptBox["x", "2"], "+", RowBox[{"3", "x"}], "-", "4"}], TraditionalForm]]], " when ", Cell[BoxData[ FormBox["x", TraditionalForm]]], " is replaced by ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"2", "m"}], "+", "7"}], TraditionalForm]]], " and label the result ", Cell[BoxData[ FormBox["h", TraditionalForm]]], ". Then have ", StyleBox["Mathematica", FontSlant->"Italic"], " express ", Cell[BoxData[ FormBox["h", TraditionalForm]]], " in simplest form. 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First without any assumptions, and then repeat with the added \ assumption that ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", "+", "y"}], ">", "0"}], TraditionalForm]]], ". Can you explain the different outputs produced ? 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", FontSlant->"Italic"], "As a first example, we will consider the linear function f(x) = 5 x + 13. \ The ", StyleBox["Mathematica", FontSlant->"Italic"], " command to define this function is ", Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{ RowBox[{"5", "x"}], "+", "13"}]}]], "InlineFormula"], ". The ", Cell[BoxData["_"], "InlineFormula"], " (referred to as \[OpenCurlyDoubleQuote]blank\[CloseCurlyDoubleQuote]) on \ the left\[Hyphen]hand side is required. Remember to put a ", Cell[BoxData["_"], "InlineFormula"], " on the left\[Hyphen]hand side, but not on the right\[Hyphen]hand side, of \ your definition. Also note that we have used := instead of just =. 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