Create2Dand3DPlots 53
 Example e Plotx2y3
1.Click
or,fromtheInsertmenu,chooseMathtostartmathematics.
2.Typex,click
,type2,andpressthespacebar;thentypey,click
,and
type3.
3.Click
or,fromtheComputemenu,choosePlot3DandthenchooseRec-
tangular.Thecomputationalengineplotstheexpressionx
2
y
3
:
4.Ifyouwantthisplottoappearmoreclearlyinprint,youcanchangeitsproperties:
a.SelecttheplotandclicktheGraphicPropertiesicon
inthelowerrightcorner
oftheplot.
b.ChoosetheItemsPlottedtab.
c.IntheDirectionalShadingarea,chooseFlat.
d.IntheBaseColorarea,chooseBlack.
e.IntheSurfaceStylearea,chooseWireFrame.
f.SelecttheAxestab.
g.IntheAxesTypearea,chooseNone.
h.SelecttheViewtab.
i.IntheOrientationarea,setTurnto34.
j.ChooseOK.
Here'stheresult:
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54
Chapter3 ComputingandPlotting
 Example e Plot[xsinxcosy;xcosxcosy;xsiny]
1.Click
.
2.Typexsinxcosy,xcosxcosy,xsiny.
3.Click
or,fromtheComputemenu,choosePlot3DandthenchooseRec-
tangular. Thecomputationalengineproducesaplotwhosecomponentsyoucan
change:
4.Changetheplotproperties:
a.SelecttheplotandclicktheGraphicPropertiesicon
inthelowerrightcorner
oftheplot.
b.ChoosetheItemsPlottedtab.
c.IntheDirectionalShadingarea,chooseFlat.
d.IntheBaseColorarea,chooseBlack.
e.IntheSurfaceStylearea,selectWireFrame.
f.ChooseVariablesandIntervals.
g.InthePlotIntervalsarea,settheintervalvaluesforxto0to6.28.
h.Settheintervalvaluesforyto0to3.14andchooseOK.
i.SelecttheAxestab.
j.IntheAxesTypearea,chooseNoneandchooseOK.
Thecomputationalenginereplotstheexpression[xsinxcosy;xcosxcosy;xsiny]:
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ComputeinPlace 55
Plottheseexpressions
UsePlot2D,Rectangulartoplotxsin
1
x
UsePlot2D,Parametrictoplot(sin2t;cos3t)
UsePlot2D,Implicittoplot(x 2)
2
+(y 3)
2
=25,where 3x7
and 2y8;edittheplottochooseEqualScalingfromtheAxestab
UsePlot3D,Cylindricaltoplot1 z,where02and0z1
UsePlot3D,Sphericaltoplot2,where02and0z2
ComputeinPlace
Youcanusemanycomputationalcommandstocomputeinplace,replacingpartofan
expressionwiththeresultofanoperation. Youcanusethistechniquetodemonstrate
thestepsinvolvedinthesolutiontoaproblem.
 Example e Simplify
x
2
5x+6
x2 2x 3
andshowthestepsinthesolution
1.Click
,typex,click
,type2,pressthespacebar,andtype-5x+6.
2.Press
TAB
,typex,click
,type2,pressthespacebar,andtype-2x-3.
3.Positiontheinsertionpointaftertheoriginalexpressionandtype=.
4.Selecttheoriginalexpression.
5.Holddownthe
CTRL
keywhileyoudragacopyoftheexpressiontotherightofthe
rstequalssign.
6.Selectthenumeratorinthecopiedexpression,thenholddownthe
CTRL
keywhile
youchooseFactorfromtheComputemenu.
7.Selectthedenominatorinthecopiedexpression,thenholddownthe
CTRL
keywhile
youchooseFactorfromtheComputemenu.
8.Click
.Thecomputationalenginereturnsthisresult.Now,youseeallthesteps
inthesolution:
x
2
5x+6
x2 2x 3
=
(x 2)(x 3)
(x+1)(x 3)
=
1
x+1
(x 2)
Computeinplacetoshowthestepsinthesolutionsofthisproblem
Simplify
x
2
4x 21
x3+3x2 x 3
to
1
(x 1)(x+1)
(x 7),showingthestepsintheprocess
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56
Chapter3 ComputingandPlotting
PerformMatrixOperations
Youcanperformafullrangeofmatrixoperationsincludingaddition, multiplication,
andinversion.
 Example e Transposethematrix
2
4
1 4
2 5
3 6
3
5
1.Click
andspecifyamatrixof3rowsand2columns.
2.IntheBuilt-inDelimitersarea,specifyBrackets[m]andchooseOK.
3.Fillthematrix:
a.Type1,press
TAB
,type4,andpress
TAB
.
b.Type2,press
TAB
,type5,andpress
TAB
.
c.Type3,press
TAB
,type6.
4.FromtheComputemenu,chooseMatricesandthenchooseTranspose.Thecom-
putationalenginetransposesthematrix:
2
4
1 4
2 5
3 6
3
5
,transpose:
1 2 3
4 5 6
 Example e Invertthematrix
1
2
 3
1.Click
andspecifyamatrixof2rowsand2columns.
2.IntheBuilt-inDelimitersarea,specifyBrackets[m]andchooseOK.
3.Fillthematrix:type1,press
TAB
,type2,press
TAB
,type7,press
TAB
,andtype-3.
4.FromtheComputemenu,chooseMatricesandthenchooseInverse.Thecompu-
tationalengineinvertsthematrix:
1
2
 3
,inverse:
2
4
3
17
2
17
7
17
1
17
3
5
Performthesematrixoperations
Adjugate
97 50
56 49
Concatenate
a 5
6 b

9 c
d 4
Findthedeterminantof
a b
c d
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SolveDifferentialEquations 57
SolveDifferentialEquations
Manydifferentialequationshaveanswersintermsoffamiliarfunctions. Youcanuse
theSolveODEcommandtondthosefunctions. Ifyouspecifyinitialconditionsfor
anequation,youcansolvetheequationnumerically.
 Example e Compute
dy
dx
=x
1.Click
.
2.Typedy,press
TAB
,typedx,andpressthespacebar.
3.Type=x.
4.FromtheComputemenu,chooseSolveODE,andthenchooseExact.Thecom-
putationalenginegivesthisresult:
dy
dx
=x,Exactsolutionis:
1
2
x
2
+C
2
 
 Example e Findthesolutionoftheinitialvalueproblem
y
0
=y
y(0)=1
1.Click
andspecifyamatrixof2rowsand1column.
2.IntheBuilt-inDelimitersarea,specifyBrackets[m]andthenchooseOK.
3.Typey'=yandpress
TAB
.
4.Typey,click
,type0,andpressthespacebar.
5.Type=1andpressthespacebar.
6.FromtheComputemenu,chooseSolveODE,andthenchooseExact.
7.Typexastheindependentvariableyouwantthecomputationalenginetouseand
chooseOK.Thecomputationalenginereturnsthisresult:
y
0
=y
y(0)=1
,Exactsolutionis:fe
x
g
Computethesedifferentialequations
dx
dy
=2xy
y
00
=y
y
00
+y=0
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58
Chapter3 ComputingandPlotting
ComputeStatistics
Basicandadvancedstatisticalcomputationsareavailable.
 Example e Findthemodesof1;1;3;4;4;4;5;3;8;1;9;5;2
1.Click
or,fromtheInsertmenu,chooseMathtostartmathematics.
2.Typethenumbers1,1,3,4,4,4,5,3,8,1,9,5,2.Includethecommas.
3.FromtheComputemenu,chooseStatistics,andthenchooseMode. Thecompu-
tationalenginereturnsthisanswer(themodesarethenumbersinbracketsandthe
nalnumberindicatesthenumberoftimesthateachmodeappearsintheset):
Mode(s):[1;4];3
 Example e Findthemediansofthecolumnsofthematrix
2
4
1:5 6:7
3:9 2:2
5:5 4:3
3
5
1.Click
,andspecifyamatrixof3rowsand2columns.
2.IntheBuilt-inDelimitersarea,specifyBrackets[m]andthenchooseOK.
3.Fillthematrixwiththevalues1.5,6.7,3.9,2.2,5.5,and4.3,pressing
TAB
tomove
fromcelltocell.
4.FromtheComputemenu,chooseStatistics,andthenchooseMedian. Thecom-
putationalenginereturnsthesemedians:
Median(s):[3:9;4:3]
 Example e Findthestandarddeviationof2:5;6:8;3:5;1:9;2:3;4:5
1.Click
or,fromtheInsertmenu,chooseMathtostartmathematics.
2.Enterthenumbers2.5,6.8,3.5,1.9,2.3,and4.5,separatedbycommas.
3.FromtheComputemenu,chooseStatistics,andthenchooseStandardDeviation.
Thecomputationalenginereturnsthisanswer:
Standarddeviation(s):1:8357
Computethesestatistics
Findthemeanofthesevalues:
1;2;3;4
1:5 6:7
3:9 2:2
Findthevarianceof2:5;6:8;3:5;1:9;2:3;4:5
Usingmultipleregression,tacurvetothesepoints(dependent
variableincolumn2):
2
6
6
4
x y
1 2
2 4
3 7
3
7
7
5
ComputewithUnitsofMeasure 59
ComputewithUnitsofMeasure
Youcanconvertvaluesfromoneunitofphysicalmeasuretoanotherandperformcom-
putationsonequationscontainingunits.
 Example e Convert28:6pound-forcetonewtons
1.Click
or,fromtheInsertmenu,chooseMathtostartmathematics.
2.Type28.6andthenclick
or,fromtheInsertmenu,chooseUnitName.
3.InthePhysicalQuantitybox,selectForce.
4.IntheUnitNamearea,selectPound-force,andthenchooseInsert.Theprogram
insertstheunitofmeasureandleavestheUnitNamedialogboxopen.
5.Type=x.
6.IntheUnitNamearea,selectNewton,chooseInsert,andclosethedialogbox.
7.Click
or,fromtheComputemenu,chooseSolve,andthenchooseExact.
Thecomputationalengineyieldsthisresult:
28:6lbf=xN,Solutionis:f127:22g
 Example e Express20:0miles/hourinkilometers/minute
1.Click
or,fromtheInsertmenu,chooseMathtostartmathematics.
2.Type20.0andthenclick
or,fromtheInsertmenu,chooseUnitName.
3.InthePhysicalQuantitybox,selectLength.
4.IntheUnitNamearea,selectMileandchooseInsert.
5.Type/.
6.InthePhysicalQuantityarea,selectTime.
7.IntheUnitNamearea,selectHour,andchooseInsert.
8.Type=x.
9.InthePhysicalQuantityarea,selectLength.
10.IntheUnitNamearea,selectKilometer,andchooseInsert.
11.Type/.
12.InthePhysicalQuantityarea,selectTime.
60
Chapter3 ComputingandPlotting
13.IntheUnitNamearea,selectMinute,andchooseInsertandclosethedialogbox.
14.Click
or,fromtheComputemenu, chooseSolveandthenchooseExact.
Thisistheresult:
20:0mi=h=xkm=min,Solutionis:0:53645
Computetheseconversions
Express53:7lbf=in
2
innewtonspersquaremeter
Compute3A6Vandthenconverttheanswertowatts
Convert3:7N=cm
2
topoundspersquareinch
CreateExamsandQuizzes
InSWPandSNB,youcancreatealgorithmically-generatedcoursematerialssuchas
exams,quizzes,tests,tutorials,problemsets,drills,andhomeworkassignments.Instead
ofwritingaseriesofexams,eachcontainingavariationofyourquestionsandanswers,
youcanusetheExamBuildertowriteasingleexamandstatethequestionsandanswers
withalgorithms. Studentscandrillandpracticeaskillatlengthbyopeningthesame
ExamBuilderlerepeatedly,obtainingadifferentsetofquestionseachtime.Similarly,
youcantesteachstudentwithadifferentversionofanexam,witheachversiondrawn
fromthesameExamBuildersourcele.
TheExamBuilderisappropriateforanylevelofmathematicsinstruction—elemen-
taryarithmetic, algebra,trigonometry,calculus,linearalgebra, differentialequations,
probability,orstatistics.CoursematerialscreatedwiththeExamBuildercanbeworked
andgradedonlineorinthetraditionalpencil-and-paperform. TheonlineHelpsystem
containsdetailedinstructionsforusingtheExamBuilder.
YoucanndmanysamplequizzesintheQuizzesdirectoryofyourprogramin-
stallation.Theseinstructionsexplainhowtoopenandtakeoneofthesampleexams.
IToopenaquiz
1.OpenSWPorSNBandfromtheFilemenu,chooseOpen.
2.SpecifytheQuizzesdirectoryofyourprograminstallation.
3.IntheFilesoftypebox,chooseQuiz(*.qiz).
4.SelectoneofthelesinthedirectoryandchooseOKtoopenthesampleexam.
5.Enteryournameontheexamandanswereachquestion.
6.ChooseClicktograde. Theprogramgradestheexamandopensalecontaining
theresults.
7.Openthesame.qizleagainandnotethattheprogramhasautomaticallygenerated
adifferentsetofquestions.
4
TypesettingYourDocument
WithMacKichanSoftwareproducts, youcancreatebeautifuldocumentsforuseon-
lineorinprint. IfyouhaveSWP P orSW, , youcantypeset t yourdocuments with
L
A
T
E
X,whichcreatesnelyformatteddocuments withautomaticallygeneratedtables
ofcontents,cross-references,citations,andotherdocumentelements.WithVersion5of
SWPandSW,youcanalsocreatetypesetPortableDocumentFormat(PDF)leswith
PDF
T
E
X,whichprocessesdocumentsthrough
PDF
L
A
T
E
Xtoprovideallthebeautyand
featuresofL
A
T
E
XtypesettinginPDFform. IfyouhaveSNBoryou'reusingSWP or
SWtoproducedocumentsthatdon'trequiretypesetting,youcanprintattractivedocu-
mentswithoutLAT
E
X.
SWPandSW aresuppliedwithTrueT
E
X,whichincludesaT
E
Xformatter,aT
E
X
screenpreviewer,andscalableTrueTypefonts. TheversionofTrueT
E
Xshippedwith
SWPandSWalsoincludes
PDF
T
E
Xsupport.Noothersoftwareisrequiredtogenerate
PDFles,butyoumusthaveaPDFviewertobeabletopreviewandprintPDFles.
Moreinformationaboutusingotherpreviewersandprintdriversisavailableintheonline
HelpandinCreatingDocumentswithScienticWorkPlaceandScienticWord.
WerefertotheprocessesthatinvolveL
A
T
E
Xtypesettingastypesetcompile,type-
setpreview,andtypesetprint,andtothosethatinvolve
PDF
T
E
Xtypesettingastypeset
compilePDF,typesetpreviewPDF,andtypesetprintPDF.(Theprocessesaresimilar;
generalstatementsabouttypesettingrefertobothsetsofprocesses.)Werefertothe
processesthatdon'tinvolveanytypesettingassimplypreviewandprint.
YoutypesetyourdocumentusingcommandsontheTypesetmenuorthebuttonson
theTypesettoolbar(availableinSWP andSWonly):
Menu
Command
Button
Typeset Compile
Typeset Preview
Typeset Print
Menu
Command
Button
Typeset CompilePDF
Typeset PreviewPDF
Typeset PrintPDF
YouproduceyourdocumentwithouttypesettingusingthecommandsontheFilemenu
orbuttonsontheStandardtoolbar:
Menu Command Button
File
Preview
File
Print
EachtimeyouprevieworprintyourSWPorSW document,youcanchoosewhether
ornottotypesetit.Theresultsdiffernoticeably.
62
Chapter4 TypesettingYourDocument
UnderstandingtheTypesettingProcess
Whenyoutypeset,theprogramcompilesyourdocumentwithLAT
E
Xor
PDF
LAT
E
X. The
compilationappliesspecialL
A
T
E
Xformattingfeaturestoresolvetypographicdetailssuch
ashyphenation,ligatures,linespacing,andlineandpagebreaking. Theprocessalso
creates automaticnumbering, cross-references, citations, andfootnotes. . Itgenerates
anydocumentelementsspeciedinthedocumentshell, suchasatableofcontents,
bibliography,orindex. Dependingonthecomplexityofyourdocument,theprogram
mayprocessitthroughL
A
T
E
Xor
PDF
L
A
T
E
Xmorethanonce. Duringthecompilation,
SWPandSWremainopen,buttheyaresuspended.
Theresultsofthecompilationdifferdependingonwhetheryoutypesetyourdocu-
mentwithLAT
E
Xor
PDF
LAT
E
X.Ineithercase,youroriginaldocumentisunchanged.
 IfyoutypesetwithL
A
T
E
X(usingthePrevieworPrintcommandsontheTypeset
menu),thecompilationyieldsadeviceindependent,orDVI,lethatcontainsyour
typesetdocumentinaformindependentofanyoutputdevice.Thecompilationmay
alsoresultinothergeneratedles,suchastableofcontentslesorbibliography
les,thatarerequiredbytheDVIle.
 Ifyoutypesetwith
PDF
L
A
T
E
X(usingthePreviewPDF orPrintPDFcommands
ontheTypesetmenu),thecompilationyieldsaPDFlethatcontainsyourtypeset
documentembeddedwithallnecessaryfontsandgraphics. Ifyouhaveaddedthe
hyperrefpackagetoyourdocument,thecompilationcreateshypertextlinksinplace
ofcross-referencesandlinksthetableofcontentstotherestofthedocumentwith
hypertextlinks.
IfyoutypesetwiththeCompileorCompilePDFcommand,theprogramcompiles
thedocumentandcreatestheDVIorPDFlebutdoesn'tprevieworprintit.Otherwise,
followingthecompilation, theprogrampreviewsorprintsthele,accordingtoyour
choice. Becauseofthetypesettingspecicationsandthefeaturesandelementsadded
duringcompilation,theappearanceofyourdocumentmaybequitedifferentfromits
appearanceinthedocumentwindow.
Whenyoudon'ttypesetyourdocument,theprogramusesmanyofthesamerou-
tinestopreviewandprintasitdoestodisplaythedocumentonthescreen.Theprogram
doesn'tusespecialformattingfeatures,nordoesitautomaticallygenerateanydocu-
mentelements.Therefore,theappearanceofthepreviewedorprinteddocumentisquite
similartoitsappearanceinthedocumentwindow.
Thesegeneralguidelinesmayhelpyoudecidewhichdocumentproductionmethod
touse:
 Whenanelytypesetdocumentappearanceisahighpriority,typesetpreviewor
typesetprintthedocumentwiththecommandsontheTypesetmenu.
 WhenyouneedanelytypesetPDFdocumentforviewingonmultipleplatforms,
typesetthedocumentwiththePDFcommandsontheTypesetmenu.
 Whenanelytypesetdocumentappearanceandautomaticallygenerateddocument
elementsaren'tapriorityoryouneedoutputquickly,previeworprintthedocument
withthecommandsontheFilemenu.
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