Applied Calculus for the Managerial, Life, and Social Sciences

964 Pages·2001·7.293 MB·English

by  Soo T. Tan

L A
IST OF PPLICATIONS
BUSINESSANDECONOMICS DemandforRNs,317 Housingprices,401,497,647
Accumulatedvalueofanincomestream, Demandforwine,413 Housingstarts,89,222,254
564 DepletionofSocialSecurityfunds,353,355
Accumulationyearsofbabyboomers,219 Depreciation,101,411,499 Illegalivorytrade,101
Advertising,100,172,272,309,370,513, Designingacruiseshippool,657 IncomesofAmericanfamilies,405,414
605,640 Determiningtheoptimalsite,635 Incomestreams,590
Agedistributionofcompanydirectors,754 DigitalTVservices,52 Increaseintemporaryworkers,195
Ailingfinancialinstitutions,148,169 DigitalTVshipments,107 Indiangamingindustry,105
Airporttraffic,593 Disposableannualincomes,100 Inflation,244
Alternativeenergysources,514 Documentmanagement,100 Installmentcontractsales,546
Amusementparkattendance,218,564 Drivingcosts,134 Internalrateofreturn,843,847
Annuities,526,532 Drivingrangeofanautomobile,13 Internationalemailusage,100
Assemblytimeofworkers,315,430 Inventorycontrolandplanning,148,363,
Autointerestrates,496 Effectofataxcutonspending,803,805, 364,367
Autooperatingcosts,644 851 Investmentanalysis,399,402,524,525
Autoreplacementpartsmarket,101 Effectofadvertisingonhotelrevenue,317 Investmentgroups,847
AverageageofcarsinU.S.,341 Effectofadvertisingonsales,100,172,195, Investmentoptions,402
309,315,317,434,514 Investmentreturns,402,556
Banking,66,315,453 Effectofhousingstartsonjobs,222 IQs,610
BlackMonday,321 Effectofinflationonsalaries,402 IRAs,526,532
Bookdesign,366 Effectofinventoryandfloorspaceon
Boxofficereceipts,133,207,338 profit,667 Keepingwiththetrafficflow,80
Businesscycles,878,882,894 Effectofluxurytaxonconsumption,221 Keoghaccounts,546
Effectofmortgageratesonhousingstarts,
Cableadrevenue,107 89,272 Landprices,621,686
CableTVsubscription,275,452,499 Effectofpriceincreaseonquantityde- Laserdiscsales,201
Capacityofaman-madelake,542 manded,271 Launchingafighteraircraft,453
Capitalvalue,592,807 EffectofTVadvertisingoncarsales,514 Lifespanoflightbulbs,733,743
CDs,401 Efficiencystudies,194,317,487 Lineardepreciation,73,101
Cityplanning,137,207 Elasticityofdemand,233,235,238,239, Loanamortization,415,607
Coalproduction,498,546 258 Loanconsolidation,402
Cobb-Douglasproductionfunction,615, Energyconservation,503,509 Locatingapowerstation,635
620,658,689 Energyconsumptionandproductivity,148, LocatingaTVrelaystation,633
COLAs,73 401 Lorentzcurves,528,532,547,564
Commissions,149 Energyefficiencyofappliances,412
Commodityprices,49,52,149,413 Establishingatrustfund,591,851 Magazinecirculation,449
Commuterairlines,554 Expecteddemand,437 Mail-orderphonesales,738
Compactdiscsales,556 Expresswaytollbooths,738 Managementdecisions,317,525
Comparisonofbankrates,402 Manufacturingcapacity,79,298,319
Complementarycommodities,617,621,689 Factoryworkerwages,766,837 Manufacturingcapacityoperatingrate,349
Computersecuritycosts,91 Federalbudgetdeficit,81,284 Manufacturingcosts,88
Constructioncosts,108 Femaleself-employedworkforce,351 Marginalaveragecostfunction,227,228,
Constructionjobs,89,209 Financingacollegeeducation,402,532 235,236,237
Consumerdecisions,35 Financingahome,270,272,607 Marginalcostfunction,224,226,235,236,
Consumerdemand,195,206,272,370,437 Forecastingcommodityprices,272 237,487
Consumerpriceindex,195,244,310,402 Forecastingprofits,272,317 Marginalproductivityoflaborandcapital,
Consumers’surplus,521,531,546,563 Forecastingsales,100,461 615,621
Consumptionfunction,73 Franchises,531,556,564 Marginalproductivityofmoney,659
Consumptionofelectricity,483 Fueleconomyofcars,192,278,578 Marginalprofit,231,487
Consumptionofpetroleum,577 Fueltankcapacityofaspaceshuttle,540 Marginalpropensitytoconsume,237
Costoflayingcable,31,35 Marginalpropensitytosave,238
Costofproducingcalculators,320 Gasolineprices,329 Marginalrevenue,230,236,487,545
Costofproducingguitars,452 Gasolineself-servicesales,69 Marketequilibrium,96,103,106,521,546
Costofproducingloudspeakers,345 Gendergap,72 Marketshare,171,450
Costofproducingsolarcellpanels,460 Grossdomesticproduct,172,191,245,265, Markuponacar,13
Costofproducingsurfboards,172 269,313,338,353 Masstransitsubsidies,645
Costofremovingtoxicwaste,206,333,338 Growthofbankdeposits,66 Maximizingcropyield,366,708
Creationofnewjobs,222 GrowthofHMOs,193,556 Maximizingproduction,413,661
Cropyield,170,415 Growthofserviceindustries,579,723,785 Maximizingprofit,345,351,352,631,634,
Cruiseshipbookings,223 635,655,660
Health-carespending,196 Maximizingrevenue,352,353
Demandforagriculturalcommodities,272 Healthclubmembership,181,215 Maximizingsales,661
Demandforcomputersoftware,594 Homemortgages,607,847 Maximumcapacityofanoilwell,413
Demandforelectricity,646 Homesales,193,299 Medianpriceofhomes,647
Demandforperfume,413,569 Home-shoppingindustry,68,153 Meetingprofitgoals,14
Demandforpersonalcomputers,222,434 Hoteloccupancyrate,89,222,897 Minimizingconstructioncosts,365,367,661
Minimizingcontainercosts,661 Salespromotions,412 Educationallevelofseniorcitizens,48,643
Minimizingheatingandcoolingcosts,636 Salestax,73 Effectofbudgetcutsoncrimerate,316
Minimizingproductioncosts,346,352,366 Shoppinghabits,753 Effectofimmigrationonpopulation
Minimizingshippingcosts,35 Sinkingfunds,527,714 growth,714
Morningtrafficrush,299 Sizeofaveragefarm,645 Endowments,591,595,804
Mortgagerates,562 SocialSecuritybeneficiaries,156 Energyconservation,509
Multimediasales,247,319 SocialSecuritycontributions,51 Energyneeds,483,546
Multipliereffect,803,805,851 SocialSecuritywagebase,645
SolvencyoftheSocialSecuritysystem,336, Femalelifeexpectancy,220,464
Net-connectedcomputersinEurope,648 353,355
Netinvestmentflow,498,697 Stockprices,881,889,894 Gendergap,72
Netsales,644 Substitutecommodities,617,621 Globalepidemic,487
Newsmagazineshows,464 Supplyanddemand,102,103,172,196,255, Gradedistributions,767
Nielsentelevisionpolls,152,170 258,268,272 GrowthofHMOs,319
Oilproduction,498,553 Tax-deferredannuities,402 Health-carespending,87,196,648
Oilshortage,329 Taxplanning,402 HMOs,92
Oilspills,222,464,574,595 Televisionpilots,737
Onlinebanking,648 Testingnewproducts,248 Immigration,432
Onlineshopping,196 Timeintervalsbetweenphonecalls,738 Increaseinjuvenileoffenders,415
Onlinespending,107 Timeonthemarket,319,355 Indexofenvironmentalquality,370
Operatingcostsofatruck,265 Trainingpersonnel,714
Optimalcharterflightfare,366 Tread-livesoftires,581 Learningcurves,74,141,148,207,269,295,
Optimalsellingprice,413 Truckleasing,73 430,434,464,714
Optimalspeedofatruck,367 Trustfunds,591 Logisticcurves,431
Optimalsubwayfare,360
VCRownership,564 Malelifeexpectancy,221
Packaging,108,361,365,635,749,763 Marijuanaarrests,107,489
Pensions,401,402 Wages,167 Masstransit,360
Perpetualnetincomestream,591 Waitingtimes,737,740,741,745,738
Perpetuities,589,807 Warranties,767 Narrowinggendergap,51
Personalconsumptionexpenditure,237 Wilsonlotsizeformula,607
Populationdensity,679,685 Workerefficiency,73,100,194,317,338, Oilspills,222,464,574
Portablephoneservices,196,648 370,483 Overcrowdingofprisons,88,300
Presentvalueofanincomestream,531 Worldproductionofcoal,498
Price-earningsratio,668 WorldwidenetworkedPCs,275
Primeinterestrate,148 Worldwideproductionofvehicles,219 PercentageofhouseholdswithVCRs,435
Producers’surplus,521,531,546,564,579 Percentageofpopulationrelocating,413
Productdesign,366 Percentageofwomeninthelaborforce,
Productlife,738,753 Yieldofanappleorchard,108 415
Productreliability,766,767,837 Politics,74
Productioncosts,236 SOCIALSCIENCES Populationgrowth,73,134,195,207,209,
Productionofsteamcoal,555 Ageofdriversincrashfatalities,295 453,489,514,547,713
Productivityfueledbyoil,413 Airpollution,221,295,299,320,352,452, Populationgrowthinthe21stcentury,435
Productivityofacountry,621 579,785 Prisonpopulation,106
ProjectedProvidentfunds,295 Alcohol-relatedtrafficaccidents,556
Arsonforprofit,606 Qualityofenvironment,370
Qualitycontrol,13,452
Burstsofknowledge,141 Recyclingprograms,564
Rateofbankfailures,247,298,355 Researchfunds,591
Rateofreturnoninvestment,556 Civilserviceexams,767
Realestate,402,410,476,497,578,621 Closingthegendergapineducation,72 SATscores,644
Reliabilityofmicroprocessors,738,795 Collegeadmissions,51,644 Scholarshipfunds,589
Reliabilityofrobots,738 Commutertrends,360,545 Spreadofrumor,413,435,714,725
Resalevalue,433,545 Continuingeducationenrollment,221,463, Studentenrollment,463
Restaurantrevenue,878,882,894 785
Retirementplanning,401,402 Costofremovingtoxicwaste,202,333,338 Televisionviewing,464
Reverseannuitymortgage,532 Crime,245,272,291,353 Thurstonelearningmodels,181,222
Cuberule,74 Toxicpollutants,206
Salesforecasts,52,181,545,644 Curbingpopulationgrowth,195 Trafficstudies,194,196,222,299
Salesgrowthanddecay,46,464 TVviewingpatterns,170,221
Salesofdigitalsignalprocessors,196 Declineofunionmembership,80
SalesofdigitalTV’s,101 Diffusionofinformation,435 U.S.Census,248,487
Salesofhandheldcomputers,487 Distributionoffamiliesbysize,737
Salesofprerecordedmusic,72 Distributionofincomes,14,405,528,532 Vacationtrends,785
Salesofvideogames,594 Drivingagerequirements,755 Voterregistration,564
Wastegeneration,647 Harborcleanup,74 CelsiusandFahrenheittemperature,13
Welfarecosts,645 Coastguardpatrolsearchmission,259
Worldpopulationgrowth,415,433,713 Idealheight–weightsforwomen,51
Importanceoftimeintreatingheartat- Designingagrainsilo,367
LIFESCIENCES tacks,208 Drivingcosts,95
Absorptionofdrugs,416 IVsystems,149
AIDSinMassachusetts,501 Effectofanearthquakeonastructure,885
Airinhaledduringrespiration,880,894 Lengthofahospitalstay,770 Effectofstoppingonaveragespeed,194
Allometricgrowth,698,705 Lengthsofinfants,579 Endowments,806
Amountofglucoseinthebloodstream,698, Lifespanofaplant,738,752
704 Findingthepositionofaplanet,883
AnticipatedriseinnumberofAlzheimer’s Nuclearfallout,434 Fisk’slaw,698,704
patients,78,246 Flightofarocket,189,195,256,295,320,
Arterialbloodflow,668 348,351,453
Arteriosclerosis,217,222 Oxygencontentofapond,131,202,338, Flightpathofaplane,153
Averageweightsandheightsofinfants, 352 Forcegeneratedbyacentrifuge,611
169,464,762 Ozonepollution,453
Gridlock,222
Bloodalcohollevel,413 Poiseuille’slaw,73,606
Bloodpressure,390,870 Predator–preypopulation,865,870,877, IQs,610,767
Brentano-StevensLaw,725 881,897
Preservationofspecies,189
Pulserates,222,513 Keepingwiththetrafficflow,80
Carbon-14dating,428,434
Carbonmonoxideintheair,85,193,221,
Lambert’slawofabsorption,697,713
462 Qualityofenvironment,370
Launchingafighteraircraft,453
Cardiacoutput,565,573,581
Lotteries,532
Clark’srule,181 Radioactivedecay,427,433,434,697
Concentrationofadruginanorgan,465 Reactionofafrogtoadrug,100
Magnitudeofanearthquake,390
Concentrationofadrugintheblood- Reactiontoadrug,353
Mortgagepayments,270
stream,133,206,295,338,435,464, Residualeffectofadrug,804,807
Motionofamaglev,111,155,243,451
496,499,555,697
Conservationofspecies,195,244 Seniorcitizen’shealthcare,101
Contractionofthetracheaduringacough, Serumcholesterollevels,765,835 Newton’slawofcooling,434,498,698,713,
346 Speedofachemicalreaction,134 725
Cowling’srule,100 SpreadofHIV,193 NumberofdaylighthoursinChicago,893
Cricketchirpingandtemperature,101 Surfaceareaofahoneycomb,883
Cropyield,170 Surfaceareaofahorse,272 Postalregulations,74,365,366
Probabilityofsnowfall,738,753
Surfaceareaofasingle-celledorganism,73
Doomsdaysituation,133 Surfaceareaofthehumanbody,453,606,
Drugdosages,100,206 624,668 Reactiontimeofamotorist,753
RingsofNeptune,266,271
Effectofbactericide,170,206 Toxicpollutants,133
Effectofenzymesonchemicalreactions, Transmissionofdisease,795 Soundintensity,390
338 Speedboatracing,487
Energyexpendedbyafish,149,353 Stimulusresponse,693
Uncloggingarteries,269
Epidemicmodels,413,431,434,563,710 Stoppingdistanceofaracingcar,195
Eradicationofpolio,412 Strengthofabeam,366
Velocityofblood,194,353
Exponentialdecay,433,704
Extinctionsituation,414 Televisingarocketlaunch,882
Walkingvs.running,103 Terminalvelocity,332
Femalelifeexpectancy,220 Waterpollution,206,315 Trackingacriminalsuspect,882
Flightsofbirds,367 Weightofwhales,51 Traveltime,35
Flowofbloodinanartery,453,499,886 Whalepopulation,189,499 Trialrunofanattacksubmarine,578
Forensicscience,390 Turbo-chargedengineperformance,514
Forestry,169,295 GENERALINTEREST
Formaldehydelevels,207 Accelerationofacar,245,453 Usedcarmarkup,13
Friend’srule,73 AreaofaNormanwindow,108,366
Atmosphericpressure,390 Velocityofacar,172,451,499
GompertzGrowthCurve,445,698,714 Averagehighwayspeedofavehicle,196, Velocityofadragster,555
Growthofacanceroustumor,194,269 295 Volumeofafootball,541
Growthofbacteria,172,217,426,433,713 VTOLaircraft,245
Growthoffruitflypopulation,121,434, Blowingsoapbubbles,259
564,714 BostonMarathon,293 Waterlevelinaharbor,882
Growthrateofaspeciespopulation,697 Boyle’slaw,73 Weber-Fechnerlaw,711
Applied Calculus
for the Managerial, Life, and Social Sciences
FIFTH EDITION
S. T. Tan
Stonehill College
Australia•Canada•Mexico•Singapore•Spain•UnitedKingdom•UnitedStates
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LibraryofCongressCataloging-in-PublicationData Canada
Tan,SooTang.
Appliedcalculusforthemanagerial,life,andsocial
sciences/S.T.Tan.—5thed.
p. cm.
Includesindex.
Rev.ed.of:Collegemathematics.4thed.1999.
ISBN0-534-37843-9
1. Calculus. I. Tan,SooTang.Appliedcalculus.
II. Title.
QA303.T14 2002
515—dc21 2001025725
C
O N T E N T S
Chapter 1 PRELIMINARIES 2
1.1 PrecalculusReviewI 4
1.2 PrecalculusReviewII 14
1.3 TheCartesianCoordinateSystem 28
1.4 StraightLines 37
Chapter1SummaryofPrincipalFormulasandTerms 55
Chapter1ReviewExercises 56
Chapter 2 FUNCTIONS, LIMITS, ANDTHE DERIVATIVE 58
2.1 FunctionsandTheirGraphs 60
UsingTechnology:GraphingaFunction 76
2.2 TheAlgebraofFunctions 81
PORTFOLIO:MichaelMarchlik 86
2.3 FunctionsandMathematicalModels 90
UsingTechnology:FindingthePointsofIntersectionofTwoGraphs
andModeling 104
2.4 Limits 110
UsingTechnology:FindingtheLimitofaFunction 130
2.5 One-SidedLimitsandContinuity 135
UsingTechnology:FindingthePointsofDiscontinuityof
aFunction 150
2.6 TheDerivative 155
UsingTechnology:GraphingaFunctionandItsTangentLines 176
Chapter2SummaryofPrincipalFormulasandTerms 179
Chapter2ReviewExercises 179
Chapter 3 DIFFERENTIATION 182
3.1 BasicRulesofDifferentiation 184
UsingTechnology:FindingtheRateofChangeofaFunction 192
3.2 TheProductandQuotientRules 198
UsingTechnology:TheProductandQuotientRules 208
3.3 TheChainRule 211
UsingTechnology:FindingtheDerivativeofa
CompositeFunction 218
*Sectionsmarkedwithanasteriskarenotprerequisitesforlatermaterial.
iii
iv (cid:4) CONTENTS
3.4 MarginalFunctionsinEconomics 224
3.5 Higher-OrderDerivatives 240
UsingTechnology:FindingtheSecondDerivativeofaFunctionata
GivenPoint 246
*3.6 ImplicitDifferentiationandRelatedRates 249
3.7 Differentials 261
PORTFOLIO:JohnDecker 262
UsingTechnology:FindingtheDifferentialofaFunction 270
Chapter3SummaryofPrincipalFormulasandTerms 273
Chapter3ReviewExercises 274
Chapter 4 APPLICATIONSOFTHEDERIVATIVE 276
4.1 ApplicationsoftheFirstDerivative 278
UsingTechnology:UsingtheFirstDerivativetoAnalyze
aFunction 296
4.2 ApplicationsoftheSecondDerivative 301
UsingTechnology:FindingtheInflectionPointsofaFunction 318
4.3 CurveSketching 321
UsingTechnology:AnalyzingthePropertiesofaFunction 334
4.4 OptimizationI 341
UsingTechnology:FindingtheAbsoluteExtremaofaFunction 354
4.5 OptimizationII 357
Chapter4SummaryofPrincipalTerms 369
Chapter4ReviewExercises 369
Chapter 5 EXPONENTIALANDLOGARITHMICFUNCTIONS 372
5.1 ExponentialFunctions 374
UsingTechnology 380
5.2 LogarithmicFunctions 383
5.3 CompoundInterest 391
PORTFOLIO:MisatoNakazaki 403
5.4 DifferentiationofExponentialFunctions 405
UsingTechnology 414
5.5 DifferentiationofLogarithmicFunctions 417
*5.6 ExponentialFunctionsasMathematicalModels 425
Chapter5SummaryofPrincipalFormulasandTerms 436
Chapter5ReviewExercises 437
Chapter 6 INTEGRATION 438
6.1 AntiderivativesandtheRulesofIntegration 440
6.2 IntegrationbySubstitution 455
6.3 AreaandtheDefiniteIntegral 466
6.4 TheFundamentalTheoremofCalculus 477
UsingTechnology:EvaluatingDefiniteIntegrals 488
CONTENTS (cid:4) v
6.5 EvaluatingDefiniteIntegrals 491
UsingTechnology:EvaluatingDefiniteIntegralsfor
Piecewise-DefinedFunctions 500
6.6 AreaBetweenTwoCurves 503
UsingTechnology:FindingtheAreaBetweenTwoCurves 516
*6.7 ApplicationsoftheDefiniteIntegraltoBusiness
andEconomics 519
UsingTechnology:Consumers’SurplusandProducers’Surplus 533
*6.8 VolumesofSolidsofRevolution 535
Chapter6SummaryofPrincipalFormulasandTerms 543
Chapter6ReviewExercises 544
Chapter 7 ADDITIONALTOPICSININTEGRATION 548
7.1 IntegrationbyParts 550
*7.2 IntegrationUsingTablesofIntegrals 557
*7.3 NumericalIntegration 565
PORTFOLIO:JamesH.Chesebro,M.D. 580
7.4 ImproperIntegrals 582
Chapter7SummaryofPrincipalFormulasandTerms 593
Chapter7ReviewExercises 594
Chapter 8 CALCULUSOFSEVERALVARIABLES 596
8.1 FunctionsofSeveralVariables 598
8.2 PartialDerivatives 608
UsingTechnology:FindingPartialDerivativesataGivenPoint 622
8.3 MaximaandMinimaofFunctionsofSeveralVariables 626
8.4 TheMethodofLeastSquares 637
UsingTechnology:FindinganEquationofaLeast-SquaresLine 646
8.5 ConstrainedMaximaandMinimaandtheMethodof
LagrangeMultipliers 650
*8.6 TotalDifferentials 663
*8.7 DoubleIntegrals 669
*8.8 ApplicationsofDoubleIntegrals 677
Chapter8SummaryofPrincipalTerms 687
Chapter8ReviewExercises 687
Chapter 9 DIFFERENTIALEQUATIONS 690
9.1 DifferentialEquations 692
9.2 SeparationofVariables 699
9.3 ApplicationsofSeparableDifferentialEquations 706
9.4 ApproximateSolutionsofDifferentialEquations 716
Chapter9SummaryofPrincipalTerms 724
Chapter9ReviewExercises 724
vi (cid:4) CONTENTS
Chapter 10 PROBABILITYANDCALCULUS 726
10.1 ProbabilityDistributionsofRandomVariables 728
UsingTechnology:GraphingaHistogram 736
10.2 ExpectedValueandStandardDeviation 739
UsingTechnology:FindingtheMeanandStandardDeviation 754
10.3 NormalDistributions 756
Chapter10SummaryofPrincipalFormulasandTerms 769
Chapter10ReviewExercises 770
Chapter 11 TAYLORPOLYNOMIALSANDINFINITESERIES 772
11.1 TaylorPolynomials 774
11.2 InfiniteSequences 787
11.3 InfiniteSeries 796
11.4 SerieswithPositiveTerms 808
11.5 PowerSeriesandTaylorSeries 819
11.6 MoreonTaylorSeries 829
*11.7 TheNewton–RaphsonMethod 839
Chapter11SummaryofPrincipalFormulasandTerms 849
Chapter11ReviewExercises 850
Chapter 12 TRIGONOMETRICFUNCTIONS 852
12.1 MeasurementofAngles 854
12.2 TheTrigonometricFunctions 860
12.3 DifferentiationofTrigonometricFunctions 871
UsingTechnology:AnalyzingTrigonometricFunctions 884
12.4 IntegrationofTrigonometricFunctions 887
UsingTechnology:EvaluatingIntegralsof
TrigonometricFunctions 892
Chapter12SummaryofPrincipalFormulasandTerms 896
Chapter12ReviewExercises 897
TABLE 899
TheStandardNormalDistribution 900
ANSWERSTOODD-NUMBEREDEXERCISES 903
INDEX 945
P
R E F A C E
Applied Calculus for the Managerial, Life, and Social Sciences, Fifth Edition,
is suitable for use in a two-semester or three-quarter introductory calculus
course for students in the managerial, life, and social sciences. As with the
previouseditions,ourobjectiveinApplied CalculusfortheManagerial,Life,
and Social Sciences is twofold: (1) to write a textbook that is readable by
students and (2) to make the book a useful teaching tool for instructors. We
hope thatwith thepresent edition wehave come onestep closerto realizing
ourgoal.Thefiftheditionofthistextincorporatesmanysuggestionsbyusers
of the earlier editions.
FEATURES
Thefollowinglistincludessomeofthemanyimportantfeaturesofthebook:
(cid:1) Coverage of Topics The book contains more than enough material for
the usual applied calculus course. Optional sections have been marked with
an asterisk in the table of contents, thereby allowing the instructor to be
flexible in choosing the topics most suitable for his or her course.
(cid:1) Approach Theproblem-solvingapproachisstressedthroughoutthebook.
Numerousexamplesandsolvedproblemsareusedtoamplifyeachnewcon-
cept or result in order to facilitate students’ comprehension of the material.
Figures are used extensively to help students visualize concepts and ideas.
(cid:1) Level of Presentation Our approach is intuitive, and we state the results
informally.However,wehavetakenspecialcaretoensurethatthisapproach
doesnotcompromisethemathematicalcontentandaccuracy.Proofsofcertain
results are given, but they may be omitted if desired.
(cid:1) Applications Thetextisapplicationoriented.Manyinteresting,relevant,
andup-to-dateapplicationsaredrawnfromthefieldsofbusiness,economics,
socialandbehavioralsciences,lifesciences,physicalsciences,andotherfields
ofgeneralinterest.Someoftheseapplicationshavetheirsourceinnewspapers,
weeklyperiodicals,andothermagazines.Applicationsarefoundintheillustra-
tive examples in the main body of the text as well as in the exercise sets. In
fact,onegoalofthetextistoincludeatleastonereal-lifeapplicationineach
section (whenever feasible).
(cid:1) Sources We have included sources for those applications that are based
on real-life data.
(cid:1) Exercises Each section of the text is accompanied by an extensive set of
exercises containing an ample set of problems of a routine, computational
nature that will help students master new techniques. The routine problems
are followed by an extensive set of application-oriented problems that test
students’ mastery of the topics.
vii