Applied finite mathematics

567 Pages·1978·20.421 MB·English

by  Howard Anton, Bernard Kolman

APPLIED
FITNEI
MATHEMATICS
SECOND
EDITION
HOWARD ANTON
BERNARDK OLMAN
UNIVERSITY
DREXEL
ACADEMIC
PRESS
NEWYCRK
SANF RANCISCO
LON[X)N
A SubsidioafHr ayr courtB rocJeo vanoviPucbhl,i shers
Cover Permission
art, by Kenneth:\T oland.
Whirl
by DesM oinAerstC se ntCeorff,i n
granted The Fine
ArtTrsu stu nd, 1974.
F
COPYRIGH'r@ 197149,7 B8Y ,A CADEMIC PRESS, INC.
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PRINTED IN 'fHE UNI1'EDS TATES OF AMERICA
To ourm others
NEWF EATURES
INT HE
SECOND
EDITION
• A news elf-cocnhtaapiotnneet rdh mea themaotffii ncasn ce
Stochapsrotciecas rsieen st roduced
•
Tredei agraarmesu semdo ree xtensaisva e tloyo iln p robabilit.y
•
problems
• Additieoxnearlc ises
• BASIrCe plFaOcReTsR ANt hiceno mpucthearp ter
x
PRFEACE
Thibso opkr esetnhtfesu ndameonftfi anlimsta et hemaitni scats y le
tailfoorbree dg innbeutar tst ,h sea mtei mceo vetrhse subjeicnt matter
sufficideenptst hot hatths et udceansnte aer icvha rioefrt eya liansdt ic
relevaapnptl icaStiinmocanens sy.t udeinntt hsic so urhsaeva em inimal
mathemabtaiccksg rowuenh da,vd ee votceodn sideerffaobrtltote h e
pedagoagsipceaoclftt hsib so ok-exampillelsu satnardba otuiWnoedn .s
havaev oicdoemdp limcaattheedm antoitcaatalin odhn a vpea instakingly
workteodk eetpe chndiicffiaclu lftriohemis d iontgh erswiimspeil dee as.
Wheraep propreiaacethxe e,r csieste bwegiitbnhas s ciocm putational
"driplrlo"b lemtsh eapnnr do gretsops reosb lweimtsmh o rseu bstance.
Thew ritingi lsltuyslteerx,aa tmipvelexe esr,c ainsdae psp,l ications have
beedne sigwnietdoh n eg oailnm indT:op roduac tee xtbtohoaktt h e
studweinlfitln dr eadaabnldve a luable.
Sintchee irsem ucmho rfien imtaet hemamtaitcesra ivaali ltahbalne
cabne i ncluidne sdai ngle resaisztoeendxa itbtw,l a ysn ecesfsoaurrs y
tob es elecitnti hvceeh oiocfme a terWieah la.v ter iteods eltehcots e
topitchsaw teb eliaervmeeo slti ketlopy r ovues eftuotl h mea joroift y
readeGrusi.d beydt hipsr incwiepc lheo,s teoo mitth et raditional
symbolloigmcia ct erial oifan c hfaapovtnoec rro mputaenrdcs o mputer
programmCionmgp.u tpreorg ramrmeiqnugi rseasm keti hneod fl ogical
precissiyomnb oallsoi gcbi uct, miosrl ei kelpyr ovuese fumlo st
to to
studeTnhtecs o.m pucthearp itsoe prt ional naonrtde qduaoicercseet sos
anyc ompuftaecri lHiotwieevste.hr i,cs h apitseer x tenesniovuetg hha t
thset udweinbltel a blteor upnr ogroanam c so mpuitdfee rs,i red.
Ink eepwiintgth h tei tAlpep,l iFeidn iMtaet hematwiehc asv,ie n cluded
a hosotfa plpicatTihoenrysa .n ge from" aaprptliificcwaihtaiiloc nhs "
ardee sigtnope odi onutst i tuaitniw ohnisc hm attheer ialb eum siegdh,t
altlh wea yt ob onfiad er elevaapnpitlc atbiaosnoesdn " livdea"ta an d
acturaels eapracphe Wres h.a vter iteodi nclau bdael anced sampling
frobmu sinfiensasn,bc ieo,l boeghya,v isocriaelna cnesdso ,cs icaile nces.
xi
1
SetT heory
�
2
Coordinate
Systemasn dG raphs
'
3
LineaPrr ogramming 6.1-6.5
...--- Probabilitr-y --
(Geometric)
' r
4 6.6 7
Matricaensd BayesF'o rmulaan d
Statistics
LineaSry stems StochasPtriocc esses
5
LineaPrr ogramming
(Algebraic)
1
9
Mathematics 8
Applications 10
of Computers
(Setea blbee low.)
Finance
Prerequisites
2 3 4 6.516 .6
-6.5
2 •
r--
3 • •
r-
4 • •
5 • • • •
Topitco 6.1-6.•5
bec overed • •
6.6
7
•i · • •
...-
8.1• I •
• •
8.2
8.3• •t
8.4-8.•5 • • • •
+. -,__ - t
8.6• • • •
I �,-
9
10 l -
PREFACE
/x iii
Theries e nougmha terii:nt1 hli bso oks ot haeta chin strucctaonsr e lect
thet opitchs atbe sfitt t hen eedosf t hec lasTso. h elip nt hisse lection,
wc havei ncludae ddi scussoifot nh es tructoufrt eh eb ooka nda flow
charstu ggestpionsgs ibolrega nizatoifto hnesm aterial.p rTehree quisites
fore actho piacr es howinn t het ablbee lotwh efl owc hart.
Chaptdeirs custsheees l ementsaertty h eornye edeidn l atecrh apters.
l
Chaptegirv easn introducttoic oanr tescioaonr dinsaytset emasn d
2
graphEsq.u atioonfss traiglhitn easr cd iscussed and apaprlci cations
givetno p robleimnss implien terelsitn,ed aerp reciaatnidop nr,e diction.
We alscoo nsidtehrel easstq uarmeest hofdo rfi ttinag s traiglhitnt eo
empiridcaalt a, waen dd iscumsast erioanll ineianre qualitthiaewtsi ll
ben eeded lfionre parro gramming.
Portioonfst hicsh aptmeary bef amilitaors omes tudenitnsw ,h ich
casteh ei nstrucctaonrr e vietwh imsa teriqauli ckly.
Chaptiesdr e votetdoa ne lementianrtyr oducttoil oinn eparro gram­
3
mingf roma geometrpioci notf v iewA. moree xtensidvies cussoifo n
lineparro grammiinngc,l udtihnegs implmeext hoda,p peairnsC hapte5r.
SincCeh apte5r i st echnicmaolrleyd ifficulsto,m ei nstrucmtaoyrc sh oose
tol imitth eitrr eatmeonftl ineaprr ogrammienngt iretloCy h apte3r,
omittiCnhga pte5r.
Chaptdeirs cusbsaessi mca terioanl m atrictehse,s olutioofln i near
4
systemasn,d a pplicatiMoannsy. o ft hei deahse rea reu sedi nl ater
sections.
Chaptgeirv easn e lementparreys entaotfit ohnes implmeext hofdo r
5
solvilnign eaprr ogrammipnrgo blemAsl.t hougohu rt reatmeinsta s
elementaarsy possitbhleme a,t eriiasli ntrinsically stoet chhanti cal,
somei nstrucmtaoyrc sh oosteoo mitt hicsh aptFeorr.t hirse asowne h ave
labeltehdic sh aptweirt ah stairn t het abloefc ontents.
Chaptienrt rodupcreosb abifloirtfi yn itsea mplsep aceTsh.i sm aterial
6
buildosn t hes et-thefooruyn datoifoC nh apte1r.W e carefuelxlpyl ain
then aturoef a probabilmiotdye sl ot hatt hes tudeunntd erstands the
relationbsehtiwpe etnh em odealn dt hec orresponrdeianlg- woprrlodb lem.
Secti6on. o6n B ayesF'o rmulaan ds tochasptriocc esisses so mewhat
mored ifficutlhta nt her esotf t hec haptaenrd i ss tarrIends.t rucwthoor s
omitt his section sohmoiutSl edc tailosnow hicahp plitehsem aterial
8.1
top robleimnsm edicdaila gnosis.
Chaptdeirs cusbsaessi cco ncepitnss tatisSteiccst.i7 o7.n introduces
7
hypothetseisst ibnyg m eanso ft hec hi-squtaersett h,e reebxyp ositnhge
studetnots omer ealissttiact istical apSpelcitcia7ot.ni4 oo nn Csh.e by­
shev'isn equaliisti yn cludbeedc ausieth elpgsi vteh es tudean tb etter
feeflo r tnhoet ioonfsm eana ndv arianWcee .m arkedi ta sa starred
PREFACE
/ xiv
sectsiionnic tce a nb eo mitftreodtm h ceh apwtietrh looustos fc on­
tinuitiyn.s trwuhcotsosert udewnitltsla kae s eparsattaet istics
An
coumrasyec hootos oem itth cihsa petnetri rely.
Chaptiesir n tentdoge idvt ehs et udseonmtse o lrieda,l aipsptliicc a­
8
tioonfts h mea terTihaetl o.p iinct hsic sh apatrederr awfnr oamv ariety
offi elsdost hatth ien strcuacsnte olrte hcotss eec ttihoabntes s fittt he
neeadnsid n teroefts hctels a ss.
Chaptecro vearsn umboefrt opiicnts h mea themaotffii ncasn ce,
9
Thec hapitsse ercl ofn taainndie ndc laundo epst iroenvailse ewc toino n
exponaenndlt osg arithms.
Chap1t0ei rn trotdhusect eusdt eocn otm puteprrso garnadmW mhiinlge.
theirsne o n eetdoh avaec cetsoas n yc ompuftaecri ltihtmeia etse,r ial
isp resenstueffidc iidenen ttta hialtt h set udweinlbtle a blteor upnr o­
gramso na c ompuIttei rsn. ot th peu rpoofst eh icsh apttome ark teh e
studienntatoc ompuetxepre rratt;hw eear r ceo ncernedp rowviitdh ing
ani ntelulnidgeernstt oafwn hdaiatnc go mpuitsae nrhd o wi wto rkWse.
touch on binaarnydt heapnrr iotchtemoese dot miBecA S ICp rogram­
minagn dfl owc hartWienh ga.vs et artrheicdsh apstienrwc eer egairtd
aso ptional.
ACKNOWLEDGMENTS
We gratefualclkyn owletdhgeec ontributoifto hnesf ollowpienogp le
whosec ommentcsr,i ticiasnmdas s sistagrnecaet liym provetdh ee ntire
manuscript.
RoberEt. B eck-Villanova DaniePl. M aki- Ind iana
University University
ElizabeBtehr man-oRckhurst SamuelL . Marateck-eNw York
College University
AlanI .B rooksS-peryr UNIVAC J.A .M oreon-SanD iegCoi ty
JerrFye rr- yChripshetroN ewportC ollege
College DonaldE . Myer-sUniverosfi ty
Arizona
MaryW . Gray-Amercain
University JohnQ uigg-DrxeelU niversity
ElleRne ed-Univeorfs ity
BerylM . GreenO-regoCno llege
MassachuastAe mthtse rst
ofE ducation
JamesS now-LaneC ommunity
AlberJt.H err-DrxeelU niversiCtoyl lege
RoberLt. H iggins-QUANTICS LeonS teinberg-UTneimvpelres ity
LeoW . Lampoe-nSpringG ardeWni lliaHm. W heeler-Indiana
College StatUen iversity
We alstoh anko urt ypists: RS.uG scarns hunJiu,d yA .K ummerer,
Amelia MaurainzdiK oa,t hleRe.nM cCabef ort heisrk illwfourlk a nd
infinite patience.
We thankI:B M, SperrUyN IVAC,a ndT eletypCeo rporatfioorn
providiilnlgu straftoirto hnecs o mputmeart erial.
Finallwye, thank entthiesr tea ffo fA cademiPcr esfso rt heisru pport,
encouragemaenndit m aginatciovnet ributions.
xv
SETTH EORY
A herodfb uffaalb ou,n cohfb anantahsce,o lleocfat ilpolon s iteivveen
integaenrdts h,se e otfa lslt oclkiss otnet dh Nee wY orSkt oEcxkc hange
havseo methinic nogm motnh;ea yr e exampolfoes b jetchtahsta vbee en
all
groutpoegde tahnedr viaesaws eidn egnltei Tthyi.s oifgrd oeuap ionbgj ects
togetgihveesrr isteot hmea themantoitciaoolfan s etw,h icwhe s hall
stuidynt hicsh aptWeers .h aulslte h imsa teriinla alt cehra ptteohr esl p
solavv ea rioefit myp ortparnotb lems.
1.1I NTRODUCTTIOOS NE TS
A seits ac olleocfto ibojne ctthoesb ;j eacrtcesa lltehedel ements
orm emberosft hsee t.
Onew ayo fd escriab sieintsgt ol itshtee l emeonftht es s ebte tween
bracTesh.u st,h see otf positiinvtee gtehraastr lees sthan 4 be
all can
written
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thsee otfa lplo siitnitveecg aebnr esw ritten
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andt hsee otf UnitSetda tPerse sidwehnotslsea nsatm ebse gwiint thh e
all
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