Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications PDF
Preview Computing for Scientists and Engineers: A Workbook of Analysis, Numerics, and Applications
COMPUTING FOR STSITNEICS DNA ENGINEERS COMPUTING FOR STSITNEICSDNA SREENIGNE A Workbook of Analysis, Numerics, and Applications MAILLIW .J NOSPMOHT University of North Carolina Chapel Hill, North Carolina enconietiacc siArlebtunPI-yeliW NHOJ YELIW & ,SNOS.CNI New York / Chichester / Brisbane / Toronto / Singapore .re peaeprf- d dinecota n ti sxrsiepithT thgirypoC © 2991 yb nhoJ yeliW& ,snoS.cnI yl slulo Aed.s nedtnahehitsvg.liriaulerdmbsaiuensPraC k r s oti fw rhnyofatonopiatals n naroroittcudorpeR eht fo 801 ro 701 noitceS yb dettimrep taht dnoyeb noissimre peh ttuohti wtc Athgirypo Cetat Sdetin U6791 fo tehhgt irreynpwooc .sslitusfewuaqlrenoRuf d ed slnos uoteeoirbhtdsa dm narrooe ifhrsntosiriumfrep ,tn ensmhn tooyr JieaeslphsietiWDm r&e P,sn,o.ScnI 605 Third Avenue, New York, NY 10158-0012 Library of Congress Cataloging in Publication Data: m,,an)i o nlms9 olap3.siim9JkWlo1clhaiTJ-W( gnit us ptrmsooifCt nsdernieaceSnig n:E akoobkr o,fwsoisylana ,sci rse n mmoduainnitalalciiWl /p.p.JanospmohT .p .mc .veR .de g:nfiotup mn o idC.eeic.ln4pe8pi9ac1sc A“ ecneicsretnI-yeliW”.noitacilbup .sexe ddsnneiacnere flearcihpargoil bsiebdulcnI NBSI 2-81745-174-O)htolc( .1 laciremuN ataD-sisylana .gnissecorp .2ataD-ecneicS .gnissecorp .3 ataD-gnireenignE .gnissecorp .I ,nospmohTmailliW .J mai l,l)inWo(skc a-J93 9g1nitupmoC ni deilp.peacneics .II.eltiT QA297.T5 1992 519.4–dc20 92-16744 acirem Af osetat Sdetin Ueh tn idetnirP 01 9 8 7 6 5 4 3 2 ECAFERP sihT ecaferp si desserdda ot sredaer ohw era detseretni ni gnitupmoc tub ohw-les .,so e. Slcf I laes e ifildbrweraa orbuetpnrlau msrne ohmctoide hcihw ni ,hcaorppa detargetni na seriuqer gnitupmoC cifitneics lacitamehtam dna , ,slsmaihcst iyigr lrnedaoimnngmuaalmnaa r egdroearppole vdenda d.erseuhtegot ehT esoprup fo siht koob si ot edivorp na noitcudortni ot ,sisylana ,sciremundna sd o shdtt npegae mncc ni niteeid.osahvns c ahte unmabtiIoorlriiegtfbaci lrpipeaht ni eseht saera si yrassecen fi uoy hsiw ot esu laciremun sepicer .ylevitceffeehT scipot taht I pole vyeldevisnetxe era nward yltsom morf dei l,pspcaitamehtameht l a,csiescyn he.pi gcdnsniare eyneihgTne era dedi vtisdo myllalau qgenomaweiver ,noitar g,entoniitait nhsecd r uosesshifa(tsfeyimldana-laci r,esmcuint afm oeehhttam dn no sailntaouii l ttmofnaosoeurrqfee fes,fhe)itcgdnne i idrdcnensaean-iagtnaed .)snois n ra,e pgidxnr neiusatoetFriafuqs- t , shssacen eunoslsiia(ltpasc islipspyalana I llac siht a ,koob kerconwis I kniht taht eht tseb yaw ot ynlrlaaeclir-eimruon gni t,dsueei prtumo n oofeeo.ly c ectsl,kriei dretlwynohopnawTnm aaIm,xeepoh evlos ynam fo eht sesicrexe taht era nwerts tuohguorht eht txet ekil skcor nieht maerts . sfsoensuoics nIoc yrt ot ecudortni uoy ot a ,euqinhc ewtohs uoy emosfo eht ,spets neht tel uoy krow tuo rehtruf spets dna stnempoleved .flesruoy Iosla tseggus wen dna cine cssetu orrehta rd en.lasehyvtaawr htegrrieehvhoT era-sacco nt ten, wo utimtotcof oaah ioeapehepwr-troteat s d mnseoinhraotfmisr elvaindoi gnipolev stif ni htiw srehto ni gnitupmoc dna sti.snoitacilppa genh iTemgmaaurggnoarlp ni hcihw I tn essmearrpgorp si .C si heTgaugnalsi won ydleesvuis nneo t inx,tiesi lms, aeitsctunmisqeerycmtesapsm-oyualsnteavded ,sdoh tdenma . snnio igetn t aiysaocrnrdTieaeolemdmpnampi eoagorcnhcewa-erp eva h Idn a Cf ostra pdetneir oyllaciremu neh tyln odes ueva h I,lacsa Pr onartro Fref v vi derutcurts eht smargorp os taht yeht nac yllausu eb de teanlisln-ayrbt-enil oteseht rehto segaugnal fi uoy .tsisni ehT xidneppa sezirammus eht secnednopserroc-eb neew t e.hs teege arsluhmlgtaAnra gldonrap s neoh itytechntu fesu e rdaetsi lnieht xedni ot .smargorp edheTpolev esdm-ayrlglourfp era yllausu dedulcni ni eht-orp .retpah chca ef odn eeh trae nstcej sihT koob yam eb desu rehtie ni a raluger esruoc ro rof .yduts-fles nI a-eno ree stsr s tueernogmoece efdltsulatos c erh otlieen vtugeaj nluri dodeauvrlogcbnai( ,)s tenreo dmnuath stflah e hstcipo tni eht ko odbluoc edberev on.cil iearteehdTsi s resoc efrocutno esnr oe oif,tt esinrrdiedt apnaehe cwgtneibcnerefer-s seotracuqeda noitaraperp dna rof rehtruf noitarolpxe fo .scipot tI si erofereht elbissop oteb evitceles fo scipot nihtiw hcae.retpahc !etupmoc dna gniog teg s’tel ,gnidaeh er’ew erehw fo aedi na evah ew taht woN mailliW .JnospmohT lepahC ,lliH yluJ 2991 CONTENTS 1. Introduction to Applicable Mathematics and Computing 1 1.1 tahW si elbacilppa ?scitamehtam1 ,sisylanA ,sciremun dna snoitacilppa2 gnikooC ,loohcs neht sepicer3 snoisreviD dna wen setuor4 sdaoR ton nekat4 2.1 ,gnitupmoC ,gnimmargorp gnidoc5 ehT C egaugnal rof ehtsmargorp 6 gninraeL ot margorp ni C7 gnitalsnarT ot nartroF ro lacsaP morfC 8 ehT gnitupmoc stcejorp dna ehtsmargorp 9 taevaC rotpme tuoba ehtsmargorp 10 ehT xedni ot retupmocsmargorp 11 1.3 enO erutcip si htrow 0001 sdrow11 yhW dna nehw uoy dluohs esuscihparg 11 evisserpmI ,scihparg ro lacitcarpscihparg 12 4.1 snoitsegguS rof gnisu siht koob21 skniL neewteb eht sretpahc31 ehT sesicrexe dnastcejorp 13 secnerefeR rof eht noitcudortni41 lareneG secnerefer41 secnerefeR no gninrael dna gnisuC 15 2. A Review of Complex Variables 17 2.1 ag srn xrb iheeedttlbgnuipml8apwmuA1monocc ehT arbegla fo xelpmocsrebmun 18 gnimmargorP htiw xelpmoc srebmun02 xelpmoC ,noitagujnoc ,suludom tnemugra32 A margorp rof xelpmo cetagujnoc dnasuludom 25 vii viii CONTENTS 2.2 x eee nlhy apTr dlmtenpoenac7ma2olepg naisetraC dna ralop-enalp setanidrooc82 eD s’ervioM meroeht dna sti sesu92 3.2 snoitcnuF fo xelpmoc selbairav13 xelpmoC :slaitnenopxe s’reluEmeroeht 31 snoitacilppA fo s’reluEmeroeht 32 cilobrepyH snoitcnuf dna rieht ralucricsgolana 34 seirotcejarT ni eht xelpmoc enalp83 4.2 esahP ,selgna ,snoitarbiv dna sevaw14 seess lardghonnPsaaahp 4 1 snoitarbiV dna sevaw24 5.2 :noisreviD gniterpretnI xelpmoc srebmun34 erA xelpmoc srebmun ?laer34 Analytic continuation 44 2.6 tcejor P: 2margor Pso ett trnaeenveinwd5otr4ceoboc gnippetS otni eht tcerroc tnardauq54 ,gnidoC ,gnitset dna gnisu ehtmargorp 46 secnerefeR no xelpmoc srebmun94 3. Power Series and Their Applications 51 3.1 noit arv o isfmg:t’ensorrieMoosileuryh1eat5sT ehT cirtemoeg seires25 gnimmargorP cirtemoeg seires35 Alternating series 56 s’rolyaT meroeht dna sti foorp85 gniterpretnI rolyaT seires95 3.2 rol ysanToisnapxe fo lufe ssunoitcnuf06 noisnapxE fo slaitnenopxe16 gnitupmoC eht laitnenopxe seires26 seireS rof ralucric snoitcnuf56 esrevnI ralucric snoitcnuf07 cilobrepyH noitcnuf snoisnapxe17 smhtiragoL ni seires snoisnapxe27 seireS noisnapxe fo x (nI x ) 73 3.3 ehT laimonib noitamixorppa67 gnivireD eht laimonib noitamixorppa67 snoitacilppA fo eht laimonibnoitamixorppa 78 deziraeniL toor-erauqs snoitamixorppa87 laicnaniF tseretni semehcs08 3.4 gn3i8tu psdmcnoiactam en hontiiatmit e:pneoRisreviD Iteration 84 Recurrence 84 Recursion 84 3.5 tcejo r :gPe3ncint eseg ehrfT teosveniorces58 gnidoC dna gnikcehc hcae seiresnoisnapxe 85 gnidulcnI eht cilobrepyh snoitcnuf19 eliF tuptuo dna scihparg snoitpo29 ehT etisopmoc margorp rof ehtsnoitcnuf 92 gnisU eht margorp ot tset seireecsnegrevnoc 97 secnerefeR no rewop seires89 CONTENTS ix 4. Numerical Derivatives and Integrals 99 1.4 ehT gnikr onwoitcnuf dna sti seitreporp001 seitreporP fo eht gnikrownoitcnuf 100 A C noitcnuf rof s’remoHmhtirogla 103 gnimmargorP eht gnikrownoitcnuf 106 4.2 s0c1i1tame hltaacmir e admetnutaanedrcsiD e hsTsenetercsi dfoatad 110 laciremuN scitamehtam 111 3.4 laciremuN esion ni gnitupmoc111 ffodnuoR dna noitacnusrrtorre 112 elbatsnU smelborp dna elbatsnusdohtem 114 srorrE morf evitcartbus noitallecnac611 margorP rof stoor fo citardausqnoitauqe 119 4.4 woH ot etamixorppa sevitavired221 ecnereffid-drawroF sevitavired321 sevitavireD yb lartnec secnereffid521 laciremuN dnoces sevitavired621 retteB smhtirogla rof dnocessevitavired 128 4.5 yll astce0civ3e ri1jge tonm:ariuAvPtn4iurpemdoC sevitavireD fo eht laitnenopxenoitcnuf 130 gnitaitnereffiD eht enisoc noitcnuf231 6.4 laciremuN noitargetni sdohtem331 diozeparT alumrof dna margorp rofnoitargetni 135 nospmiS alumrof dna margorp rofslargetni 140 slargetnI htiw senisoc341 redro-rehgiH laimonylop noitargetni441 4.7 5 4e1r idwegra hmaco rlfaitnet ocpitatsortce l:E Bt4cejorP slaitnetoP yb lacitylana noitargetni741 slaitnetoP yb noitargetni-laciremun sdohtem841 secnerefeR no laciremun sevitavired dnaslargetni 151 5. Fitting Curves through Data 153 5.1 woH ot tif sevruc gnisu senilps451 tahW si a?enilps 154 seitreporP rof enilps stif651 gnivireD eht enilps snoitauqe651 ehT enilps mhtirogla851 2.5 yradnuoB snoitidnoc rof enilps gnittif951 Natural splines 160 5.3 tcejorP :5 margor Prof en iglnpisttif161 ehT niam ,margorp cibuC senilpS661 ehT noitcnuf tiFenilpS761 4.5 gnitalopretnI yb senilps861 gnitalopretnI seulav dna sevitavired861 ehT C noitcnuf pretnlenilpS961 gnitalopre tnnoIitcnuf-gnikrow seulav dnasevitavired 170 gnitalopretnI enisoc seulav dnasevitavired 173 x CONTENTS 5.5 noitargetnI sdohtem gnisu senilps571 gnivireD eht noitargetnimhtirogla 175 ehT C noitcnuf rof enilpsnoitargetni 176 gnitargetnI eht gnikrow noitcnuf dnaenisoc 177 6.5 :noisreviD ,sretupmoC ,senilps dna scihparg871 secnerefeR no enilps gnittif971 6. Least-Squares Analysis of Data 181 6.1 noitcudortn Iot eshetra unqosi-rtestaierlc281 mumixaM doohilekil dna tsaelserauqs 182 tsaeL serauqs dna eht evitcejbnooitcnuf 185 6.2 lsannooigtoc hndtunrfaO raen itls aseelrauqs581 tahW era lanogohtro?snoitcnuf 186 ytilanogohtrO dna tsaelserauqs 188 6.3 srorrE ni eh nt:ioslbe-lt bhtagsiiarae arlsvteSrauqs091 Weighting models 190 tnatsnoC oitar fosthgiew 192 seitreporP fo eht serauqs-tsaelsepols 196 4.6 serauqs-tsaeL noitazilamron srotcaf991 gnizilamroN noitcnuf-gnittif seulav otatad 200 gnizilamroN atad ot gnittifseulav 201 ehT tif-tseb evitcejbo noitcnuf302 margorP rof gnizilamron srotcaf402 6.5 snoit a cmdrirnemoath fetssmienarsaraaragitpobL802 ehT nigiro fo saib902 ytilibaborP sisylana rof saib012 ecnednepeD fo saib no rornroeitubirtsid 212 6.6 tcejorP :6 margor Ps ee rnraioulfq-st -hstgtsiiaaferlts412 noitazinagrO fo eniL-thgiartS tsaeLserauqS 214 gnitseT dna gnisu eht serauqs-tsaelmargorp 217 secnerefeR no serauqs-tsael sisylana812 7. Introduction to Differential Equations 221 7.1 l asintonietraeuf qfdeinD alac issmyehtpsys222 yhW era er elhatitn?esrneofiftiaduqe 222 noitatoN dna noitacifissalc322 suoenegomoH dna raenil snoitauqe422 raenilnoN laitnereffid snoitauqe522 2.7 redro-tsriF raenil :snoitauqe drocer-dlroW stnirps522 scitameniK fo drocer-dlrowstnirps 226 gnimraW pu ot ehtmelborp 227 margorP rof gnizylana tnirpsatad 229 nemoW sretnirps era gnitteg retsaf432 3.7 raenilnoN laitnereffi d:snoitauqe citsigoL htworg532 ehT htworg-citsigol evruc532 gnirolpxE htworg-citsigol sevruc 832 dezilareneG citsigol htworg932
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