Table Of Content

I I -I /11I --- I-/- /---1- /" )':.�-I 1..--..,.. -. - -- / -...J / introducttoi on vectaonrd t ensaonra lysis ROBERT c. WREDE, PR OFESSOR OF MATHE- MATICS, SAN JOSE STATE COLLEGE, SAN JOSE, CALIF ORNIA DovePru blicatIinocnN.se,,w Y ork Copyrig©h t 1972b y Dover PublicaItnico.n s, Copyrig©h t1 963b yR oberCt. W rede. Allr ightrse servuendd erP anA mericaann dI nter nationCaolp yrigChotn ventions. PublishiendC anadab yG eneraPlu blishiCnogm pany,L td.3,0 LesmilRlo ad,D on MillsT,o ronto, Ontario. Publishiednt heU nitedK ingdomb y Constable andC ompanyL,t d. ThisD overe ditiofinr,s ptu blishiend1 972i,s a n unabridgaendd c orrectreedp ublicaotfit ohne w ork originaplulbyl ishbeyd J ohnW ileya ndS onsI,n c., in1 963. InternatioSntaaln daBrodo kN umber:0 -486-61879-X LibraroyfC ongreCsast aloCga rdN umber7:2 -79300 Manufacturiendt heU nitedS tateosf A merica DoverP ublicatiIonncs., 180V aricSkt reet New YorkN,. Y.1 0014 Tom yM other andt he Memoryo fm y Father preafc e Vectoarn dt ensaonra lyasriesm athematitcoaolla sp proprifoart teh e developmoefnc to ncepitnsm anya reaisn,c ludgienogm etrya,n alysis, andl ineaalrg ebrEav.e nt hougvhe ctoarn alyissia s p ropesru bseotf tensaonra lysiiths a,sg rowunp s eparatFeolryt .h irse asotnw od istinct notatihoanvse d evelopweidt hm anyv ariatioofne sa chT.h ev ector notatiionnt,r odupcreidm arbiylG yi bbsh,a sfo undw ideu sei nd iffer entigaelo metersyp,e cicaulrlvyte h eorayn,di nc lassmieccahla niTchse. vectoarp proaicshr apidfilnyd inigt wsa yi ntcoa lculaunsdv arious engineetreixntagsn di ntwor itionnga ss pecotfbs i oloegcyo,n omiacnsd, othesrc iencwehsi chha dl ittulseefo r sucha viewpoian fte wy ears ago. Thet ensonro tatiaonndc oncepgtrse wu p witthh ed evelopmoefn t differengteioamle trpya,r ticulsaurrlfayct eh eorayn d tehxet ensoifo n geometirdiecat sos pacoefsn dimensioFnosrs. o mey eartsh teh eoretical physicainsdtt h ea pplimeadt hematihcaivafoenu ndt ensaonra lytsoib se a valuabtloeol . Ine mphasiztihneug t ilitaasrpieacnot fvs e ctaonrd t ensaonra lyswies , mustn oto verlotohkefa ctt haeta cthh eoirnyv oltvheesd evelopmoefn t a complemtaet hematical tshyasitts we,im t;rh e spetcovt e ctaonra lysis, basiecn titciaelsl,ve edc toarrsei, n troduacnedtd h ea lgebarnadc alculus oft hesoeb jecatrsed evelopTehde.s ituatfoirot ne nsaonra lyisssi ism ilar butm orec omplex. Int hitse xIth avter iteodp oinotu tt her olpel ayeidnt hed evelopment ofv ectaonra lybsyic so nceptthsaa tr ea parotf l ineaalrg ebrTah.e ries ane mphasoinst hei nterrelatoifgo enosmheitpa rnidca lgebraic modes of expressTihoenc .l assical onfov teacttaionoran l ysis ibsu tn uosteadt,i on vii ViiPiR EFACE morea ppropritaott een saonra lyissig sr aduailnltyr oduacneddc orre latewdi tthh ec ommonv ectnoort atiTohni.is sd onei np artto fa miliarize thes tudewnitt the nssoyrm boalnsd i np artto fa cilittahtese t atemoefn t proofHso.w evetrh,e m ajodri stincbteitowne tehni tse xatn do thers of ani ntroducntaotruyir set hee mphasoinst ransformatthieoonary n dt he ramificatoifto hnaset m phasiIsnt. h fei rfosutr c haptietri ssa ssumtehda t thes paciesE uclideaanndo, r thogonal CagretneesrCiaaalrn t,e siaandn , genercaolo rdintartaen sformations, raersepp reecsteinvteeldy., Simul taneouns-ltyu polfer se anlu mberasr ea ssociawtietdoh r thogoCnaarl tesisayns tecmosl,l ectoifso uncsnh - tup(laec so llecctoinosni sotfio nnge n-tupfrloem eacohr thogoCnaarlt essiyasnt eamr)ed efineadsC artesian vectoarnsd,t hev ectcoorn ceipste xtendteodt hem oreg enertarla ns formatiognr oupsT.r ansformatliaownsr elatviencgt coorm ponents in differecnoto rdinsaytset eamrsec arefusltlayt eTdh.e s ignificoafnt chei s modeo fi ntroducotfti hoevn e ctfoorrm isi ndicabtyev da rioeuxsa mples. Inp articutlhaeir m,p ortaonfct eh ei nvariaonffoc rem ,a ccomplibsyh ed thep rocedudrees cribiesdd e,m onstraitnCe hda pt2e,rS ecti6o.nT his developmoefsn pte ciraell atirveiqtuyi nroeg sr eadte ptohf m athematical knowledagned s ervetsoi llusttrhaeti em portaonfcte r ansformation theorIyb .e lietvheam ta nyo fm y studenfotusn di tt ob ea brigshpto t int hec oursfreosm whicthh ibso oki sd erived. Ih avea pplimeyd n ote(so rI s houlsda ys erioefsn oteisn)t wow ays. Thef irfosutr c haptewristt hh es tarrseedc tidoenlse tweedr eu sefodr a one-semetshtreere, -vuencittao nra lycsoiusr sweh,i chha da differential equatipornesr equibsuitnt oeta na dvanced calculus Tphree requisite. studenwtesr em ostlmya thematpihcyss,i acnsd,e ngineemraijnogr sI. havael suos etdh es tarrseedc tiownistC,hh apt5e,ra st heb asifosr a one semesttehrr,e e-cuonuirts ient ensaonra lyfosri ss enioarnsdb eginning graduastteu denTthse.s ectioonn g enerraell atiwvaistn yo ti ncluded. Ih avues etdh em ateroinag le nerraell atiivnai nte yx pandfoerdm ,a sw ell asm ateroinas lp eciraell atiivnia t tyh,r ee-cuonuirtos nea pplicatoifo ns tensaonra lysIis su.g geaslts o tthhaibtso okc ould serpvuer ptohsoeef s ani ntegrated twoc-osuermisenes tveerca tnodtr e nsaonra lysis. Iti sm y belitehfa itti sp articusluairtlayab slp er eparafotri odni ffer entigaelo metarpyp,l imeadt hemataincdst ,h eoretpihcyasli cIst .h inikt wilall spor oviad ber idbgeet weeelne mentaasrpye cotfsl ineaalrg ebra, geometarnyd,a nalysainsdI, h avter ietdoa dds omep erspecbtyit vhee inclusoifao sni gnifiacmaonutno tf h istoriincfoarlm ation. SanJ oseC,a lifornia RoberCt.W rede Augus1t9 63 acknowledgments A textboioskn ecessaar icloym pilatoifoh ni storiincfoarlm aticoonn cernitnhge s ubjeactth and.M y choicoef t opiacns dp roceduhraess beeni nfluencbeydm anys ourceOsf.t hesIe w ouldl ikpea rticultaor ly acknowletdhgeie n fluenocfme y formert eachPerro fesVsaocrl aHvl avat) (IndiaUnnai versity). I am indebtteod P rofessoErrsw inK reysz(iGgr azA,u striaan)d BernarFdr iedma(nU niversoifCt ayl iforniBae,r kelebyo)t,ho fw hom carefurlelaydt hem anuscrainpdtm adem anyv aluable suggaensdt ions correctiaonndas l,s too D r.D aleR uggl(eSsa n JSotsaetC eo llegweh)o, eliminantuemde rouesr rofrrosm them anuscrainpdtd iscustsheepd o int ofv ieowf t het exwti tmhe . Iw isht oe xpremsys t hanktsom y wifeJ eannSe.W redew,h od rafted thei nitsieatlo fi llustraftoirto hnesb ooka ndp erformemda nyo ther tasktsh acto ntributtoie tdcs o mpletion. Ia m gratetfuolM rs.G errDyu nckefolr typitnhge m anuscrainpdtfo r doinagn e xcelljeonbit n t het ediotuass okf c ompilitnhgei ndex. FinalIlw yo ulldi kteo e xtenmdy thanktsot hes taofff J ohnW ile&y Sonsfo r theicro nsideraatnidco anr ien t hep reparatoifto hni tse xt. R.C.W. ix contents 1 chaptert hea lgeborfav ector1s , Historsiucmamla r1y , 1.I ntroducctoonrcye p7t s, 2.L inedaerp endeonric ned ependoefan s ceeot f n umbenr- tup2l3es , 3.T ransformeaqtuiaotnir oenlsa triencgt angCualratre sian coordisnyasttee 3m5s, 4.D efinitioofCn asr tessicaanl aanrdv ect5or1, 5.T hei nneprr odu5c6t , 5*.G eneral Cartesian6 5c oordinates, 6.& systeamnsdd etermin8a5n ts, 7.T hec rospsr odu9c6t , 7*.&s ysteamnsdt hcer opsrso duicngt e nerCaalr tessiyasnt e1m1s1, 8.T hea lgeborfma a tric1e1s4, 2 chaptert hed ifferentioaftv ieocnt or1s2,3 I.T hed ifefrentiaotfvi eocnt o1r2s3, 2.G eometorfys pacceu rve1s3,9 3.K inemat1i4c7s , 4.M ovinfgr ameosfr efere1n5c5e , 4*.A tensofro rmulatoifto hne t heoroyf r otatifnrga meosf refere1n6c6e , 5.N ewtonioarnb i1t7s1, 6.A n introdtuoEc itnisotne sipne'csti haelo orfyr elati1v7i6t y, xi