303 Solutions

303 Solutions - H_________._ EIGHTH EDITION Elementary...

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Unformatted text preview: H_________._ EIGHTH EDITION Elementary ifferential Equations and Boundary Value Problems William E. Boyce Edward R Homilmn Prflfi’j'j'rfl' Emerimr Richard C. DiPrima formerly Eli-EH Rinks”; medurifln PFrfiiWEHI‘ Depm‘rmem of Mmhwnmhuf Karim-5 Renarefner Pob'rerhufr fHHHth." .- I I anal!“ II‘I 1".I._ II ' -.-. .—I _. ; _ “11:1.- _ r.1 fill-.1311- ' L i]... ._ I'll an... - I '* :‘F'F' In . NJ. _ I_.,:l: ‘ I '.ll ' I I '_ I J. j I'- I. E _1,h I ' II' I ‘ _ : III 1“ :— r:_III--._ 'g. - . 1| I". .. ‘1 - -r'lerfl-fiz. . ..I I -'I'-':_L"'I" _I I I ":"l I, 1;. - "‘ I I'_l . . PRflJEfl Enrrflfl Jenny Wfilter I ~ - IE; .-_. -- . - .5: II r I II I .. ::-_I .‘II __ I _‘ II ._ II II II I EDlTflmALAS-SISTANT may-BU?” - _ '1'. . . 7 .-L - -- _ . . _ '. . ._ ‘._ _.__ EXECUTIVE MARKETING MANAGER Julie Lljndalrnm ' II " ' _ .I I _. ;' . _ ' ‘I.'I;I:-I*III‘I:'IIIi .I ._ .. _I u - - - Ken Snlnr .. - ~‘- i - .' . . '-' " " - " ' Tfififififififiim-m " bhl‘dlflk PRGDUE NON EDITCIR .r _ r1-" .1: “'1 .L' .- {ruvm DESIGN Cam] (3: Grab: .- ' file? What. SENIGR DESIGNER Karin WWI“ ‘ ' a ' H ‘ ‘ ' " ll_l.llfi1'HATlf_lN I-jiJrrnR Sigmund William“ . , _ __ I u _ ' ' I Thia I'h'InL wan ‘ifli in “may Ten hyTuchfiellers. Inc. and primed and bound 113W!“ Hflffinflflni'mfinii l2" _ I I I I .' ._ ' I: 1' un-rr war. prmlttd hy Van Hull'mann. Inc. r I- ‘1 '.'J' ' ‘. I '- i" - .l .-..-.| I _-'-__._ _ I—I- l- : - I .- 1' 1‘" -‘J:f:r:r-;. 1-,“: _...._- I ._— . “I . _: - . u- "* r. .1 ...:. Eli's-"'- " ' ' :13' ,i LII-h' .--._ J1- fr- _'_"r -'II- _I' 1 i I r "H .I an”; -.-_,_ . - ‘ I I. -‘ '-'= _ filiafgfim .. II" 1 III I r " I I ELL—r ' i. I, I'- .... '- ,I:_. a “"15. .1; 1111-: him it. prinlcd nn and Inn: mpur. 1. Ti; --::'|". I: lull", Fupyligliz .I': LEWIS lnhn Wily}. J;- Hum. 11:1. All rlglzls [flan-red. I ,: I _ II:_I,I~I_ — _ _ .13. _ l ‘ . . run u! tr.-— puhllmlil-u “1:13 h: rcpchuLtlL slnrcd in n l'iill'it'l-fli ayalcm ctr usnmniued .u my 1mm nr l‘ly' an}- mtum. ulfllruul-g. Il'lfiéhulticifl. phumcnpying. rrt-mling. squirming .'__ - m +-II'-:-ru,-i-;~::. .:.~.-.T¢:pl :tr. pcrmlufld m:ch St'flhmh 1'1":II m HIE nl' 1hr: mm Unilml Smlfifi .I II I I I I I I I I .I I; AI [inf-u.ng r‘u-I wuhum clihflf lhl: priur written pcrnflscsiun nl' lhu Publiahflr. ur .I,I :I_I.._.I_IJI,I‘I.~:—.I.RI,-*IHI-‘I- - F'I -' “FEE-I :I I.I. I_ “IT ,I I H 'I. '5- . _ +I'lJl'lthl'Jflle‘H thmugh rmymcm r-l the appmpi'iale per-cum fm: In the {'upyrighl ,I,_III:IIIJI,:IIIII FEIEE-i‘éhijw IIEEI‘; {i {TIE I .II_I III_ I I I I I [ileummr {Trnwn 221' Ewen-mad Drivc. Dfiflh‘cfi. MA [IV-fl]. 1‘}?!le Tfill‘llalllll. fax _" I- - I _ I. II'ILII.IIIIIIIIII'IIII2III_.;I:I,I _III:IIIIIIII.IIII_II.III.-I- IIII.I. = IIIIIIIIIII I. I II.' ,I -_ _ IIIII lul'hl Mull-INK}. thlwsm In the Puhlifillfl fur pennifiiun shfluld M Jflil‘l’flfiflfd la the "‘1; ZIIIIII; I IIII ' I 'I I ' - ' Ptnmeflun-i [itpunman Jnhn Wilcy & Sum. Inca. Hi River Surat. Hubrllwn. NJ {WHSU‘ ' '..--'-'*'.I.I_II - rIlE-lr-IIAII: -_'-I _ ' ‘ [ZUI}14H-hflll.fflIIZUIJ?43-ffl}fl. a riff” air-:HIE'J'R - -‘ I " “ * ~ “ +‘3‘F‘fic- , J’L'.‘ _.‘-._ ‘ Tn nl'dfl hulk:- ur I'm cuslnrncr Hewitt pleml call llEflfll-CALL-WILEY [2235-59-45}. I I _ I_ “I III II IIIIII: I, II :1: Li'wa offlungrm Culafagfng-Ind’ubflmflnn flaw ,— LI _.j -r. * nummmum E. - ‘ -' -'-‘..I'*-" ‘I '~ Elcmflnlnry diflemnlinl cqualiuns and hounqu value prublcms! William E. Ewen. Rififiafd_fl._..I. - - r =4 * - ' fl '_ I p. cm. Include: indtx. ISBN 0-411-43333-1 {clam} a; l. Dil’fumnlinl uqualiunn. '2. Haundnry value prublems. I. DiPrima. Richard C. II.'I"it_I¢-. * +. s flhflhflfllm a 515?!!de a w." ' -E flmuudlmhe Unitasd-Blnlel nfhmarlm- ' fi ‘ -_ ' . ‘ '~*' ' - I _I '- _ -.I I ‘1" "I - u” _ :r -1" a a; {I The Authors William E. Bovce received his BA. degree in Mathematics from Rhoda; (F‘flnfi-gea and his MS. and PhD. degrees in Mathematics from Carnegie-Mellon niversity. He is a mem her of the American Mathematical Society. the Mathematical Assoc}- ation of America. and the Society for Industrial and Appltcd Mathematics. Hg ,5 cu rrentlv the Edward P. Hamilton Distinguished Professor Emeritus of Science Ed- tication tDepartment of Mathematical Sciences} at Rensselaer. He is the author- iit' numerous technical papers in boundary value problems and random dtt'ferautflal equations and their applications. He is the author of. several textbooks Utflllelng [on differential equations tests. and is the coauthor {With M.H. Holmes. lG. Ecken anti 'it-’.t.. Sieemanni of a test on using Maple to explore Calculus. He is also can“- thor {with RiL. Horrelli and CS- Coleman] of Differential Equations“ Laboratory limit-roos- tt-‘r'ilev lvvl‘i. which received the EDUCOM Best Mathematics Curricu- lar lnnosation Ari-ind in luv}. Professor Boyce was a member of the NSF-sponsored (Ulth l; tl‘onsortiunt tor Ordinary Differential Equations EapcrimcthISJ that led to the widely-iieeliiirned UNI-j .slrcliiirccr. He has also been active in curriculum limo- stilt-Ht and retorni. stoning other things. he was the initiator ot' the “Computers in t aleulUs" [‘tt'iltect at Reitssel.-ier. [.tartit-illtr supported by" the NSF. In 1991 he received the William ll. t‘s'ilcy Distinguished Faculty s‘sttard eiten by chsselaer. Audience and Prerequisites Richard if. llil-‘rittiit lLthtSL’tlHI.'4_Il lt'L-‘.'l‘l-t.’t.'i ltis 8.5%.. hill. and PhD. degrees in Mathe- fig or liIL.‘- tum-it .rnceic-i‘ttt-lion I. nit cisity joined the faculty of Rensselaer Poly- This cditiflnilikc its predecessorsiswritten from the viewpoint of the applied in ithes l-nn lrc iliLttI'. ..-|=tet' lit-Hulla- itch tsositttinsat h-llT._l--larvard. and Hughes Air- maticiflfltWhflscintercstin differentialequations mavsometimesbe uite theorhiil .h-I ,.iu_ .+i« 1.. hi 1 his It” ' t “simian-tn Protessorship ol Mathematics at Rens- ' sometimes intensely practical. and often somewhere in between its: hase s suititwiili 1-“ it r :. -: the. “tits. .‘*_:is.i:...-r. :sce'cty ynt' h-techanical Engineers. the American combine asound and accurate-(but riot abstract} exposition ofthe elements; tittifll': “fir... : I: ilk-ill. n h-r:l-:'_Ititl:!h:-lIF-_'liq-Til II- :Illsgfafityegther of differential equations with considerable material on methods of solutionanalysis. .Illti i3;-_- ‘si .. :I_ it. it c Lil'till'sll Lil .tlliifi 'ii'l"'illL"Li ‘K-‘litll'ttit'I-thtit‘; IHLL: serit'tid '15; the {31:33, and flpprflxlwfltlgn that PflVEPI-GVEd usemi in a Wide Val-ileu- flf applicatinng‘ t:- .11 -:2 Hr. lis'l” lt [l1|'_‘ill r-Ii Trial ltt't‘ttLttiL‘Fttl Sflti't'lccs ttl Licit'lh‘itfiqtfl ttS Pfé'ildfl'fll Elf flit: Thalbflflk‘ IS wnufin primarily far undfirgradume Sindents 0f mfllhfi-mfltmi ECiencc. :hli=.ll_i'. ‘1 c mow :ri'il .iiii totalled .‘sl.:it|t-_-i.-::.i=ics and as tiltaiirntan of the Executive Dr engmeermg‘Whmwmfluy {aka-a murfifi mil giffemmifll Equaiium during mt” rim t. mutilate. . ll lit ‘ ;-]‘tl 5 [their llllL" if}? isttit‘i tit—.i‘tSi‘lej in 19:30 he W33 the t'ECi - fir SECflnd Yfiflr flf Stu‘jy‘ -The mam pre‘rflqmsue for reading the barij H “l u firm”?! iein oi it._ o.- riis-i: I t, is .l. - i'nstitieuished iiieiiltv Award sliven [iv Rensselaer Hpe knigmlfldg'e flfcalcmuswgalflefj'frgmfl Emma} [Fm—W [hFEE—SEITWHEF murw fit-timing: .. . s - - or Its equrvalent. Some familiarity with matrices will also be helpful in the chapters luv—1H Ht 1” I“ I clays-t. ll'. Halli—{ml}? am! tv- _~' and a {illggti'nilctll'l'l fellowship in an WEED-15 Bf difffiremifll Equatiflm i- . _ . .. . . .1 _ in.” in t'ttitTteriitl‘s technical papers In hvdrodvnamic stabilitv * and '“hri‘i‘tl'l'm 'li'~"'t'i will its“ tests on thl't’crential ctluations and houndary value l‘llllll's'mits Printout lilil’rinia t.llt;*Li on Ss‘t‘tcnther It]. Iss4. FL'L‘L'i‘. I. ti l Ilii‘rl'lLttl {L- A Changing Learning Environment The environment in which instructors teach. and students learn deli-rec; .i -. tictns has changed enormously in the past seseral years anti contit us tt' - a rapid pace. Computing equipment ot' some kind. 1'.t'itr:‘*tlt-.er a at ital-trite Lerle'ii notebook computer. or a desktop workstation is available to nit-st staticai ferential equations. This equipment makes it relatively easy to esectite numerical calculations. to generate graphical displays ot a set}. hieh attains. :F-.il. - many cases. to carry out complex symbolic manipulations- it. high-specs i".t .. rat: connection offers an enormous range of further possibilities. The fact that so many students now have these capabilities enables Instructors .| they wish. to modify very substantially their presentation of the sultiect .tttcl its. l'. t'ii ex ectalinns at student perfe ' -. L . i _ r _ _ _ . __ tugs piniens as [anew a ceurse en diffs rent-rat equajiens shutggfi: _ ti ___ ‘ I colleges an universi - - 1' my circumstances. Nevertheless. at many _ I _ _ i tial equatiuns are heceming mere visual. mere quantitative}. mere pretest errant _ and less lurmuia—centercd than in the past. . _ I'llrl A Flexible Approach Tu he widely useful a textbuuk must he adaptable in a Vfll'iElY “f instrucufmaifitra ., __ _ . glee This implies at least twu things. First. mstructurs shuuid have maximum 5;, ; - hililv lu chuuse truth the particular tupics that they Wifih ['3 WV” and 315” the “Hi-liar: 2'.- i" which “we, want in enver them. Secnnd. the [seek shnuid be useful tci smdenrlgttl L'- . L_ _ ' _ -. Iii-J e tie-net'state-iri how the; he having access in a wide range at technulugical capability. E}. I I WWW m :5 I. dent-s shenldlsnltteshefifirtihletns""f flay" "arith' ' term ‘ " er perhapshuth With respect in cement. we pruvide this flexihility by making sure that, an far-am: ' I}??? i they want an emulate enmputer-gcnerated pussihle. individual chapters are independent ut" each either. Thus, after the I I .. plflt er a handsdrawnsltetehenr parts at the lirst three chapters are cumpleted {rnughiv Seetiuns "1.1 thruugh ._;‘- ~* - 3.! tl'irrtuuh 2.5. and .l.l thruueh lit] the selectiun cit additiuna] topics. and the circle: is; .uid depth in which they are r. ttt'erccl. is at the tliscretiun ut‘tlte instruetur. Fer eattttt‘tpleii EI- u,” manmflm. “a!” Mame I” I_'JI]]I':1|;_1'5LII._‘ a strain ms appruaelt in differential equatiunsj I Mathematical MfldEliflg can tale up ("hauler 7 li,inear Systems] and perhaps even Chapter 9 (Nonlinear i I wuinnumuue “it stertisl lilltl'tui;ii;ili;i}' utter Chapter 2. Cir. while we present the hash: ' Iiitznrv nl linear I‘t|tlitll=_lil‘s iirsl in the clinical till. it single seeund urder equatiun Building hum Basic Mfldfls ll 'htipl-sr ll. nautv utslrtictur-. have cnittiiiued this material with the eerrespcinding. treatii'teut ll: lupl'a-riirdei euuutiuns {tfhupterr-ll uruliinearsysterns-(Chapter 7). Or, ulule tlii' I'l'ttilll Liisctlssinn rtl ttLlittL'rtL‘tli ntetht'it'ls is in Chapter 3. an instruetur what U wishes t: = empiiasire this uppiuaeh can inlruduce sunte ut'lhis material in eenjunetiun with [trainer 3 h-laui' i'itltti til-.iiees and cunthiualiuns are alse pussihle and have The main reasen for sewing many differential equaticms is te try to learn snmettiiag aheut an underlying'pliysical precess that the equatiun is believed te menial. it is basic tn the impedance. at differential equatiuns that even the simplest equations cnrr‘espund tn useful physical 'ntcidel-s such as exponential grnwth and decay. spring. hecu used ellecliielt with earlier editiuns ul‘ this intuit. lt't'ltniilnut With respect in technulupv. we nule repeatedly in the test that ecimputers are ex.- tremer useful l'ur investigating dil't'erential equatiuns and their selutiuns and many at the pruhlems are best appruaehed with cumputatiunai assistance Nevertheless, the [stink is adaptable tu euurses having variuus levels at cumputer invulvemenl ranging [rum little ur name In intensive. The text is independent uf any articular: pfiirdware platlurm'ur saltware package. Mere than 450 pruhlems are masked with firlspnthtfllf—-htu indicate that we ennsider them In he technulugically intensive. 1x prp . ems may call fur a‘plut. ur fur substantial numerical cumputatiun, er fur liq Editflpuiilttfln. ur fur surne eumhinatinn at these requirements. fiuhlemw l d ‘g t n u a Emblem as technulngicaliy intensive is a sumewhat in gmcnt. and the ‘L- is intended unljir as a guide. Many at the marked pruhlems can be suited at least in ' ' l * . part. wtlhuut cumputatiunal hel ' can he used etlectively un man}r til the unmarked pruhlems Pi and a campuwr mass systems, in electrical circuits Gaining an understanding at a eempie‘t natural prucess is usually accnmpiished by cembining er building upon simpler and men hasie medels Thus a theruugh knuwledge at these basic models the equate-its that describe them. and their sututiens. is the first and indispensable step intend the selutinn nf mere cumples and realistic prehlems We describe the at. eieli i. prise. s - in detail in Sectiuns 1.1. Lil. and 2.3. C are let censtruetiuns et’ medals apps-u sits Sectiuns 2.5.3.3.ancl in the appendices In Chapter ltl. Differential equalities iese -t+i.‘_ {rent the mudeling precess appear frequently titre-aghast the heart-t especia-ilv in re. -- pruhlem sets A Cnmhinaliun ef Tunis—Analytical and Numerical Nunruutine prnhlems uften require the use at a variety ut tu-uis. huh .tnalt is. fill .ir-el numerical. Paper and pencil methods must at ten he enmhined with el'iettin -.' use is a centputer. Quantitative results and graphs nften predeced h} a cumputer. sen e in illustrate and clarifv cunclusicins that may he ubscured by cumpheateil unattri- cal espressiens On the ether hand. the intplementatiun at an efficient numerical pruceclure typically rests cm a good deal at print-tintinarar flflfll}’ats-tct determine the _ _ . t I. t .I 3' Eflm‘afl . ' invests a e Imrt- ' '- - magnum infirm - - . _ -- s. . _. .- _ _ ' ' -- tr tures at the selutien as a snide In sawmill“! “3 gm 5 m: _ _ ' a?“ 1 , - ltui‘l'lal'll‘. w I . d' ear which ranges ef the variables er PERTH!“ _r a? 9- “a” 3"“ “Wilma” 1." 10-5 unheateendm in the preset-es of manual mg m Rpm“! #35” [if m ml} Thus, a student sheuld came it] 1' 3311353 that Invest!“ heal Weasel“ 103 “‘1 diFPeflifl “finned in 193m the flow W require nr merit special attentlen. ysis and mmpmafiflm that gflnd an aquifflrl . _ y _ , s * bethanal . sting a drills-uh prehlem that.t uell rsqgiiich [ml is bflsbsuimd [rm a particular task; .. Judgment may he required to determin * I I “firms; AS the Sflhjflcl matter Hf diflemnfial equalities millilitres 1e grew. as new tech— and that results can eften he presented In a starlet}- e ncslegtes become- enmme.nplaee-,as flld areas efapplieatitrn are expandeéand asnew . i _ H Jh {mm “t- ,1 Prime; enes appear en the herizenJheeentent and viewPeint ef courses and their textbooks til" ml” 1 1" ' L ' ' d wand that {except perhaps in must else evelve This is the spirit we have seaght 1e express in this book. EELS [fl 1111 E C . t. ' tantlerstud _ . . We bLllL‘rL that It ts IntPL‘tt' lflffifllvingadiffgrenttalequatlflflts aeldflm -' - 'r * * l J '1 m - - WilliamE ED ee - _. wendtftertnttaltqunttnns] the at L t . 1 - y ttr trhtain the sttlutittn Rather. tine is Interested In the salutten 1a erder tn '1 _’ ' ' - Graften, New Yerlt trhtain insight intn the behat-‘itrr t'if tilt? ill-“W51? [hm ll“: Eflu?ufln pu.?§;§;§ February 23' 2004 in ether u-‘ttrt'ls. the sttlutititrt is net an end in itself. Vitus, we“ Easte1t filusmns ill be. mam prtrl'tlcttts. as well as sense esarnplcs in the test. that ta: nrfeeph v l fifth drawn sheet the striatittn. Sentetitncsthistahesthe term elf asking at data lie: the independent t'ariahle at which the sultttinn has a certain Nepal-13.9110 IE 31:ml_ne .3 lnne term hehas'inr III' the 's'tii'tliltll'l. Gilli” Prl‘blumfi :1le “if the Elia“ '3 Vflnimfls 1“ a parameteer It” the delerntirtatien et' a critical talue til it PilmmFler 3ft: “3h :33 Mum" Lj‘Pmungcs .L. cutistnntiai change. huch prnhients are typical a t eset at ,-,,-.tL- in im- .tlit‘rlta‘;-tltttltfi t'Il differential equatinns and- depending an the geals ef the Ll“ tutti-Hem. tut the martian tit" assigning tea at many at these preblerns. a training: lnsi t_ I till '~|_'_ Notable Change-tin tits Eigith edition .. fir . r-.'1.'III...'-|'.Ir.hirflt-I"' e" " - -—_...___——-—_ ._I— it -i-iei *:-.t.- it -.. it uh lite in: etetiitse tthtttet will le‘sti't‘t'e that the general structure crf th-- in It. l-ltt'Lli.--|..'_l..l. i'he It." «I in: that we hart. made in this editien have several l_'|.I.Ii'- :u tut.” t-t the neat-s tr-pttcstinnt that are. ennsidered. ttt make the presen- t.ttt--i. ii'I-_-t't' t ts-Ial le' aniline: write new lie-ares, and it} intprcn'e the espnsitien by tritltttt-w: v ---r.i| at i.- imtr-utrtt esantptt-t attire speciiicallttthe most impertant Clittlltllf'w Ire tht lttll‘ttlitttti 1. There .ne -_:;tintt'- l'l'r.l'-_'l_". r15 itct'.‘ ['tl'tll.tir;'thH scitt lured flirttualtt‘tut the bunk. There are alafl ahnut |:'- nix". ii;_=||it" tl':-'.l :4 ttI:‘.'- in inn-hired etttrtiples. l. Sectinn ll. ' I tilt .ti litgilttllttl'i»; il-lallttttl nt' Integrating Factcrrs.“ has been substantially rewritten. with Its-tr tit-e. t_'_'-t.tlt'l:'tlt_'~' tn t't-tittce r'epeiititrtt. 3. Sectinn 2.5, “Autttntrnttttts Equatitrns and Pnpulatiun Dynamics." has been medified tn piste mere prurninertee tn the phase line as an aid tn sketching salutiens. 4. In Sectinn It}! the general case at damped sibratiens is ctrnsideretl beltrre the special case at nndamped ethratiens. reversing the arder ul presinus editions. The presentation is mere detailed and there are three new figures. . the [treat at the eenenlutiun theerem in Sectien as has been rewritten and sis new prtthlems an integral and tntegrrndifferential equatit‘rns have been added. ti. 'l‘n illustrate the eecurrenee at systems at higher cnupletl trscillaters has been adde several related prtthlems. 7. An esantple has been added tn Seetien It} in de inr nenhemngeneuus littear systems. than secend arder a new example en 1'] In Secttnn 7th, with three accempanying figures and menstrate the use at Laplace transferrrts . - Administer Ynnr cum infinite-Plus Ba" n. . ' ._ . ' _ - - -- .. eaeil bemteg. {media mu “"3 and Students 3 u' H wagging“! WEN: in: elite: year. a: Imag' in Se Iemental Resources for lastruc .. . . . - . 0 D E Ambit“! is yflur Elam [JEWIde YD“ With the fl'flfihility It! build ynur muse, wit my, . "I ' ' - I ‘l f . -' i r-i t D is included wnh in“) ‘59P?!“ . . ' - . - Tht H” L A n Iii-iiiite-nf-ti'te-art NSFssPnnsnred learning Software PRCkflgfls Whiflh 15 Fur mam mmrmatmn about the feat-“IE5 and mam-5 “f EGTadE Hus- Pm fit“ ‘Er'indl-jxvq‘cfln]Pulib]fl_ fit fifli'i'fll' [DUI fliiflWg FDU [ID yfllll" {J‘Wfl flifldfllfi Bur flflllne dflmfl at “may.wilfiy‘mmftflflflgegegmdeplm and studs them in a truly interaetive pnint-and-eliek enwrnnm'enjt. ThelArehrreg-i ineiudes an interaetiee library at more than nne hundred madel diffs. retina equating“ sestenis with graphs ul' snlutiuns. The Arehr'reer also has 14 IHIEFHCIWE mUIHHIE-‘dla inndules. whieh prns'ide a range at medals and phenomena. train a gulf game m a prise—winnng Chitlh_ I E An instruetiir's Snlutinns h-Ianual. ISBN {l-4?l-fi?9?E-U. includes salutinns far all prnhlems in the le‘tt- A Student .‘itfilntit'ins. M prnhlenis in the test. :‘t ("eliminnin thigh sin; 1.". suurees lru stanenls .Irni Instruelnrs. including: anual. ISBN tint? ] «13340-3. includes snlutinns fflr selected a.ale-ii.»uni-allege Eunice. prrwides a wealth nf re- Ir i’tlt'se'l'i’ifrll‘ll silties ni' ininnitanl ideas and graphics l'nr stud}.’ and ante taking, 1" tailines in help students prepare far quiaaes and exams. enahle students In test their knflfi-‘Edgfi {if key enn— -- ieedhaflk is prueided that refers tn pertinent ' i~'e1. is v. .il'lii "ilttu'x it I J'Iiim-g i14_~.1u_-is'l_it]t?itt.'slit |_I..'E-Ii"~ ' u- 'eii'lhasl renewelitignnille Hi In Iil [r_'s_[ ‘3 ’ i. ttI|__ . [Uri nui- -' Jr :-. is. t.'. This guide intrnduees students and pra— m“! ii. .- :.«'te-_::_.'.-:-.-~ 'IT'ELi inulinnmiia. * ' ' val-II j'-'Ii‘i~.'la= '-- .'~‘ -.:I.h ‘-i.-.-'i'|u.*.nalie;i. Miple. and MATLAB. alinwing i-grl- -~i.ur- i..._-- i=I| tun-1.. -.i‘i-."|L|ii..'f- iillttn'u'ltttll' ideas in the enurse utilizing t-li 1+1”: -r -.|:_;- i':_.- 3|-_*]‘.n r:-_"-.i allultiis gnael Ligtfri. L1“ ' 3-. ill. i etiri-ule l"|a-. |":- .1 lim- ._-: :-.:| Ul'ililili. trsni that [‘Ilin.iiJL'f-i instruelnrs with an integrated fiLlilt.’ tll le.IL.i'lItli_' .It'l-J its-II i‘lllit; i'e'ailill't t. s in nth: tfi-.i."i-"i'it.i"i.lhtf Web Sit-E. etiratle Plus. is. .u-guue-t-i: mania ti't'. essential aetis-ines enu perform in class: 1' Prepare & Present: t 'l'eate el.iss }'ir'i.'s~.-.'nl:-itinns using a wealth nf Wiley-presided resnurees—sueh as an unline eersiun ut' the testhenk. PessierPnint slides. and interaetiae simulatinns—rnaking gnur elass preparatinn mere efficient. Ynu rant.r L‘Lthi}' auapmastnrniae. and add tn this enntent ta meet the needs at year enurse. ' Create Assignments: Autumate the assigning and arading {if hnmewnrk nr names by using Wilejr-prt_n-'idet.l questinn hanks. er lie writing enur nwn. Stu- Llent respunses will he graded autnrnatiealItr and the-results ie‘enrded in your gradehnnk. efirade Plus ean link htimesvnrk prnhlems; 1n the relevant 5361mm at the nniine test. prrwiding students with cement-sensitive help. I Track Student Prngress: Keep traek nt‘ gear students‘ prngress via an instruetnr‘s sfflds‘hs'tik which nllnws gnu tn analyze individual and ueeiallielass results In determine their prngress and level at understanding. i _ ‘_' ' ' ‘ ' _.__ displayed the law . "C . . Fmalls arr-mar hours spent It is a In._-.-.-~'..n'c tn til'fer my grateful appreciatitin tn the malt}t peeple whet have: I am; bath t'rrittsiv amine-.1 Hi varieav t'ftljs'a in the preparatinn It]! [hi5 hflflk. 3. I I. emgement during the m1- iz- 'r~.tll~. idttais listed I'Ieltjitv tvhu i'evicv ed that fliElI‘IUSCI'iPt 311d Prflvmfid _ Elfin-pram Ifiifl' Isa-Jam! m .rnv i."rl.i!..i£.ti"‘i1_' at 1_t't.'-1litin'; tar its intri'cnvernent William E. Efljiefi I iiteltur'ili iii-antitin. Carnegie J‘vieilttn University ‘I 1 James i'. ttrannan. Cientstm University is -_ Philip i" ate... meet-an Unit’claitt' ~ Hunts: IJui‘ilttEch.li1UT-{tlfifléi:M Universin .. Juan H. (at. Penn State r'tltnena ivh mes t'tiasner. i’cnnsvlvania Slate Universityr I; tvturli M. (.iuptafihe Genrge Washingtan University 3:." Dtlntlid l-Iartig. t'ialifernia Pelvtechnic State Universitjv. San Luis Obispa Thamas Hill. Lafavette Ft.iilege Richard Hitt. University {if Snuth Aiahama i {-7 Melvin D. Lee. Califnrnia State University. Lang Beach Gary M. Lieberman. irivva State Universitv Rafe Marleen. Stanford Universitj.t ' Diegu A. Marie. Universin at Cincinnati Marlin Nakashima. Califernia Polytechnic State University. Pemena David Nicitnlls. University,J nf Nntre Dante Bent E. Petersen. Oregen State University Chris Schneider. University at Missnuri ~ Relia Av}; Suffer. Rutgers University Steve Zelditch..iehns Hepkins University Te my celieagues and threugh the years have dene mueh te she I i I #1” ' .I- I '.' I ." I I._ :— 't-H.‘ 1' ;'_ 1--l-- a. ,‘rlh' - I’refaee v1: Chapter 1 Intredufliflfl 1 I I i 5.5 Euler Equatiens m E 1.! Sun": Basie Mathematieai Models; Direetien FIEIdS ] 5‘6 Series Salufiflnfi Near a Regular Singular Paint PM I m 1.3 Snlulians at Same Differential Eqaattans 1" 5.”! Series Selufiens Near a Re lar Singular PD' 1‘ P rt 11 336 [.3 t'iassil‘iei'itinn of Differential Equatiuns 19 5-3 Beggars Equatifln m gu 1“ " a 1,4 HihltlfiL'Eli Remarks 26 _ . Chapter 6 The Laplace Transform 307 Chapter 2 First Order Differential Equatiens 31 ____....——-__-_——-.___—'—___ I i 2.! l inear Filtratiuns: Methud tit Integrating Faetnrs 3'1 6‘1 Definftmn [If Eh? Laplace Tmsfflrm 3'” 3.: sit-smas- ELfULtliHI‘I‘H 42 5-2 Sfllullfln 01: InitiaWalue Problems 314 1}. Hindi-Int: with l'tl'H't (thlet' Etttlatinns SH 6'3 Strap Fumfuflns 325 3.4 |.1ttt:.'+-..-Hee_w Heineen Lineat anti Nrmlineitr eqtatirins 63 6.4 Differential Equatians with Diseentinueas Fereing Funetiens 332 if? Mutant-litmus i'.‘.L|lJil[lE.1'lT"i anti Peptilaliun Dynamics 78 6'5 Impu‘se Funfliflfls 34“ 3 1'1 Int. “.1 iT'.]L1t1iii.+|1s and Integrating Faelrirs 94 6'6 Thfl canvalmifln Integral 346 *.‘.lr-H.__“L~IJIgal-11.“rimmi-.:'|~.. I 1ii-_.t -. T‘x'ielhnil 1”] HI | -. a an..- .th |_~|:IL._1HL.-.i-..-~;.'1 is...,...'-m III! “M Systems of First Order Linear Equations 355 w i t at!” Fuller-“v.1 Ills-whet” “9 w 7.1 Intreduetien 355 7.2 Review ef Matrices 364 Chapter 3-; “Trait-“vii ’7" 'JH Li‘s-‘3” Ett'-r:'Li"-"'---‘-~ 1J5 13 Linear Algebraie Equatiens: Linear Independence. Eigemalues _—mnvn——- ' t Hm...» I .2 11.; -.||_i.lr11ii"t-'-'.:l.:}'- mist.th I;"'I.iei'itt;'ii."|tl.s 1.35 Eigenvecmrs 374 5. “ml-.. HUI mu...“ Hi L in.“ [.].,|,.H.E1L.m..,m Efilufltiunfi 143 7-4 Basie Thee-r3! af Systems af First Order Linear Equatiens 385 [ In. M HM" I...l_1._ I“... In“ It.” tH.-i...mm;m 153 15 Hamegeneeus Linear Systems with Censtant feettieients .390 H I “mils-a tun-1.». mt rh; t'l1.:rt-..-t-.-rjslit: Finn-"itinn 15*} 7.6 Cerepies Eigenvalues 401 3.5 living-'14 . Ii Hum ~1 Hu'tltlL-JHH III E iTLiL'I' Hiil 7*? Fundamental Matrices 414 Mi Nnnih Ittil'gettt‘tnls i'ttiil'iil'iisfi Melitta] Hi i 't‘itJeleI'mined Cneffieients 175 7.3 Repeated Eigenralaes 2:". 3.? Val'islmn wt P.“ :n-:tt..t'-. this 19 Nenhemegenenns Linear Systems 43] RH Mechanleai .md i_|et.'lt'it;.tl ‘s'il‘rt'tiiiHIts 1‘93 3.” Fureed Vibraliuns 2“? Chapter 3 Numerical Metheds 441 8.1 The Euler arTaneent Line Methud 4-11 Chapter 4 Higher Order Linear Equatiens 219 ‘- :- s..__._ _ 3.2 Improvements en the Enter steam 451 -L| lieneral'fiienry ni' nth Order Linear Equatinns 219 8.3 The Runge—Kutta Melhed 45'? 4.2 Hnningenenus Equaliiins with ("nastith (Tneilieients 324 8.4 Mullislep Methads 463 4.3 'Hie Pi‘itliiifld nt' Undetermined (“iiet'lieients 233 8.5 Mare en Errers: Stabiliti' “‘3 4-4 “1L” ML‘HIUL} Hi thrialii'tn Dr Parameters 23'? 811 Systems t‘if First Order Equatiuns 473 xvi u '7‘ Autunumnus Systems and e; stems 5m IntTOdllCthl'l “.4 (trumpeting Species 515 *Jfi PtedstnrJ’rey Equalinns 523 |_,ittptinttt"s Secttnd Methnd 536 it? Perindic Sulutiuns end Limit Cycles 547 its (“linens and Strange Attrticturs: The Lnrenz Equations 553 Partial Differential Equations and Fourier Series 559 Htl 'l'tt-n—i’nirtl l'h'tunthtrjt- Value Prnhlents 569 ML? Ftturit+rHeI'ies 5% NH I‘ltei-tuuriel'{'nneereeneeThctit‘ent 537 tit—1 liten and field i‘llt'IIIIit'tFIH 594 “this 1"'rL'|"+.tl'LtllHFrHi ‘t’uriuhies: Heat ("tinduetittn in a Red 603 lth {Illitei iii'itl {I 'ttl‘rtitJL'tittn Plul'tiet't'lfi III? Ih- We. - r Lititi'itTli' ‘t ihiernuus u! an Elastic String 623 iii "i I I-1' I-'-' i_1'liri'.| "" {IJH . * _ In this eha ter we I in v ' I ' - - me. i f.~ Heiv .tllttti u; the Hex-tit ._utLtuetien Equatlen 649 (THE t. r , 1? 5E Era] different “HI-*3 “3' 2-1“? PefiPC-Em'e In 301.1! stuet e-t _ 1 . r . , H I- I i H. m H . iqmlinn fl,“ 1 TE“ 13 Equallflns First.we use two: problems teillustrate scene of the haste-idem rJI_r i_!.- '1 I L i“: ~t [:1' , '._ _ L _ __._ .. _ _ that we mu W’th m and Eiabflmw “P0” [TEQUEflliF lht'eugheut the remainder at the banks Latenwe indicate several ways ef classifying cqustiens in etder tn preside urgentzattnnal structure fer the beek. Finali}: tte eutline senme cit" the major trends Chapter 11 III-L IJHd r1; 1'.i-I'itt Fr-.i_tiett.-s [i537 mg. 1 I I “in I “I! I m- l“ 1 Pum- Hmmdm hm: thlemfi 657 in the htstertcsl devetepment of the subject and mentic-n a tee eut the etutstsndtne .. I I] , _ _ _ I _ _ ' mathflmfltlfllflflfi Whfl have eentrihuted In it. The studs ef differential equsttem this it sun .11, r .41: tile mun-thus Hill-'6 FINIJIL'IW fifi-‘J attracted the attentien et' mans ef the world‘s greatest mdthimdlifiiinh dunner the HA t.1t..,t..,.,s..ld,_,m” l';l,L”-H_Lm. mu“; [ll-Hmcme (,79 past three centuries Nevertheiesse it remains :1 estimate fielel ett' iantrt ladder-s Eh ILL! hmeului HHII m- | inm-ille i’ruhieitts (395 many interesting GPEH Clue-slicing 11.5 Further I‘let.'il1ttl'i't*-ttll the stetlmtt nl' Septu‘stien nt‘Varit-tbles: A Bessel Serieslzsl‘stl'ishut 7H2 [1h Series tit th‘tlmennni i’unelinus: Mean (femeergcnce 709 1 1 Same Basic Mathematical Mfld8|5 D-TECt' t ; l IUD it? 3 Answers tn Pruhlernte 7'19 . . . . . Befnre entbarktngen a serious study ell dtlletettlml .-e.,_=.t-iti=tt:- t‘: -r e t. . e ing this heel-t er majer portions nt' it]. you sitt'tulJ heme sans. iete. :‘ee . ~ benefits In he gained [1}; doing set. Ft‘tt' sum-e students the emit-I» -. ._..e.:. subject itself is eneugh ntetit'atitin. but hit most tt is the tit-“him- . applieatiens In other fields ll'tttl makes the untlettgtsitte 'I‘In1'iih‘thil‘i‘ti- Many ef the principles er huts. underttint: the hehnt itu‘ nut the :1 tutu. .i'. t- - _ statements er relatieins insulting rates Ltl tthtch lhll'ttlt- were: “ten -_ e. . : in mathematical terms. the relations are equtttmns and the Lites the tte ::-..t1--.._ Equalitiescentsiningdcrh'sth'esaredtflerentinlequstium. [hetetttteretest-t . e- and to itwesligate prnbletus il‘tt't‘ti‘t'ilttl the nttttien ert' fluids the item etutfi . electric circuits. the dissipatien e!" heat in sentid t‘tbieets. the prnpseetttt In .H'lti :e e1 we: I Indes ?31 ...
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303 Solutions - H_________._ EIGHTH EDITION Elementary...

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