Principles of Partial Differential Equations (Paperback, 2010 ed.)

ThisbookisintendedtogivethereaderanopportunitytomastersolvingPDEpr- lems. Ourmaingoalwastohaveaconcisetextthatwouldcovertheclassicaltools ofPDEtheorythatareusedintoday'sscienceandengineering, suchaschar- teristics, thewavepropagation, theFouriermethod, distributions, Sobolevspaces, fundamentalsolutions, andGreen'sfunctions. WhileintroductoryFouriermethod -basedPDEbooksdonotgiveanadequatedescriptionoftheseareas, themore advancedPDEbooksarequitetheoreticalandrequireahighlevelofmathematical backgroundfromareader. Thisbookwaswrittenspeci?callyto?llthisgap, sat- fyingthedemandofthewiderangeofenduserswhoneedtheknowledgeofhow tosolvethePDEproblemsandatthesametimearenotgoingtospecializeinthis areaofmathematics. Arguably, thisistheshortestPDEcourse, whichstretchesfar beyondcommon, Fouriermethod-basedPDEtexts. Forexample, Hab03], which isacommonthoroughtextbookonpartialdifferentialequations, teachesasimilar setoftoolswhilebeingabout?vetimeslonger. Thebookisproblem-oriented. Thetheoreticalpartisrigorousyetshort. So- timeswereferthereadertotextbooksthatgivewidercoverageofthetheory. Yet, - portanttheoreticaldetailsarepresentedwithcare, whilethehintsgivethereaderan opportunitytorestoretheargumentstothefullrigor. Manyexamplesfromphysics areintendedtokeepthebookintuitiveforthereaderandtoillustratetheapplied natureofthesubject. Thebookwillbeusefulforanyhigher-levelundergraduatecourseandforse- studyforbothgraduateandhigher-levelundergraduatestudents, andforanys- cialtyinsciences. ItsRussianversionhasbeenastandardproblem-solvingmanual atMoscowStateUniversitysince1988, andisalsousedbystudentsofSt. Pete- burgUniversityandNovosibirskUniversities. ItsSpanishversionisusedatMorelia UniversityinMexico, whiletheEnglishdrafthasalreadybeenusedinViennaU- versityandatTexasA&MUniversity. Forfurtherreadingwerecommend Str92], Eva98], and EKS99]. Mu]nchen, AlexanderKomech August2007 AndrewKomech v Acknowledgements The?rstauthorisindebtedtoMargaritaKorotkinaforthefortunatesuggestionto writethisbook, toA. F. Filippov, A. S. Kalashnikov, M. A. Shubin, T. D. Ventzel, andM. I. Vishikforcheckingthe?rstversionofthemanuscriptandfortheadvice. BothauthorsaregratefultoH. Spohn(TechnischeUniversita]t, Mu]nchen)andto E. Zeidler(Max-PlanckInstituteforMathematics, Leipzig)fortheirhospitalityand supportduringtheworkonthebook. BothauthorsweresupportedbyInstituteforInformationTransmissionProblems (RussianAcademyofSciences). The?rstauthorwassupportedbytheDepartment ofMechanicsandMathematicsofMoscowStateUniversity, bytheAlexandervon HumboldtResearchAward, FWFGrantP19138-N13, andtheGrantsofRFBR. The secondauthorwassupportedbyTexasA&MUniversityandbytheNationalScience FoundationunderGrantsDMS-0621257andDMS-0600863. vii Contents 1 Hyperbolicequations. Methodofcharacteristics. . . . . . . . . . . . . . . . . . . 1 1 Derivationofthed'Alembertequation. . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Thed'Alembertmethodforin?nitestring . . . . . . . . . . . . . . . . . . . . . . 7 3 Analysisofthed'Alembertformula. . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4 Second-orderhyperbolicequationsintheplane . . . . . . . . . . . . . . . . . 19 5 Semi-in?nitestring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 6 Finitestring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 7 Waveequationwithmanyindependentvariables . . . . . . . . . . . . . . . . 46 8 Generalhyperbolicequations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2 TheFouriermethod. . . ."

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Problem Books in Mathematics
Release date:	March 2012
First published:	2010
Authors:	Alexander Komech • Andrew Komech
Dimensions:	235 x 155 x 9mm (L x W x T)
Format:	Paperback
Pages:	161
Edition:	2010 ed.
ISBN-13:	978-1-4614-2462-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
LSN:	1-4614-2462-3
Barcode:	9781461424628

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