Inequalities: With Applications to Engineering PDF
Preview Inequalities: With Applications to Engineering
Michael J. Cloud · Byron C. Drachman Leonid P. Lebedev Inequalities With Applications to Engineering Second Edition Inequalities Michael J. Cloud • Byron C. Drachman Leonid P. Lebedev Inequalities With Applications to Engineering Second Edition 123 MichaelJ.Cloud ByronC.Drachman DepartmentofElectricalEngineering DepartmentofMathematics LawrenceTechnologicalUniversity MichiganStateUniversity Southfield,MI,USA EastLansing,MI,USA LeonidP.Lebedev DepartmentofMathematics NationalUniversityofColombia Bogota´DC,CUNDINAMARCA Colombia ISBN978-3-319-05310-3 ISBN978-3-319-05311-0(eBook) DOI10.1007/978-3-319-05311-0 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014936604 MathematicsSubjectClassification(2010):26Dxx,00A69,00A06 ©SpringerInternationalPublishingAG1998,2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpub- lication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityforany errorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespect tothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) To DanielLee Pokora—MJC To MichaelEverettDrachman—BCD Foreword Thisbookischockfullofinteresting,beautiful,andusefulmathematics.Itshouldbe studiedandconsultedbyengineerswhowishtounderstandtheorigins,properties, andlimitationsofmathematicalmodelscommonlyused,forinstance,incomputer simulationsofengineeringreality.The studyofinequalitiesisessentialfor under- standingtheapproximationmethodsrequiredforcomputinginengineering,which onestouse,andhowtousethem. You will find this second edition of Inequalities full of enlightening exercises. Youwillbetterunderstandhowtoanalyzeandimprovecomputermodelsofengi- neering designs. Learn by working through the exercises. You will find it is well worththeeffort.Trythemfirst.Ifyougetstuck,thereareoverthirtypagesofgen- eroushintsto encourageyourprogress.Seta reasonablepace foryourselfaswith anyexerciseprogram,andyouwillgetstrongerandtheexerciseswillseemeasier asyougoalong. Iampleasedthattheauthorsdecidedtoaddachapter,inthisnewedition,intro- ducingintervalanalysistothereader.Itconcernsmethodsforcomputingintervals enclosingexactresults,thatistosaysimultaneousupperandlowerboundsonso- lutionsofequations.This,inspiteoferrorsduetofiniteapproximationoflimiting processes,roundofferrors,anduncertaintyininputvaluesofmeasuredquantities. Worthington,Ohio RamonE.Moore January2014 vii Preface Onemightwonderwhyitisnecessarytostudyinequalities.Manyappliedscience andengineeringproblemscanbepursuedwithouttheirexplicitmention.Neverthe- less, a facility with inequalitiesis required to understand much of mathematics at intermediateandhigherlevels.Inequalitiesserveanaturalpurposeofcomparison. Theycanprovideindirectroutesofreasoningorproblemsolvingwhenmoredirect routesseeminconvenientorunavailable.Unfortunately,theyaremuchneglectedin thetypicalWesternengineeringcurricula. Thissmallguidetoinequalitieswasoriginallywrittenwithengineersandapplied scientists in mind. Commentsfrom mathematicianswho saw the first edition lead ustohopethatsomemathematicianswillfindtheapplicationsinteresting,andthat students of mathematics will also find the book useful. A Japanese translation of thefirstedition,renderedbySatoshiKaizuofIbarakiUniversity,waspublishedby MorikitaShuppanin2004. Thebookisintendedtohelpfillthegapbetween“collegealgebra”treatmentsof inequalitiesandthetreatisesthatexistinthemathematicsliterature.Unlikeclassic booksoninequalities,itconsiderstopicssuchascontinuityandmax–minproblems insomedetail;althoughthesearetraditionaltopicsincalculus,wewishtoempha- size that they are based on the solution of inequalities. Important techniques are reinforcedthrough problems at the end of each chapter, and hints are included to expeditethereader’sprogress.We reviewafewtopicsfromcalculus,butmakeno attemptatathoroughreview.Inordertosimplifythediscussion,weusehypotheses strongerthannecessaryinsomeofthestatementsorproofsoftheoremsandinsome oftheproblems.Forareviewofcalculus,werecommendthefineclassicbyLandau [45].Amongthemanygoodbooksonanalysis,wecanrecommendStromberg[86]. Twonewchapterswereaddedforthesecondedition.Chapter6presentscertain inequalitiesthatplay importantrolesin the study of differentialequationsand the boundaryvalueproblemsofmechanics.Chapter7offersanintroductiontointerval analysis, a branch of mathematics that provides (among other things) a powerful wayofautomatingworkwithinequalities.Inaddition,Chap.1hasbeenrestructured andnewexamplesandproblemsappearthroughoutthebook. ix
The list of books you might like
