<p> </p><p></p><p> </p><p>HANDBOOK OF MATHEMATICS FOR ENGINEERS AND SCIENTISTS<br> Andrei D. Polyanin<br> Alexander V. Manzhirov</p><p>PREFACE<br>Thisbookcanbeviewedasareasonablycomprehensivecompendiumofmathematical<br>de?nitions,formulas,andtheoremsintendedforresearchers,universityteachers,engineers,<br>andstudentsofvariousbackgroundsinmathematics.Theabsenceofproofsandaconcise<br>presentationhaspermittedcombiningasubstantialamountofreferencematerialinasingle<br>volume.<br>Whenselectingthematerial,theauthorshavegivenapronouncedpreferencetopractical<br>aspects,namely,toformulas,methods,equations,andsolutionsthataremostfrequently<br>usedinscienti?candengineeringapplications.Hencesomeabstractconceptsandtheir<br>corollariesarenotcontainedinthisbook.<br>? Thisbookcontainschaptersonarithmetics,elementarygeometry,analyticgeometry,<br>algebra,differentialandintegralcalculus,differentialgeometry,elementaryandspecial<br>functions,functionsofonecomplexvariable,calculusofvariations,probabilitytheory,<br>mathematicalstatistics,etc.Specialattentionispaidtoformulas(exact,asymptotical,and<br>approximate),functions,methods,equations,solutions,andtransformationsthatareof<br>frequentuseinvariousareasofphysics,mechanics,andengineeringsciences.<br>? Themaindistinctionofthisreferencebookfromothergeneral(nonspecialized)math-<br>ematicalreferencebooksisasigni?cantlywiderandmoredetaileddescriptionofmethods<br>forsolvingequationsandobtainingtheirexactsolutionsforvariousclassesofmathematical<br>equations(ordinarydifferentialequations,partialdifferentialequations,integralequations,<br>differenceequations,etc.)thatunderliemathematicalmodelingofnumerousphenomena<br>andprocessesinscienceandtechnology.Inadditiontowell-knownmethods,somenew<br>methodsthathavebeendevelopingintensivelyinrecentyearsaredescribed.<br>? Fortheconvenienceofawideraudiencewithdifferentmathematicalbackgrounds,<br>theauthorstriedtoavoidspecialterminologywheneverpossible.Therefore,someofthe<br>methodsandtheoremsareoutlinedinaschematicandsomewhatsimpli?edmanner,which<br>issuf?cientforthemtobeusedsuccessfullyinmostcases.Manysectionswerewritten<br>sothattheycouldbereadindependently.Thematerialwithinsubsectionsisarrangedin<br>increasingorderofcomplexity.Thisallowsthereadertogettotheheartofthematter<br>quickly.<br>Thematerialinthe ?rstpartofthereferencebookcanberoughlycategorizedintothe<br>followingthreegroupsaccordingtomeaning:<br>1.Themaintextcontainingaconcise,coherentsurveyofthemostimportantde?nitions,<br>formulas,equations,methods,andtheorems.<br>2.Numerousspeci?cexamplesclarifyingtheessenceofthetopicsandmethodsfor<br>solvingproblemsandequations.<br>3.Discussionofadditionalissuesofinterest,givenintheformofremarksinsmall<br>print.<br>Forthereader!ˉsconvenience,severallongmathematicaltables?nitesums,series,<br>inde?niteandde?niteintegrals,directandinverseintegraltransforms(Laplace,Mellin,<br>andFouriertransforms),andexactsolutionsofdifferential,integral,functional,andother<br>mathematicalequations!awhichcontainalargeamountofinformation,arepresentedi<br>thesecondpartofthebook........</p><br>