[ Pobierz całość w formacie PDF ]
//-->31CRCstEDITIONstandardMathematicALTABLESandformulaeDANIEL ZWILLINGERCHAPMAN & HALL/CRCA CRC Press CompanyBoca Raton London New York Washington, D.C.© 2003 by CRC Press LLCEditor-in-ChiefDaniel ZwillingerRensselaer Polytechnic InstituteTroy, New YorkAssociate EditorsSteven G. KrantzWashington UniversitySt. Louis, MissouriKenneth H. RosenAT&T Bell LaboratoriesHolmdel, New JerseyEditorial Advisory BoardGeorge E. AndrewsPennsylvania State UniversityUniversity Park, PennsylvaniaMichael F. BridglandCenter for Computing SciencesBowie, MarylandJ. Douglas FairesYoungstown State UniversityYoungstown, OhioGerald B. FollandUniversity of WashingtonSeattle, WashingtonBen FusaroFlorida State UniversityTallahassee, FloridaAlan F. KarrNational Institute Statistical SciencesResearch Triangle Park, North CarolinaAl MardenUniversity of MinnesotaMinneapolis, MinnesotaWilliam H. PressLos Alamos National LabLos Alamos, NM 87545© 2003 by CRC Press LLCPrefaceIt has long been the established policy of CRC Press to publish, in handbook form,the most up-to-date, authoritative, logically arranged, and readily usable referencematerial available. Prior to the preparation of this31stEditionof theCRC StandardMathematical Tables and Formulae,the content of such a book was reconsidered.The previous edition was carefully analyzed, and input was obtained from practi-tioners in the many branches of mathematics, engineering, and the physical sciences.The consensus was that numerous small additions were required in several sections,and several new areas needed to be added.Some of the new materials included in this edition are: game theory and votingpower, heuristic search techniques, quadratic elds, reliability, risk analysis and de-cision rules, a table of solutions to Pell’s equation, a table of irreducible polynomialsin¾Ü, a longer table of prime numbers, an interpretation of powers of 10, a col-lection of “proofs without words”, and representations of groups of small order. Intotal, there are more than 30 completely new sections, more than 50 new and mod-i ed entries in the sections, more than 90 distinguished examples, and more than adozen new tables and gures. This brings the total number of sections, sub-sections,and sub-sub-sections to more than 1,000. Within those sections are now more than3,000 separate items (a de nition , a fact, a table, or a property). The index has alsobeen extensively re-worked and expanded to make nding results faster and easier;there are now more than 6,500 index references (with 75 cross-references of terms)and more than 750 notation references.The same successful format which has characterized earlier editions of theHand-bookis retained, while its presentation has been updated and made more consistentfrom page to page. Material is presented in a multi-sectional format, with each sec-tion containing a valuable collection of fundamental reference material—tabular andexpository.In line with the established policy of CRC Press, theHandbookwill be kept ascurrent and timely as is possible. Revisions and anticipated uses of newer materialsand tables will be introduced as the need arises. Suggestions for the inclusion of newmaterial in subsequent editions and comments regarding the present edition are wel-comed. The home page for this book, which will include errata, will be maintainedØØÔ »»×ÑØ ºÑ Ø Ø Ðatº ÓÑThe major material in this new edition is as follows:Chapter 1:Analysisbegins with numbers and then combines them into series andproducts. Series lead naturally into Fourier series. Numbers also lead to func-tions which results in coverage of real analysis, complex analysis, and gener-alized functions.Chapter 2:Algebracovers the different types of algebra studied: elementary al-gebra, vector algebra, linear algebra, and abstract algebra. Also included aredetails on polynomials and a separate section on number theory. This chapterincludes many new tables.Chapter 3:Discrete Mathematicscovers traditional discrete topics such as combi-natorics, graph theory, coding theory and information theory, operations re-© 2003 by CRC Press LLCsearch, and game theory. Also included in this chapter are logic, set theory,and chaos.Chapter 4:Geometrycovers all aspects of geometry: points, lines, planes, sur-faces, polyhedra, coordinate systems, and differential geometry.Chapter 5:Continuous Mathematicscovers calculus material: differentiation, in-tegration, differential and integral equations, and tensor analysis. A large tableof integrals is included. This chapter also includes differential forms and or-thogonal coordinate systems.Chapter 6:Special Functionscontains a sequence of functions starting with thetrigonometric, exponential, and hyperbolic functions, and leading to many ofthe common functions encountered in applications: orthogonal polynomials,gamma and beta functions, hypergeometric functions, Bessel and elliptic func-tions, and several others. This chapter also contains sections on Fourier andLaplace transforms, and includes tables of these transforms.Chapter 7:Probability and Statisticsbegins with basic probability information (de n -ing several common distributions) and leads to common statistical needs (pointestimates, con d ence intervals, hypothesis testing, and ANOVA). Tables of thenormal distribution, and other distributions, are included. Also included in thischapter are queuing theory, Markov chains, and random number generation.Chapter 8:Scientific Computingexplores numerical solutions of linear and non-linear algebraic systems, numerical algorithms for linear algebra, and how tonumerically solve ordinary and partial differential equations.Chapter 9:Financial Analysiscontains the formulae needed to determine the re-turn on an investment and how to determine an annuity (i.e., the cost of amortgage). Numerical tables covering common values are included.Chapter 10:Miscellaneouscontains details on physical units (de nition s and con-versions), formulae for date computations, lists of mathematical and electronicresources, and biographies of famous mathematicians.It has been exciting updating this edition and making it as useful as possible.But it would not have been possible without the loving support of my family, JanetTaylor and Kent Taylor Zwillinger.ÞÛ ÐÐ Ò Ö ÐÙÑºÑ Øº Ù15 October 2002Daniel Zwillinger© 2003 by CRC Press LLCContributorsKaren BolingerClarion UniversityClarion, PennsylvaniaPatrick J. DriscollU.S. Military AcademyWest Point, New YorkM. Lawrence GlasserClarkson UniversityPotsdam, New YorkJeff GoldbergUniversity of ArizonaTucson, ArizonaRob GrossBoston CollegeChestnut Hill, MassachusettsGeorge W. HartSUNY Stony BrookStony Brook, New YorkMelvin HausnerCourant Institute (NYU)New York, New YorkVictor J. KatzMAAWashington, DCSilvio LevyMSRIBerkeley, CaliforniaMichael MascagniFlorida State UniversityTallahassee, FloridaRay McLenaghanUniversity of WaterlooWaterloo, Ontario, CanadaJohn MichaelsSUNY BrockportBrockport, New YorkRoger B. NelsenLewis & Clark CollegePortland, OregonWilliam C. RinamanLeMoyne CollegeSyracuse, New YorkCatherine RobertsCollege of the Holy CrossWorcester, MassachusettsJoseph J. RushananMITRE CorporationBedford, MassachusettsLes ServiMIT Lincoln LaboratoryLexington, MassachusettsPeter SherwoodInteractive Technology, Inc.Newton, MassachusettsNeil J. A. SloaneAT&T Bell LabsMurray Hill, New JerseyCole SmithUniversity of ArizonaTucson, ArizonaMike SousaVeridianAnn Arbor, MichiganGary L. StanekYoungstown State UniversityYoungstown, OhioMichael T. StraussHMENewburyport, MassachusettsNico M. TemmeCWIAmsterdam, The NetherlandsAhmed I. ZayedDePaul UniversityChicago, Illinois© 2003 by CRC Press LLC
[ Pobierz całość w formacie PDF ]