Numerical Approximation Methods: π ≈ 355/113 PDF
Preview Numerical Approximation Methods: π ≈ 355/113
Numerical Approximation Methods Harold Cohen Numerical Approximation Methods 355 p (cid:1) 113 HaroldCohen DepartmentofPhysicsandAstronomy CaliforniaStateUniversity LosAngeles,California USA [email protected] ISBN978-1-4419-9836-1 e-ISBN978-1-4419-9837-8 DOI10.1007/978-1-4419-9837-8 SpringerNewYorkDordrechtHeidelbergLondon LibraryofCongressControlNumber: 2011932169 MathematicsSubjectClassification(2010):65L-xx,65M-xx,65N-xx,65Q-xx,65R-xx,65T-xx #SpringerScience+BusinessMedia,LLC2011 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionof the publisher (SpringerScience+Business Media, LLC, 233 SpringStreet, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,evenifthey arenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyare subjecttoproprietaryrights. Coverdesign:Thecoverofthistextcontainsahighlyaccuraterationalfractionapproximationofp. This approximation was initially discovered in the 5th century by a Chinese mathematician named ZuChongzi(see,forexample,Solomon,R.,2008,p.15). Itwasrediscoveredbytheauthorin2005 duringadayofextremeboredom. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) This book is dedicated to the most important people in my life. Foremost among these are: my wife Helen, my daughters Lisa and Allyson, my son David andmy son-in-law Jeff. Itisalsodedicatedtothememoryofmyparents. IalsodedicatethisworktothememoryofDr.CharlesPine whosekindnessandacademicnurturinghelpedmetorecognize thebeautyofmathematicsanditsapplicationstoscientificproblems. Iam. ThereforeIthink. Preface Approximate solutionstomanyproblems thatcannot be solvedanalytically,arise from numerical and other approximation techniques. In this book, the numerical methods and algorithms are developed for approximating such solutions. It also includessomemethodsofcomputationthatyieldexactresults. Thisbookisappropriateasatextforacourseincomputationalmethodsaswellas areferenceforresearcherswhoneedsuchmethodsintheirwork.Thebookcontains a presentation of some well-known approximation methods that are scattered throughoutexistingliteratureaswellastechniquesthatareobscuresuchasChio’s methodforevaluatingadeterminantinch.5andNamias’extensionoftheStirling approximationtothegammafunctionforlargeargumentinAppendix3.Material that seems to be original is also presented; such as evaluating integrals using Parseval’stheoremforperiodicfunctions,betaandgammafunctions,andHeaviside operator methods, along with solving integral equations with singularkernelsand numericalevaluationofCauchyprinciplevalueintegrals. To provide the reader with concrete applications of these methods, the book reliesheavilyonillustrativeexamples.Ihaveprovidedatableofexamples(likea table of contents) with descriptive titles to give the reader quick access to these illustrations. ThismanuscriptwaspreparedusingMicrosoftWordandMathType.MathType is an equation editor developed and marketed by Design Science Co. of Long Beach, California. Because of constraints encountered using these programs, it is sometimesnecessarytopositionamathematicalexpressioninasentencethatdoes not fit on the same line as the text in that sentence. Such expressions have been placedonaseparateline,centeredonthepage.Theyshouldbereadasiftheywere textwithinthesentence.Theseexpressionsaredistinguishedfromequationsinthat theyareinthecenterofthepage,theydonotcontainan“equal”(¼),“notequal” (6¼), or “inequality” (>, (cid:3), etc.) symbol and are not designated with an equation number. Equations are displayed starting close to or at the left margin, have one or more equal, not equal or inequality symbols, and are identified by an equation number. An example of this “out of line” part of a sentence can be found at the bottomofpage133. ix
Description:The list of books you might like
