Numerical Approximation Methods: π ≈ 355/113

500 Pages·2011·1.56 MB·English

by  Harold Cohen (auth.)

Numerical Approximation Methods

Harold Cohen
Numerical Approximation
Methods
355
p (cid:1)
113
HaroldCohen
DepartmentofPhysicsandAstronomy
CaliforniaStateUniversity
LosAngeles,California
USA
[e-mail]
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
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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.
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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
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