Table Of Contentℝ
Series ISSN: 1938-1743
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Series Editor: Steven G. Krantz, Washington University in St. Louis
Monte Carlo Methods
MA Honanted sC-Oarnlo C Momepthutoadtisonal Introduction Utilizing Excel
A Hands-On
Sujaul Chowdhury, Shahjalal University of Science and Technology
This book is intended for undergraduate students of Mathematics, Statistics, and Physics who
know nothing about Monte Carlo Methods but wish to know how they work. All treatments
M Computational
have been done as much manually as is practicable. The treatments are deliberately manual to
O
N
let the readers get the real feel of how Monte Carlo Methods work.
T
Definite integrals of a total of five functions F(x), namely Sin(x), Cos(x), ex, loge(x), E C
and 1/(1+x2), have been evaluated using constant, linear, Gaussian, and exponential probability A
R
Introduction
L
density functions p(x). It is shown that results agree with known exact values better if p(x) is O
proportional to F(x). Deviation from the proportionality results in worse agreement. M
E
Two separate chapters have been dedicated to Variational Quantum Monte Carlo T
H
method applied to ground state of simple harmonic oscillator and of Hydrogen atom. The book O
D Utilizing Excel
is intended to aid hands-on learning of Monte Carlo method. S
Sujaul Chowdhury
About SYNTHESIS
TDhigisi tvaol lLumiber aisr ya porfi nEtendg ivneeresiroinng o fa an wd oCrko mthpaut taeprp eSacrise ninc eth. e SSyynntthheessiiss M
books provide concise, original presentations of important research and O
R
development topics, published quickly, in digital and print formats. G
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store.morganclaypool.com P
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Monte Carlo Methods
A Hands-On Computational Introduction
Utilizing Excel
Synthesis Lectures on
Mathematics and Statistics
Editor
StevenG.Krantz,WashingtonUniversity,St.Louis
MonteCarloMethods:AHands-OnComputationalIntroductionUtilizingExcel
SujaulChowdhury
2021
CrowdDynamicsbyKineticTheoryModeling:Complexity,Modeling,Simulations,and
Safety
BouchraAylaj,NicolaBellomo,LivioGibelli,andDamiánKnopoff
2020
ProbabilityandStatisticsforSTEM:ACourseinOneSemester
E.N.BarronandJ.G.DelGreco
2020
AnIntroductiontoProofswithSetTheory
DanielAshlockandColinLee
2020
DiscreteDistributionsinEngineeringandAppliedSciences
RajanChattamvelliandRamalingamShanmugam
2020
AffineArithmeticBasedSolutionofUncertainStaticandDynamicProblems
SnehashishChakravertyandSaudaminiRout
2020
TimeFractionalOrderBiologicalSystemswithUncertainParameters
SnehashishChakraverty,RajaramaMohanJena,andSubratKumarJena
2020
FastStartAdvancedCalculus
DanielAshlock
2019
iii
FastStartIntegralCalculus
DanielAshlock
2019
FastStartDifferentialCalculus
DanielAshlock
2019
IntroductiontoStatisticsUsingR
MustaphaAkinkunmi
2019
InverseObstacleScatteringwithNon-Over-DeterminedScatteringData
AlexanderG.Ramm
2019
AnalyticalTechniquesforSolvingNonlinearPartialDifferentialEquations
DanielJ.Arrigo
2019
AspectsofDifferentialGeometryIV
EstebanCalviño-Louzao,EduardoGarcía-Río,PeterGilkey,JeongHyeongPark,andRamón
Vázquez-Lorenzo
2019
SymmetryProblems.TheNavier–StokesProblem.
AlexanderG.Ramm
2019
AnIntroductiontoPartialDifferentialEquations
DanielJ.Arrigo
2017
NumericalIntegrationofSpaceFractionalPartialDifferentialEquations:Vol2–
ApplicatonsfromClassicalIntegerPDEs
YounesSalehiandWilliamE.Schiesser
2017
NumericalIntegrationofSpaceFractionalPartialDifferentialEquations:Vol1–
IntroductiontoAlgorithmsandComputerCodinginR
YounesSalehiandWilliamE.Schiesser
2017
AspectsofDifferentialGeometryIII
EstebanCalviño-Louzao,EduardoGarcía-Río,PeterGilkey,JeongHyeongPark,andRamón
Vázquez-Lorenzo
2017
iv
TheFundamentalsofAnalysisforTalentedFreshmen
PeterM.Luthy,GuidoL.Weiss,andStevenS.Xiao
2016
AspectsofDifferentialGeometryII
PeterGilkey,JeongHyeongPark,RamónVázquez-Lorenzo
2015
AspectsofDifferentialGeometryI
PeterGilkey,JeongHyeongPark,RamónVázquez-Lorenzo
2015
AnEasyPathtoConvexAnalysisandApplications
BorisS.MordukhovichandNguyenMauNam
2013
ApplicationsofAffineandWeylGeometry
EduardoGarcía-Río,PeterGilkey,StanaNikčević,andRamónVázquez-Lorenzo
2013
EssentialsofAppliedMathematicsforEngineersandScientists,SecondEdition
RobertG.Watts
2012
ChaoticMaps:Dynamics,Fractals,andRapidFluctuations
GoongChenandYuHuang
2011
MatricesinEngineeringProblems
MarvinJ.Tobias
2011
TheIntegral:ACruxforAnalysis
StevenG.Krantz
2011
StatisticsisEasy!SecondEdition
DennisShashaandMandaWilson
2010
LecturesonFinancialMathematics:DiscreteAssetPricing
GregAndersonandAlecN.Kercheval
2010
JordanCanonicalForm:TheoryandPractice
StevenH.Weintraub
2009
v
TheGeometryofWalkerManifolds
MiguelBrozos-Vázquez,EduardoGarcía-Río,PeterGilkey,StanaNikčević,andRamón
Vázquez-Lorenzo
2009
AnIntroductiontoMultivariableMathematics
LeonSimon
2008
JordanCanonicalForm:ApplicationtoDifferentialEquations
StevenH.Weintraub
2008
StatisticsisEasy!
DennisShashaandMandaWilson
2008
AGyrovectorSpaceApproachtoHyperbolicGeometry
AbrahamAlbertUngar
2008
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MonteCarloMethods:AHands-OnComputationalIntroductionUtilizingExcel
SujaulChowdhury
www.morganclaypool.com
ISBN:9781636390710 paperback
ISBN:9781636390727 ebook
ISBN:9781636390734 hardcover
DOI10.2200/S01073ED1V01Y202101MAS037
APublicationintheMorgan&ClaypoolPublishersseries
SYNTHESISLECTURESONMATHEMATICSANDSTATISTICS
Lecture#37
SeriesEditor:StevenG.Krantz,WashingtonUniversity,St.Louis
SeriesISSN
Print1938-1743 Electronic1938-1751
Monte Carlo Methods
A Hands-On Computational Introduction
Utilizing Excel
Sujaul Chowdhury
ShahjalalUniversityofScienceandTechnology
SYNTHESISLECTURESONMATHEMATICSANDSTATISTICS#37
M
&C Morgan &cLaypool publishers
ABSTRACT
This book is intended for undergraduate students of Mathematics, Statistics, and Physics who
know nothing about Monte Carlo Methods but wish to know how they work. All treatments
have been done as much manually as is practicable. The treatments are deliberately manual to
letthereadersgettherealfeelofhowMonteCarloMethodswork.
DefiniteintegralsofatotaloffivefunctionsF.x/,namelySin.x/,Cos.x/,ex,log .x/,and
e
1=.1 x2/, have been evaluated using constant, linear, Gaussian, and exponential probability
C
density functions p.x/. It is shown that results agree with known exact values better if p.x/ is
proportionaltoF.x/.Deviationfromtheproportionalityresultsinworseagreement.
ThisbookisonMonteCarloMethodswhicharenumericalmethodsforComputational
Physics. These are parts of a syllabus for undergraduate students of Mathematics and Physics
forthecoursetitled“ComputationalPhysics.”
Needforthebook:Besidesthethreereferencedbooks,thisistheonlybookthatteaches
how basic Monte Carlo methods work. This book is much more explicit and easier to follow
than the three referenced books. The two chapters on the Variational Quantum Monte Carlo
methodareadditionalcontributionsofthebook.
Pedagogical features: After a thorough acquaintance with background knowledge in
Chapter 1, five thoroughly worked out examples on how to carry out Monte Carlo integration
is included in Chapter 2. Moreover, the book contains two chapters on the Variational Quan-
tumMonteCarlomethodappliedtoasimpleharmonicoscillatorandahydrogenatom.
The book is a good read; it is intended to make readers adept at using the method. The
bookisintendedtoaidinhands-onlearningoftheMonteCarlomethods.
KEYWORDS
MonteCarlomethods,basicMonteCarlointegration,variationalquantumMonte
Carlomethod,simpleharmonicoscillator,hydrogenatom
