Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel

135 Pages·2021·5.112 MB·English

by  Sujaul Chowdhury

ℝ
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
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books provide concise, original presentations of important research and O
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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
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SujaulChowdhury
2021
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Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedin
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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