Multi-dimensional Monte Carlo Integrations Utilizing Mathematica
Feb 2025 · American Academic Press
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About this ebook
This book provides practical, hands-on demonstration of evaluation of multi-dimensional or high-dimensional definite integrals using Monte Carlo method. We have evaluated a large number of multi-dimensional definite integrals using Monte Carlo method. These are 2, 3, 5, 7 and 10 dimensional definite integrals. We have used mean value method for the evaluations. We have performed function evaluations at random values of the variables gathered as uniform random variates using inverse transform sampling method. We have performed symbolic computations using programs written in Mathematica. Very much smaller number of function evaluations is found to lead to much lower error compared to the case with uniform, non-random sampling i.e. without using Monte Carlo method. This is consistent with what we often hear about a virtue of Monte Carlo method in evaluating multi-dimensional or high-dimensional definite integrals.
This book provides practical, hands-on demonstration of evaluation of multi-dimensional or high-dimensional definite integrals using Monte Carlo method. We have evaluated a large number of multi-dimensional definite integrals using Monte Carlo method. These are 2, 3, 5, 7 and 10 dimensional defin...
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About the author
Sujaul Chowdhury, Ph.D., is a Professor in Department of Physics at Shahjalal University of Science and Technology (SUST). He received his B.Sc. and M.Sc. in Physics from SUST before earning his Ph.D. at The University of Glasgow in 2001. After completing his Ph.D., Dr. Chowdhury was a Humboldt Research Fellow for one year at The Max Planck Institute, Stuttgart. He is the author of many books, including 10 on different topics of Computational Physics with which to conduct the course and Lab titled Computational Physics. His research interests include nanoelectronics, magnetotransport in semiconductor nanostructures, and Nanostructure Physics. Further details about the author and his CV are available at www.sust.edu
Sujaul Chowdhury, Ph.D., is a Professor in Department of Physics at Shahjalal University of Science and Technology (SUST). He received his B.Sc. and M.Sc. in Physics from SUST before earning his Ph.D. at The University of Glasgow in 2001. After completing his Ph.D., Dr. Chowdhury was a Humboldt R...
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