Overview
- Development of an intuitive understanding that complements rigorous mathematics
- Makes advanced mathematical tools and concepts accessible to non-experts
- Presentations in all Chapters is supplied with exercises
Part of the book series: Compact Textbooks in Mathematics (CTM)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.
Reviews
“This book is an invitation to the young researcher to start using modern asymptotic methods of the applied mathematics of multiscale systems.” (Adrian Muntean, zbMATH 1441.35001, 2020)
Authors and Affiliations
About the authors
Leonid Berlyand is a Professor of Mathematics, and a member of the Materials Research Institute and Huck Institutes for Life Sciences at the Pennsylvania State University (USA) as well as an Honorary Professor (Professoris Honoris Cavza) at the Moscow State University. Leonid Berlyand is an internationally recognized expert in applied mathematics. He has made fundamental contributions to homogenization theory, mathematical Ginzburg-Landau theory, and mathematical biology.
Volodymyr Rybalko works as a senior research fellow in Mathematical Division, B.Verkin Institute for Low Temperature Physics and Engineering of National Academy of Sciences of Ukraine. He is an expert in the area of PDEs, he is known, in particular, for his contributions in homogenization theory.
Bibliographic Information
Book Title: Getting Acquainted with Homogenization and Multiscale
Authors: Leonid Berlyand, Volodymyr Rybalko
Series Title: Compact Textbooks in Mathematics
DOI: https://doi.org/10.1007/978-3-030-01777-4
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-030-01776-7Published: 29 November 2018
eBook ISBN: 978-3-030-01777-4Published: 22 November 2018
Series ISSN: 2296-4568
Series E-ISSN: 2296-455X
Edition Number: 1
Number of Pages: XVIII, 178
Number of Illustrations: 28 b/w illustrations, 14 illustrations in colour
Topics: Computational Science and Engineering, Mathematical and Computational Engineering, Partial Differential Equations