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Compact Textbooks in Mathematics

Getting Acquainted with Homogenization and Multiscale

Authors: Berlyand, Leonid, Rybalko, Volodymyr

  • 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 
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Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-01777-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-030-01776-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.


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. 


Table of contents (11 chapters)

  • Preliminaries

    Berlyand, Leonid (et al.)

    Pages 1-15

  • What Is Homogenization and Multiscale? First Examples

    Berlyand, Leonid (et al.)

    Pages 17-33

  • Brief History and Surprising Examples in Homogenization

    Berlyand, Leonid (et al.)

    Pages 35-43

  • Formal Two-Scale Asymptotic Expansions and the Corrector Problem

    Berlyand, Leonid (et al.)

    Pages 45-52

  • Compensated Compactness and Oscillating Test Functions

    Berlyand, Leonid (et al.)

    Pages 53-58

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-01777-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-030-01776-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Getting Acquainted with Homogenization and Multiscale
Authors
Series Title
Compact Textbooks in Mathematics
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-01777-4
DOI
10.1007/978-3-030-01777-4
Softcover ISBN
978-3-030-01776-7
Series ISSN
2296-4568
Edition Number
1
Number of Pages
XVIII, 178
Number of Illustrations
28 b/w illustrations, 14 illustrations in colour
Topics