Mathematical Analysis of Problems in the Natural Sciences

  • Vladimir┬áZorich

Table of contents

  1. Front Matter
    Pages i-xi
  2. Analysis of Dimensions of Physical Quantities

    1. Front Matter
      Pages 1-3
    2. Vladimir Zorich
      Pages 5-10
    3. Vladimir Zorich
      Pages 11-21
  3. Multidimensional Geometry and Functions of a Very Large Number of Variables

  4. Classical Thermodynamics and Contact Geometry

    1. Front Matter
      Pages 77-79
    2. Vladimir Zorich
      Pages 81-89
    3. Vladimir Zorich
      Pages 91-97
    4. Vladimir Zorich
      Pages 99-123
  5. Back Matter
    Pages 125-135

About this book


Vladimir A. Zorich is a distinguished Professor of Mathematics at the University of Moscow who solved the problem of global homeomorphism for space quasi-conformal mappings and provided its far-reaching generalizations. In Mathematical Analysis of Problems in Natural Sciences, he uses a lively and accessible style to unify three topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large numbers of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. This text corresponds to a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences such as hydrodynamics, thermodynamics, statistical physics and information theory. It includes a nice set of problems and contains many historical remarks. It also contains an appendix featuring Zorich's popular article, "Mathematics as language and method." It is ideal for students and professors of mathematics and physics but is also relevant to chemists and biologists as well as engineers and researchers in various areas of the natural sciences.


contact geometry dimensional analysis of physical quantities principle of concentration thermodynamics transmission of information turbulence

Authors and affiliations

  • Vladimir┬áZorich
    • 1
  1. 1., Department of MathematicsMoscow State UniversityMoscowRussian Federation

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-14812-5
  • Online ISBN 978-3-642-14813-2
  • About this book