Mathematical Analysis of Problems in the Natural Sciences

2011
ISBN: 978-3-642-43004-6
Verlag: Springer

Buch, Englisch, 133 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 236 g

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general 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 number 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. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Zorich, Vladimir

Weitere Mitwirkende

Gould, Gerald G.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Part I Analysis of Dimensions of Physical Quantities.- Part II: Multidimensional Geometry and Functions of a very large Number of Variables.- Part III Classical Thermodynamics and Contact Geometry.- References.- Appendix

Über Autor(innen)

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.