Mathematical Analysis of Problems in the Natural Sciences - Vladimir Zorich

Mathematical Analysis of Problems in the Natural Sciences

(Autor)

Buch | Softcover
XI, 133 Seiten
2014 | 2011
Springer Berlin (Verlag)
978-3-642-43004-6 (ISBN)
58,84 inkl. MwSt
This book illustrates interactions of pure mathematics with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory. It includes problems, historical remarks and Zorich s article Mathematics as Language and Method.
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."

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.

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

From the reviews:

"Vladimir Zorich has written a short and mathematically advanced text on the natural sciences as seen through mathematics. ... The text touches on many ideas: the dimension of a television signal, the molecular theory of matter, transmission line capacity, to name a few. ... if you want to see how mathematics is intertwined in nature and physics, how mathematics describes and explains our world, then this book paints that picture." (David S. Mazel, The Mathematical Association of America, August, 2011)

Erscheint lt. Verlag 29.9.2014
Übersetzer Gerald G. Gould
Zusatzinfo XI, 133 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 237 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Naturwissenschaften Physik / Astronomie
Schlagworte Analysis • Contact Geometry • dimensional analysis of physical quantities • Information and Communication, Circuits • principle of concentration • thermodynamics • transmission of information • Turbulence
ISBN-10 3-642-43004-X / 364243004X
ISBN-13 978-3-642-43004-6 / 9783642430046
Zustand Neuware
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