Mathematical Analysis of Problems in the N...

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Beschreibung

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."

Über den Autor

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.

Zusammenfassung

Short course of natural sciences Enables further developments in various directions Brilliantly manifested profound applications of fundamental mathematics

Includes supplementary material: [...]

Inhaltsverzeichnis

Part I Analysis of Dimensions of Physical Quantities: 1 Elements of the theory.- 2 Examples of applications.- 3 Further applications: hydrodynamics and turbulence.- Part II: Multidimensional Geometry and Functions of a Very Large Number of Variables: 1 Some examples of functions of very many variables in natural science and technology.- 2 Concentration principle and its applications.- 3 Communication in the presence of noise.- Part III Classical Thermodynamics and Contact Geometry: 1 Classical thermodynamics (basic ideas).- 2 Thermodynamics and contact geometry.- 3 Thermodynamics classical and statistical.- References.- Appendix. Mathematics as Language and Method

Details

Erscheinungsjahr:	2014
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xi 133 S.
ISBN-13:	9783642430046
ISBN-10:	364243004X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Zorich, Vladimir
Übersetzung:	Gould, Gerald G.
Hersteller:	Springer Berlin Springer Berlin Heidelberg
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Vladimir Zorich
Erscheinungsdatum:	29.09.2014
Gewicht:	0,236 kg