Mathematical Analysis of Problems in the Natural Sciences (Hardcover)

Vladimir Zorich

ISBN 10: 3642148123 / ISBN 13: 9783642148125

Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2010

Hardcover. 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." 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." Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783642148125

Riassunto:

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."

Informazioni sull?autore: 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.

Dati bibliografici

Titolo: Mathematical Analysis of Problems in the ...
Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
Data di pubblicazione: 2010
Legatura: Hardcover
Condizione: new