Mathematical Analysis of Problems in the Natural Sciences （2011）

Zorich, Vladimir/ Gould, Gerald G. (TRN)

Springer-Verlag Berlin and Heidelberg GmbH & Co. K（2014/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 133 p.
• 言語 ENG
• 商品コード 9783642430046
• DDC分類 501.51

Full Description

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."

Contents

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