Sequential models of mathematical physics

著者

    • Serovajsky, Simon

書誌事項

Sequential models of mathematical physics

Simon Serovajsky

CRC Press, 2020, c2019

  • : pbk

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注記

Includes bibliographical references (p. 249-260) and index

内容説明・目次

内容説明

The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc. In Sequential Models of Mathematical Physics, the author considers the justification of the process of constructing mathematical models. The book seeks to determine the classic, generalized and sequential solutions, the relationship between these solutions, its direct physical sense, the methods of its practical finding, and its existence. Features Describes a sequential method based on the construction of space completion, as well as its applications in number theory, the theory of distributions, the theory of extremum, and mathematical physics Presentation of the material is carried out on the simplest example of a one-dimensional stationary heat transfer process; all necessary concepts and constructions are introduced and illustrated with elementary examples, which makes the material accessible to a wide area of readers The solution of a specific mathematical problem is obtained as a result of the joint application of methods and concepts from completely different mathematical directions

目次

I Mathematical physics problems 1 Classic models 2 Generalized models II Sequential method 3 Convergence and Cauchy principle 4 Completeness and real numbers 5 Real numbers and completion III Sequential objects 6 p-adic numbers 7 Sequential controls 8 Distributions IV Sequential models 9 Sequential models of mathematical physics phenomenon

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