Sequential Models of Mathematical Physics

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

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

Simon Serovajsky is a professor of differential equations and control theory at al-Farabi Kazakh National University in Kazakhstan. He is the author of many books published in the area of optimisation and optimal control theory, modelling, philosophy and history of mathematics as well as a long list of high-quality publications in learned journals.