ABSTRACT
This chapter considers the classic method of obtaining mathematical models of physical phenomena. The analysis of the physical phenomenon is a work of the physicist. However, the obtained mathematical model is a real mathematical problem. Then the theorist mathematician analyses the concrete properties of this model. In mathematical physics, the difficulties encountered in justification of passage to the limit in the construction of mathematical models are often not given due attention. The analytic solution of the mathematical physics problems can be obtained only for easy enough partial cases. The convergence is one of the most important and difficult mathematical operations, in the realization of which it is necessary to have the maximum caution. The physicist tries to understand the studied phenomenon and often does not think about the technical mathematical difficulties. Indeed, the justification of mathematical procedures is the business of the professional mathematicians.
