Mathematical models. Theoretical physics and analysis of complex systems. From the formalism of classical mechanics to quantum interference. Golovinsky P.A.

This monograph sets out the most important mathematical models of material points, linear field, nonlinear vibrations and structures, as well as statistics and hierarchy of complex systems. General models are built on the basis of specific scientific and technical tasks. The peculiarity of the monograph is in the fastest transition to applications. For the convenience of readers, the material is presented in two actually independent parts.

This book is the first part of the monograph and consists of two sections. The first section is devoted to mathematical models that arise in the classical mechanics of the material point or system of material points, and the description of their movement in space and time. It gives the foundations of dynamic systems and variational calculus, symmetry and balance are considered from the point of view of the theory of disasters, as well as some asymptotic methods. In the second section of the books, linear distributed systems are studied. Models of deformation and waves are given in continuous media with small amplitudes of disturbances. These models are united by the fact that they are linear and continuous, which allows the use of a single apparatus of differential equations in private derivatives. Applications to the tasks of waves in liquid, gases and solid bodies, as well as radiation, distribution and diffraction of electromagnetic waves are considered. The possibilities of the modern mathematical apparatus of the Voyletes are shown. A brief description of the dynamics and optimal management of quantum systems, taking into account the phenomena of quantum interference.

The monograph is intended for students and graduate students of technical universities, as well as for experts in applied mathematics, physics and mathematical modeling.