Mathematical models: Theoretical physics and analysis of complex systems. From the formalism of classical mechanics to quantum.
Please sign in so that we can notify you about a reply
This monograph presents the most important mathematical models of material points, linear fields, nonlinear oscillations and structures, as well as statistics and hierarchies of complex systems. The general models are based on specific scientific and technical problems. The peculiarity of the monograph lies in the rapid transition to applications. For the convenience of readers, the material is presented in two practically independent parts.
This book is the first part of the monograph and consists of two sections. The first section is dedicated to mathematical models arising in classical mechanics of material points or systems of material points, and describes their motion in space and time. It covers the basics of dynamic systems and variational calculus, symmetries and equilibrium from the perspective of catastrophe theory, as well as some asymptotic methods. The second section of the book explores linear distributed systems. It presents models of deformation and waves in continuous media with small perturbation amplitudes. These models are characterized by being linear and continuous, allowing the use of a unified apparatus of partial differential equations. Applications to problems of waves in liquids, gases, and solids, as well as radiation, propagation, and diffraction of electromagnetic waves are discussed. The capabilities of modern wavelet mathematical apparatus are demonstrated. A brief description of the dynamics and optimal control of quantum systems considering quantum interference phenomena is provided.
The monograph is intended for students and postgraduates of technical universities, as well as for specialists in the field of applied mathematics, physics, and mathematical modeling.
Author:
Author:Golovinskiy P.A.
Cover:
Cover:softcover
Category:
- Category:History & Geography
- Category:Science & Math
Publication language:
Publication Language:Russian
Paper:
Paper:offset
Dimensions:
Dimensions:22x15x2 cm
Age restrictions:
Age restrictions:16+
ISBN:
ISBN:978-5-9710-8838-7
No reviews found