The reduction principle is a common idea which states that while researching the stability of solutions of the dynamic system (the system of differential, difference, differential-difference equations) the order of the researched system can be decreased. As the main obstacle in researching a dynamic system is a big dimension of the system, decreasing the order significantly simplifies the stability of the research process.This work contains some ways of decreasing the system order. The author aimed to keep the details to a minimum, to facilitate a better understanding of the main ideas, and the rigor of explanations is replaced by examples and references to the original works.The project Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.
This book presents the Determinant theory with the use of hypercomplex Grassmann figures. It simplifies the proof of many determinant features. It also states several ways of solutions of linear algebraic systems, most of which are connected with the Determinant theory. The teaching experience in technical universities has demonstrated that the suggested way of presenting the Determinant theory is understood more easily. The title of the book is explained by a desire to attract readers’ attention to the well-known in the algebra sphere while introducing a new and more convenient way to present the Determinant theory for technical universities.
The minimax criterion for stability is a sufficient criterion for the motion stability of a mechanical system under the influence of small-amplitude high-frequency parameter oscillations. This criterion allows to find stability conditions of oscillations within a non-stable mechanical system without making motion equations, but instead by way of using only the Lagrangian function L= T – П. Any remarks and recommendations will be appreciated and taken into considerations in the following issues. Please, write to: iaeste@i.ua.
The book "Analytical functions of Matrices" continues the series "Modern Mathematics for Engineers". This project is addressed to upper-course university students in Mathematics specialties, to graduate students, and to researchers who apply Mathematics in different spheres. The project team was inspired by the positive experience of the researchers of the University of California who published the monograph "Modern Mathematics for Engineers" in 1956. The impulse for starting the Project "Modern Mathematics for Engineers" was the fact that 2008 was announced "The Year of Mathematics in Germany".
There are different criteria for the stability of the solution of linear differential equations which are based on the characteristic equation analysis. In this work the reader will find principally new ways of frequency criteria for stability derivation which are based on Perceval formula and a resolution of operator equations in Banach space.
The reduction principle is a common idea which states that while researching the stability of solutions of the dynamic system (the system of differential, difference, differential-difference equations) the order of the researched system can be decreased. As the main obstacle in researching a dynamic system is a big dimension of the system, decreasing the order significantly simplifies the stability of the research process.This work contains some ways of decreasing the system order. The author aimed to keep the details to a minimum, to facilitate a better understanding of the main ideas, and the rigor of explanations is replaced by examples and references to the original works.The project Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.
The minimax criterion for stability is a sufficient criterion for the motion stability of a mechanical system under the influence of small-amplitude high-frequency parameter oscillations. This criterion allows to find stability conditions of oscillations within a non-stable mechanical system without making motion equations, but instead by way of using only the Lagrangian function L= T – П. Any remarks and recommendations will be appreciated and taken into considerations in the following issues. Please, write to: iaeste@i.ua.
This book presents the Determinant theory with the use of hypercomplex Grassmann figures. It simplifies the proof of many determinant features. It also states several ways of solutions of linear algebraic systems, most of which are connected with the Determinant theory. The teaching experience in technical universities has demonstrated that the suggested way of presenting the Determinant theory is understood more easily. The title of the book is explained by a desire to attract readers’ attention to the well-known in the algebra sphere while introducing a new and more convenient way to present the Determinant theory for technical universities.
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