Georgiev S. Differential Equations. Projector Analysis on Time Scales 2024

Textbook in PDF format

This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives, constraints and consistent initial values for the considered equations are defined. A linearization for nonlinear dynamic systems is introduced and the total derivative for regular linearized equations with tractability index one is investigated.
Preface
Introduction
Linear dynamic-algebraic equations with constant coefficients
P-projectors. Matrix chains
First kind linear time-varying dynamic-algebraic equations
Second kind linear time-varying dynamic-algebraic equations
Third kind linear time-varying dynamic-algebraic equations
Fourth kind linear time-varying dynamic-algebraic equations
Jets and jet spaces
Nonlinear dynamic-algebraic equations
Elements of theory of matrices
Fréchet derivatives and Gâteaux derivatives
Pötzsche’s chain rule
Bibliography
Index