A claw analysis of equations with private derivatives and secondary calculus

The book is devoted to the basics of an algebraic and geometric approach to the theory of nonlinear differential equations. It includes ideas from the theory of integrated systems, the formal theory of differential equations in its modern claws, given by D. Spencer and H. Goldschmidt, and differential calculus over the switching algebras.
The main result of such a synthesis is differential calculus on new geometric objects - many -formal decisions of the differential equation (dipphyotope) This “secondary calculus” shows the deep claw nature of the general theory of differential equations and indicates the new directions of its further development.
The author describes the existing and potential applications of secondary differential calculus, ranging from algebraic geometry and ending with the theory of field, classical and quantum, including such areas as characteristic classes, differential invariants, theory of geometric structures, variational calculation, management theory, etc. D.
The book is designed for senior students, graduate students and researchers interested in all areas of mathematics where non -linear differential equations are used and studied, including algebraic and differential geometry and topology, variational calculation and control theory, continuous media, mathematical mechanics, mathematical and theoretical physics