UID:
edoccha_9958071907302883
Format:
1 online resource (295 p.)
ISBN:
1-282-76979-0
,
9786612769795
,
0-08-095535-5
Series Statement:
Mathematics in science and engineering ; volume 28
Uniform Title:
Lineĭnye sistemy obyknovennykh different͡sialnykh uravnenii.
Content:
Linear systems of ordinary differential equations, with periodic and quasi-periodic coefficients
Note:
Translation of: Lineynyye sistemy obyknovennykh differentsial'nykh uravneniy s periodicheskimi i kvaziperiodicheskimi koeffitsiyentami.
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Front Cover; Linear Systems of Ordinary Differential Equations; Copyright Page; Author's Comments; Contents; Introduction; Chapter 1. Functions of a Single Matrix; Chapter 2. Auxiliary Theorems; Chapter 3. Functions of Several Matrices and of a Countable Set of Matrices; Chapter 4. Classes of Systems of Linear Differential Equations That Can Be Integrated in Closed Form; Chapter 5. Other Systems of Linear Differential Equations That Are Integrable in Closed Form
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Chapter 6. The Construction of Solutions of Certain Linear Systems of Differential Equations in the Form of a Series of Several Matrices (of a Series of Compositions)Chapter 7. Solution of the Poincaré-Lappo-Danilevskiy Problem; Chapter 8. Formulation of Certain Problems of Linear Systems of Differential Equations with Real Periodic Coefficients; Chapter 9. Solution of the Problems Posed in Section 8 on the Basis of Real Functions; Chapter 10. Expansion of an Exponential Matrix in a Series of Powers of a Parameter
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Chapter 11. Determination of the Coefficients in the Series Expansion of an Exponential MatrixChapter 12. Approximate Integration of Equation (10.1); Chapter 13. The Case in Which P0 (t), P1 (t), ..., Pm (t) in Equation (10.1) Are Constants; Chapter 14. The Case in Which P0 is Constant and expP0t is a Periodic Matrix in Equation (10.1); Chapter 15. An Example Illustrating Section 14; Chapter 16. Canonical Systems; Chapter 17. The System (16.3) With P0 = P1 = ... = Pm-1=0; Chapter 18. Artem'yev's Problem; Chapter 19. The Theory of Reducible Systems; Chapter 20. Shtokalo's Method
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Chapter 21. Determination of the Coefficients of the Series (20.22) and (20.23) by Shtokalo's Method [10, 38]Chapter 22. Approximate Solutions Obtained by Shtokalo's Method; Chapter 23. Inequalities Following from Shtokalo's Method; Chapter 24. Shtokalo's Theorem. Inequalities Involving Approximate Solutions Found by Shtokalo's Method (for Linear and Nonlinear Systems). Particular Problems; Chapter 25. Other Approximate Forms of Solutions That .Arise From Shtokalo's and Bogolyubov's Methods; Chapter 26. Demidovich's Problem
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Chapter 27. Another Formulation of Certain Problems and Consequences of ThemChapter 28. Solution of the Problems in Section 8 by Use of the Method of Solving the Poincaré-Lappo-DaniIevskiy Problem and Lyapunov's Contributions; Chapter 29. Remarks on Bounded and Periodic Solutions of a System of Two Differential Equations With Periodic Coefficients; Chapter 30. Periodic and Bounded Solutions of the Systems of Equations Considered in Sections 3 and 4
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Chapter 31. Questions Involving the Boundedness and Periodicity of Solutions of a System of Two Linear Differential Equations With the Aid of a Special Exponential Substitution Obtained by Lappo-Danilevskiy
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English
Additional Edition:
ISBN 0-12-241850-6
Language:
English
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