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Ordinary differential equations /
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. <br>The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stabili...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés Ruso |
| Publicado: |
Reading, Massachusetts : London :
Addison-Wesley Publishing Company, Inc. ; Pergamon Press,
1962.
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| Colección: | Adiwes international series in mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Ordinary Differential Equations; Copyright Page; PREFACE; FOREWORD; Table of Contents; CHAPTER 1. INTRODUCTION; 1. First-order differential equations.; 2. Some elementary integration methods.; 3. Formulation of the existence and uniqueness theorem.; 4. Reduction of a general system of differential equations to a normal system.; 5. Complex differential equations.; 6. Some properties of linear differential equations.; CHAPTER 2. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS; 7. The linear homogeneous equation with constant coefficients. Case of simple roots.
- 8. The linear homogeneous equation with constant coefficients. Case of multiple roots.9. Stable polynomials.; 10. The linear nonhomogeneous equation with constant coefficients.; 11. Method of elimination.; 12. The method of complex amplitudes.; 13. Electrical circuits.; 14. The normal linear homogeneous system with constant coefficients.; 15. Autonomous systems of differential equations and their phase spaces.; 16. The phase plane of a linear homogeneous system with Constant coefficient.; CHAPTER 3. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS; 17. The normal system of linear equations.
- 18. The linear equation of nth order.19. The normal linear homogeneous system with periodic coefficients.; CHAPTER 4. EXISTENCE THEOREMS; 20. Proof of the existence and uniqueness theorem for one equation.; 21. Proof of the existence and uniqueness theorem for a normal system of equations.; 22. Local theorems of continuity and differentiability of solutions.; 23. First integrals.; 24. Behavior of the trajectories on large time intervals.; 25. Global theorems of continuity and differentiability.; CHAPTER 5. STABILITY; 26. Lyapunov's theorem.
- 27. The centrifugal governor and the analysis of Vyshnegradskiy.28. Limit cycles.; 29. The vacuum-tube oscillator.; 30. The states of equilibrium of a second-order autonomous system.; 31. Stability of periodic solutions.; CHAPTER 6. LINEAR ALGEBRA; 32. The minimal annihilating polynomial.; 33. Matrix functions.; 34. The Jordan form of a matrix.; INDEX