Pontryagin / Lohwater Ordinary Differential Equations

Adiwes International Series in Mathematics
1. Auflage 2014
ISBN: 978-1-4831-5649-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 304 Seiten, Web PDF

Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.

Autoren/Hrsg.

Pontryagin, L. S.

Lohwater, A. J.

Inhaltsverzeichnis

1;Front Cover;1
2;Ordinary Differential Equations;2
3;Copyright Page;3
4;Table of Contents;6
5;PREFACE;4
6;FOREWORD;5
7;CHAPTER 1. INTRODUCTION;8
7.1;1. First-order differential equations.;8
7.2;2. Some elementary integration methods.;13
7.3;3. Formulation of the existence and uniqueness theorem.;25
7.4;4. Reduction of a general system of differential equations to a normal system.;32
7.5;5. Complex differential equations.;40
7.6;6. Some properties of linear differential equations.;46
8;CHAPTER 2. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS;48
8.1;7. The linear homogeneous equation with constant coefficients. Case of simple roots.;49
8.2;8. The linear homogeneous equation with constant coefficients. Case of multiple roots.;57
8.3;9. Stable polynomials.;64
8.4;10. The linear nonhomogeneous equation with constant coefficients.;69
8.5;11. Method of elimination.;74
8.6;12. The method of complex amplitudes.;83
8.7;13. Electrical circuits.;87
8.8;14. The normal linear homogeneous system with constant coefficients.;101
8.9;15. Autonomous systems of differential equations and their phase spaces.;110
8.10;16. The phase plane of a linear homogeneous system with Constant coefficient.;122
9;CHAPTER 3. LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS;134
9.1;17. The normal system of linear equations.;134
9.2;18. The linear equation of nth order.;144
9.3;19. The normal linear homogeneous system with periodic coefficients.;151
10;CHAPTER 4. EXISTENCE THEOREMS;157
10.1;20. Proof of the existence and uniqueness theorem for one equation.;157
10.2;21. Proof of the existence and uniqueness theorem for a normal system of equations.;166
10.3;22. Local theorems of continuity and differentiability of solutions.;177
10.4;23. First integrals.;188
10.5;24. Behavior of the trajectories on large time intervals.;196
10.6;25. Global theorems of continuity and differentiability.;199
11;CHAPTER 5. STABILITY;207
11.1;26. Lyapunov's theorem.;208
11.2;27. The centrifugal governor and the analysis of Vyshnegradskiy.;220
11.3;28. Limit cycles.;227
11.4;29. The vacuum-tube oscillator.;243
11.5;30. The states of equilibrium of a second-order autonomous system.;251
11.6;31. Stability of periodic solutions.;268
12;CHAPTER 6. LINEAR ALGEBRA;284
12.1;32. The minimal annihilating polynomial.;284
12.2;33. Matrix functions.;291
12.3;34. The Jordan form of a matrix.;298
13;INDEX;303