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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.
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. Linear Homogeneous Equation with Constant Coefficients. The 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 Coefficients
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
- No. of pages:
- © Pergamon 1962
- 1st January 1962
- eBook ISBN:
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