Pontryagin L.S. Ordinary Differential Equations

Translated from the Russian by Leonas Kacinskas and Walter B. Counts. — Addison-Wesley, 1962. — 304 p. — ISBN10: 148312407X ISBN13: 978-1483124070.First-order differential equations.
Some elementary integration methods.
Formulation of the existence and uniqueness theorem.
Reduction of a general system of differential equations to a normal system.
Complex differential equations.
Some properties of linear differential equations.
Linear Equations with Constant Coefficients.
Linear homogeneous equation with constant coefficients. The case of simple roots.
The linear homogeneous equation with constant coefficients. Case of multiple roots.
Stable polynomials.
The linear nonhomogeneous equation with constant coefficients.
Method of elimination.
The method of complex amplitudes.
Electrical circuits.
The normal linear homogeneous system with constant coefficients.
Autonomous systems of differential equations and their phase spaces.
The phase plane of a linear homogeneous system with constant coefficients.
Linear Equations with Variable Coefficients.
The normal system of linear equations.
The linear equation of nth order.
The normal linear homogeneous system with periodic coefficients.
Existence Theorems.
Proof of the existence and uniqueness theorem for one equation.
Proof of the existence and uniqueness theorem for a normal system of equations.
Local theorems of continuity and differentiability of solutions.
First integrals.
Behavior of the trajectories on large time intervals.
Global theorems of continuity and differentiability.
Stability.
Lyapunov's theorem.
The centrifugal governor and the analysis of Vyshnegradskiy.
Limit cycles.
The vacuum-tube oscillator.
The states of equilibrium of a second-order autonomous system.
Stability of periodic solutions.
Linear Algebra.
The minimal annihilating polynomial.
Matrix functions.
The Jordan form of a matrix.