Adiabatic invariants of oscillators with one degree of freedom

Adiabatic invariants for dynamical systems with one degree of freedom are derived. The method developed for linear dynamical systems with constant parameters is extended to systems with slowly varying parameters. The method is based on the field method concept of obtaining a conservation law from an incomplete solution of a partial differential equation. The method results in a complete set of adiabatic invariants specifying the approximate solutions for motion. A few examples, including the classical time-dependent oscillator and the Duffing oscillator with slowly varying parameters, are given to illustrate the theory.