Linear Differential Equations and Oscillators (1st edition.)

This fourth volume in the series "Mathematics and Physics Applied to Science and Technology": (i) follows the first three volumes on complex, transcendental and generalized functions that provide a detailed background on the theory of functions; (ii) starts the next set "On Boundary and Initial Value Problems" with the fourth volume on "Ordinary Differential Equations with Applications to Trajectories and Oscillations". The first book within volume IV (corresponding to the fourth book of the series) concerns "Linear Differential Equations and Oscillations" and consists of chapters 1 and 2 of the volume IV.

The first chapter covers linear differential equations of any order whose unforced solution can be obtained from the roots of a characteristic polynomial, namely those: (i) with constant coefficients; (ii) with homogeneous power coefficients with the exponent equal to the order of derivation. The method of characteristic polynomials is also applied to (iii) linear finite difference equations of any order with constant coefficients. The unforced and forced solutions of (i,ii,iii) are examples of some general properties of ordinary differential equations.

The second chapter applies the theory of the first chapter to linear second-order oscillators with one degree-of-freedom, such as the mechanical mass-damper-spring-force system and the electrical self-resistor-capacitor-battery circuit. In both cases are treated free undamped, damped and amplified oscillations; also forced oscillations including beats, resonance, discrete and continuous spectra and impulsive inputs.

- Desribes general properties of differential and finite difference equations, with focus on linear
equations and
constant and some power coefficients
- Presents particular and general solutions for all cases of differential and finite difference
equations without forcing

- Provides complete solutions for many cases cing including resonant cases
- Discusses applications to linear second-order mechanical and electrical oscillators with damping
and amplification
- Provides solutions with forcing including resonance using the characteristic polynomial, Green's
functions,
trigonometrical series, Fourier integrals and Laplace transforms