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