Linear Differential Equations and Oscillators
Mathematics and Physics for Science and Technology Series

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Language: Anglais
Cover of the book Linear Differential Equations and Oscillators

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Linear Differential Equations and Oscillators is the first book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set.As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This first book consists of chapters 1 and 2 of the fourth volume.

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

1. Three Cases of Characteristic Polynomials. 2. The Damped/Amplified and Forced Oscillator.