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Linear Differential Equations and Oscillators
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kr 526
Linear Differential Equations and Oscillators

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
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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
Produktdetaljer
Sprog: Engelsk
Sider: 324
ISBN-13: 9780367137182
Indbinding: Hardback
Udgave:
ISBN-10: 0367137186
Udg. Dato: 13 nov 2019
Længde: 25mm
Bredde: 162mm
Højde: 241mm
Oplagsdato: 13 nov 2019
Forfatter(e) Luis Manuel (University of Lisbon Braga da Costa Campos, Luis Manuel Braga da Costa Campos


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Hardback


Sider 324


Udgave


Længde 25mm


Bredde 162mm


Højde 241mm

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