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Linear Differential Equations and Oscillators (Mathematics and Physics for Science and Technology)

By: Luis Manuel Braga da Costa Campos (Author)

Extended Catalogue

Ksh 29,150.00

Format: Hardback or Cased Book

ISBN-10: 0367137186

ISBN-13: 9780367137182

Collection / Series: Mathematics and Physics for Science and Technology

Collection Type: Publisher collection

Publisher: Taylor & Francis Ltd

Imprint: CRC Press

Country of Manufacture: GB

Country of Publication: GB

Publication Date: Nov 13th, 2019

Publication Status: Active

Product extent: 324 Pages

Weight: 628.00 grams

Dimensions (height x width x thickness): 16.20 x 24.10 x 2.50 cms

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This is the first book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. This book starts with the simplest and most common ordinary differential equations, namely those that have a characteristic polynomial.

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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