Campos L Linear Differential Equations and Oscillators 2020 torrent

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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
Contents
Three Cases of Characteristic Polynomials
Equation of Order N and Initial Conditions
General, Particular, and Complete Integrals
Unforced Linear Equation with Constant Coefficients
General (Complete) Integral of the Unforced (Forced) Equation
Polynomial of Derivatives and Inverse Operator
Homogenous Linear Differential Equation with Power Coefficients (Euler, 1769)
Homogeneous Derivatives and Characteristic Polynomial
Inverse Polynomial of Homogeneous Derivatives
Solution of Finite Difference Equations
The Damped/Amplified and Forced Oscillator
Linear Electromechanical Circuits
Stable Attractor and Unstable Repeller
Free Motion with Critical or Supercritical Damping
Free Oscillations with Strong, Weak, or No Damping
Mechanical and Electrical Amplified Oscillations
Comparison of Zero with Small Mass
Forced Oscillations, Resonance, and Beats
Damped Resonance for the Frequency and Decay
Arbitrary, Bounded, and Exponential Forcings