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Classification and Examples of Differential Equations and their Applications - Ordinary Differential Equations with Applications to Trajectories and Vibrations (Hardcover)
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Classification and Examples of Differential Equations and their Applications - Ordinary Differential Equations with Applications to Trajectories and Vibrations (Hardcover)
Series: Mathematics and Physics for Science and Technology
Expected to ship within 12 - 17 working days
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Classification and Examples of Differential Equations and their
Applications is the sixth 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
sixth book consists of one chapter (chapter 10 of the set). It
contains 20 examples related to the preceding five books and
chapters 1 to 9 of the set. It includes two recollections: the
first with a classification of differential equations into 500
standards and the second with a list of 500 applications. The
ordinary differential equations are classified in 500 standards
concerning methods of solution and related properties, including:
(i) linear differential equations with constant or homogeneous
coefficients and finite difference equations; (ii) linear and
non-linear single differential equations and simultaneous systems;
(iii) existence, unicity and other properties; (iv) derivation of
general, particular, special, analytic, regular, irregular, and
normal integrals; (v) linear differential equations with variable
coefficients including known and new special functions. The theory
of differential equations is applied to the detailed solution of
500 physical and engineering problems including: (i) one- and
multidimensional oscillators, with damping or amplification, with
non-resonant or resonant forcing; (ii) single, non-linear, and
parametric resonance; (iii) bifurcations and chaotic dynamical
systems; (iv) longitudinal and transversal deformations and
buckling of bars, beams, and plates; (v) trajectories of particles;
(vi) oscillations and waves in non-uniform media, ducts, and wave
guides. Provides detailed solution of examples of differential
equations of the types covered in tomes l-5 of the set (Ordinary
Differential Equations with Applications to Trajectories and
Vibrations, Six -volume Set) Includes physical and engineering
problems that extend those presented in the tomes 1-6 (Ordinary
Differential Equations with Applications to Trajectories and
Vibrations, Six-volume Set) Includes a classification of ordinary
differential equations and their properties into 500 standards that
can serve as a look-up table of methods of solution Covers a
recollection of 500 physical and engineering problems and sub-cases
that involve the solution of differential equations Presents the
problems used as examples including formulation, solution, and
interpretation of results
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