Simultaneous Systems of Differential Equations and Multi-Dimensional Vibrations (Hardcover)

Luis Manuel Braga da Costa Campos

ISBN 10: 0367137216 / ISBN 13: 9780367137212

Edité par Taylor & Francis Ltd, London, 2019

A propos de cet article

Hardcover. Simultaneous Differential Equations and Multi-Dimensional Vibrations is the fourth 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 fourth book consists of two chapters (chapters 7 and 8 of the set).The first chapter concerns simultaneous systems of ordinary differential equations and focuses mostly on the cases that have a matrix of characteristic polynomials, namely linear systems with constant or homogeneous power coefficients. The method of the matrix of characteristic polynomials also applies to simultaneous systems of linear finite difference equations with constant coefficients.The second chapter considers linear multi-dimensional oscillators with any number of degrees of freedom including damping, forcing, and multiple resonance. The discrete oscillators may be extended from a finite number of degrees-of-freedom to infinite chains. The continuous oscillators correspond to waves in homogeneous or inhomogeneous media, including elastic, acoustic, electromagnetic, and water surface waves. The combination of propagation and dissipation leads to the equations of mathematical physics.Presents simultaneous systems of ordinary differential equations and their elimination for a single ordinary differential equationIncludes cases with a matrix of characteristic polynomials, including simultaneous systems of linear differential and finite difference equations with constant coefficientsCovers multi-dimensional oscillators with damping and forcing, including modal decomposition, natural frequencies and coordinates, and multiple resonanceDiscusses waves in inhomogeneous media, such as elastic, electromagnetic, acoustic, and water wavesIncludes solutions of partial differential equations of mathematical physics by separation of variables leading to ordinary differential equations This the fourth book of Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-Volume Set, in the Mathematics and Physics for Science and Technology series. It extends the methods of the first three from a single ordinary differential equation to a simultaneous system. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

N° de réf. du vendeur 9780367137212

Détails bibliographiques

• Titre: Simultaneous Systems of Differential Equations and Multi-Dimensional Vibrations (Hardcover)
• Éditeur: Taylor & Francis Ltd, London
• Date de parution: 2019
• Langue: anglais
• ISBN à 10 chiffres: 0367137216
• ISBN à 13 chiffres: 9780367137212
• Reliure: Hardcover
• État de l'article: new

A propos de ce titre

Synopsis

Simultaneous Differential Equations and Multi-Dimensional Vibrations is the fourth 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 fourth book consists of two chapters (chapters 7 and 8 of the set).

The first chapter concerns simultaneous systems of ordinary differential equations and focuses mostly on the cases that have a matrix of characteristic polynomials, namely linear systems with constant or homogeneous power coefficients. The method of the matrix of characteristic polynomials also applies to simultaneous systems of linear finite difference equations with constant coefficients.

The second chapter considers linear multi-dimensional oscillators with any number of degrees of freedom including damping, forcing, and multiple resonance. The discrete oscillators may be extended from a finite number of degrees-of-freedom to infinite chains. The continuous oscillators correspond to waves in homogeneous or inhomogeneous media, including elastic, acoustic, electromagnetic, and water surface waves. The combination of propagation and dissipation leads to the equations of mathematical physics.

• Presents simultaneous systems of ordinary differential equations and their elimination for a single ordinary differential equation
• Includes cases with a matrix of characteristic polynomials, including simultaneous systems of linear differential and finite difference equations with constant coefficients
• Covers multi-dimensional oscillators with damping and forcing, including modal decomposition, natural frequencies and coordinates, and multiple resonance
• Discusses waves in inhomogeneous media, such as elastic, electromagnetic, acoustic, and water waves
• Includes solutions of partial differential equations of mathematical physics by separation of variables leading to ordinary differential equations

À propos de l?auteur

Luis Manuel Braga da Costa Campos graduated in 1972 as a Mechanical Engineer from the Instituto Superior Tecnico (IST) of Lisbon Technical University. His tutorials as a student (1970) were followed by a career at the same institution (IST) through all levels: Assistant (1972), Assistant with tenure (1974), Assistant Professor (1978), Associate Professor (1982), Chair de Applied Mathematics and Mechanics (1985). He has been coordinator of undergraduate and post-graduate degrees in Aerospace Engineering since their creation in 1991. He is also coordinator of the Scientific Area of Applied and Aerospace Mechanics in the Department of Mechanical Engineering and director and founder of the Center for Aeronautical and Space Science and Technology.