Simultaneous Systems of Differential Equations and Multi-dimensional Oscillators: 1st Edition (Hardback) book cover

Simultaneous Systems of Differential Equations and Multi-dimensional Oscillators

1st Edition

By Luis Manuel Braga da Costa Campos

CRC Press

344 pages | 34 B/W Illus.

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Hardback: 9780367137212
pub: 2019-11-20
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Simultaneous Differential Equations and Multidimensional 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


Table of Contents

Simultaneous Systems of Differential Equations. 2. Oscillations with Several Degrees-of-Freedom.

About the Author

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 Technolo

About the Series

Mathematics and Physics for Science and Technology

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Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Differential Equations
MEDICAL / General