Classification and Examples of Differential Equations and their Applications: 1st Edition (Hardback) book cover

Classification and Examples of Differential Equations and their Applications

1st Edition

By Luis Manuel Braga da Costa Campos

CRC Press

272 pages | 10 B/W Illus.

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Hardback: 9780367137243
pub: 2019-11-20
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Description

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 to 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

Table of Contents

1. – Examples 1 to 20. 2. Recollections. 3. 500 Standards of Differential equations and 500

Apllications. 4. Back Matter – Indices

and Bibliography

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 Technology.

About the Series

Mathematics and Physics for Science and Technology

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
MED000000
MEDICAL / General