Ordinary Differential Equations with Applications to Mechanics

  • Mircea V. Soare
  • Petre P. Teodorescu
  • Ileana Toma
Part of the Mathematics and Its Applications book series (MAIA, volume 585)

Table of contents

  1. Front Matter
    Pages I-10
  2. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 11-130
  3. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 131-207
  4. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 209-237
  5. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 239-364
  6. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 365-414
  7. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 415-450
  8. Mircea V. Soare, Petre P. Teodorescu, Ileana Toma
    Pages 451-482
  9. Back Matter
    Pages 483-488

About this book

Introduction

The present book has its source in the authors’ wish to create a bridge between the mathematical and the technical disciplines, which need a good knowledge of a strong mathematical tool. The necessity of such an interdisciplinary work drove the authors to publish a first book to this aim with Editura Tehnica, Bucharest, Romania.
The present book is a new, English edition of the volume published in 1999. It contains many improvements concerning the theoretical (mathematical) information, as well as new topics, using enlarged and updated references. Only ordinary differential equations and their solutions in an analytical frame were considered, leaving aside their numerical approach.
The problem is firstly stated in its mechanical frame. Then the mathematical model is set up, emphasizing on the one hand the physical magnitude playing the part of the unknown function and on the other hand the laws of mechanics that lead to an ordinary differential equation or system. The solution is then obtained by specifying the mathematical methods described in the corresponding theoretical presentation. Finally a mechanical interpretation of the solution is provided, this giving rise to a complete knowledge of the studied phenomenon.
The number of applications was increased, and many of these problems appear currently in engineering.

Audience
Mechanical and civil engineers, physicists, applied mathematicians, astronomers and students. The prerequisites are courses of elementary analysis and algebra, as given at a technical university. On a larger scale, all those interested in using mathematical models and methods in various fields, like mechanics, civil and mechanical engineering, and people involved in teaching or design will find this work indispensable.

Keywords

Bernoulli-Euler equation Boundary value problem Cauchy problem Eigenvalues Lagrange, Clairaut, Riccati ODE, LEM Ordinary Differential Equations Sturm-Liouville problems Taylor series expansion differential equation dynamische Systeme mechanics model stability

Authors and affiliations

  • Mircea V. Soare
    • 1
  • Petre P. Teodorescu
    • 2
  • Ileana Toma
    • 3
  1. 1.Technical University of Civil EngineeringRomania
  2. 2.Faculty of MathematicsUniversity of BucharestRomania
  3. 3.Dept. of Mathematics and InformaticsTechnical University of Civil EngineeringRomania

Bibliographic information

  • DOI https://doi.org/10.1007/1-4020-5440-8
  • Copyright Information Springer 2007
  • Publisher Name Springer, Dordrecht
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4020-5439-6
  • Online ISBN 978-1-4020-5440-2