Ordinary Differential Equations With Applications to Mechanics

The present book has its source in the authors’ wish to create a bridge between mathematics and the technical disciplines that need a good knowledge of a strong mathematical tool. The authors tried to reflect a common experience of the University of Bucharest, Faculty of Mathematics and of the Technical University of Civil Engineering of Bucharest. The necessity of such an interdisciplinary work drove the authors to publish a first book with this aim (“Ecua ?ii diferen ?iale cu aplica ?ii în mecanica construc ?iilor” – Ordinary differential equations with applications to the mechanics of constructions, Editura Tehnic?, Bucharest, Romania). The present book is a new edition of the volume published in 1999. Unfortunately, the first author (M.V. Soare) passed away shortly before the publication of the Romanian edition, so that the present work is only due to the other two authors. It contains many improvements concerning the theoretical (mathematical) information, as well as new topics, using enlarged and updated references. We considered only ordinary differential equations and their solutions in an analytical frame, leaving aside their numerical approach. Compared to the Romanian edition, this volume presents the applications in a new way.

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.