Springer Ordinary Differential Equations with Applications to Mechanics: 585 (Mathematics and Its Applications, 585)

This interdisciplinary work creates a bridge between the mathematical and the technical disciplines by providing a strong mathematical tool. The present book is a new, English edition of the volume published in 1999. It contains many improvements, 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. Review From the reviews: "The purpose of this book is to present a large variety of examples from mechanics which illustrate numerous applications of the elementary theory of ordinary differential equations. It is intended primarily for the use of engineers, physicists and applied mathematicians … . It may be also useful for students who will be using the ODEs. The book contains an introduction and seven chapters. … Each chapter is provided with many illustrative and applicable examples and an Index is also added, including applications." (Antonio Cañada Villar, Zentralblatt MATH, Vol. 1123 (1), 2008) "The goal of the authors of this introductory book on ordinary differential equations (ODEs) is to create a bridge between the mathematical and the technical disciplines. This book is a translation of the Romanian edition … . the authors wrote an interesting book for technical engineers and applied mathematicians who are interested in ODEs and in mechanics." (Wim T. van Horssen, Mathematical Reviews, Issue 2008 c) From the Back Cover 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. AudienceMechanical 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.