Marin Marin – författare

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.

This book offers engineering students an introduction to the theory of partial differential equations and then guiding them through the modern problems in this subject.Divided into two parts, in the first part readers already well-acquainted with problems from the theory of differential and integral equations gain insights into the classical notions and problems, including differential operators, characteristic surfaces, Levi functions, Green’s function, and Green’s formulas. Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations. The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects ofthe theory of partial differential equations.

Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems.

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function).

This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function).

This book covers all the standard introductory topics in classical mechanics, for the first part: Statics (the analysis of forces and moments acting on a mechanical system in equilibrium with its environment).

This book covers all the standard introductory topics in classical mechanics, for main part the kinematics (the analysis of trajectories, velocities, and accelerations of different points of a body). Starting from basic liaison conditions between different bodies existing in mechanics are analyzed the principal technical pairs of bodies that assure the technical contact in a multibody system. The main problems that may arise in engineering practice are analyzed and numerous problems illustrate the presentation. As a theoretical field, classical mechanics is noted for its intrinsic beauty, richness, and depth as well as its coherence and elegance. This book aims to emphasize the harmony and beauty of classical mechanics. Because of the writers’ extensive experience, their presentation style has been put to the test throughout many years of working with pupils. Advanced undergraduates and first-year graduate students interested in the engineering application of contemporary techniques in classical mechanics are the target audience for this textbook. To encourage a thorough comprehension of the topic, the writers make an effort to write in an understandable and methodical manner. The writers used practical examples to motivate and illustrate each subject in this section of mechanics and statics.It is well known that classical mechanics, viewed as a theoretical discipline, possesses an inherent beauty, depth, and richness and presents coherence and elegance. This book tries to highlight this beauty and harmony that classical mechanics offers. The long experience of the authors means that the way of presentation is intensively tested in the decades of contact with students. The textbook is mainly addressed to advanced undergraduate and beginning graduate students who are interested in the engineering application of modern methods in classical mechanics. The authors try to use a clear and systematic style to promote a good understanding of the subject.

This book highlights the remarkable importance of special functions, operational calculus, and variational methods. A considerable portion of the book is dedicated to second-order partial differential equations, as they offer mathematical models of various phenomena in physics and engineering. The book provides students and researchers with essential help on key mathematical topics, which are applied to a range of practical problems. These topics were chosen because, after teaching university courses for many years, the authors have found them to be essential, especially in the contexts of technology, engineering and economics. Given the diversity topics included in the book, the presentation of each is limited to the basic notions and results of the respective mathematical domain. Chapter 1 is devoted to complex functions. Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions ofa complex variable plays in mathematical physics, especially in the modeling of plane problems.  In addition, the book demonstrates the importance of the theories of special functions, operational calculus, and variational calculus. In the last chapter, the authors discuss the basic elements of one of the most modern areas of mathematics, namely the theory of optimal control.

Here, much emphasis is placed on the theory of holomorphic functions, which facilitate the understanding of the role that the theory of functions ofa complex variable plays in mathematical physics, especially in the modeling of plane problems.