The exposition is self-contained. The first chapter presents all necessary results (with proofs) on the theory of matrices which are not included in a standard linear algebra course. The only prerequisite in addition to standard linear algebra is the theory of linear integral equations used in Chapter 5. The book is suitable for graduate students, research mathematicians and engineers interested in ordinary differential equations, integral equations, and theirapplications.

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

This book is a novel tutorial for research-oriented study of vibration mechanics. The book begins with twelve open problems from six case studies of vibration mechanics in order to guide readers in studying the entire book. Then, the book surveys both theories and methods of linear vibrations in an elementary course from a new perspective of aesthetics of science so as to assist readers to upgrade their way of learning. The successive chapters offer a theoretical frame of linear vibrations and waves, covering the models of vibration systems, the vibration analysis of discrete systems, the natural vibrations of one-dimensional structures, the natural vibrations of symmetric structures, and the waves and vibrations of one-dimensional structures. The chapters help readers solve the twelve open problems step by step during the research-oriented study. The book tries to arouse the interest of graduate students and professionals, who have learnt an elementary course of vibration mechanics of two credits, to conduct the research-oriented study and achieve a helical upgrade understanding to vibration mechanics.