Bücher von Antonio Romano

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa­ tions is a relevant, maybe the fundamental, aspect of the interactions be­ tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula­ tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re­ lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be­ havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization.

This unique textbook offers a mathematically rigorous presentation of the theory of relativity, emphasizing the need for a critical analysis of the foundations of general relativity in order to best study the theory and its implications.

Valuable for its wide-ranging yet thorough approach to mechanics, this textbook succeeds in bridging the often daunting divide between classical analytical and modern differential geometries, and reflects the author's decades-long teaching experience.

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject.

This book offers a new approach to third-order aberrations theory. It presents the basic elements of third-order aberrations of optical telescopes, along with the necessary mathematical background, to design almost all optical combinations used in astronomy.

Continuum Mechanics using Mathematica(R)

Many behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). This book provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, and a sophisticated use of Mathematica software for the solutions of problems related to ODEs.