Series:

Modeling and Simulation in Science, Engineering and Technology

10 total works

Cover of Continuum Mechanics using Mathematica (R)
This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica (R) provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhauser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica (R): Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

Cover of Classical Mechanics with Mathematica (R)

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. Developed by the author from 35 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field-from Newton to Lagrange-while also painting a clear picture of the most modern developments. Throughout, it makes heavy use of the powerful tools offered by Mathematica .

The volume is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton-Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others.

Unique in its scope of coverage and method of approach, Classical Mechanics will be a very useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Cover of Geometric Optics

Geometric Optics

by Antonio Romano

Published 11 October 2009
This book-unique in the literature-provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica(R). Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.

Cover of Continuum Mechanics
This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors' previous book, Continuum Mechanics using Mathematica (R), this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.

Cover of Scientific Computing with Mathematica (R)
Many interesting behaviors of real physical, biological, economical,
and chemical systems can be described by ordinary differential
equations (ODEs).
Scientific Computing with Mathematica for Ordinary Differential
Equations
provides a general framework useful for the applications, on the
conceptual aspects of the theory of ODEs, as well as a sophisticated
use of Mathematica software for the solutions of problems related to
ODEs. In particular, a chapter is devoted to the use ODEs and
Mathematica in the Dynamics of rigid bodies.
Mathematical methods and scientific computation are dealt with jointly
to supply a unified presentation. The main problems of ordinary
differential equations such
as, phase portrait, approximate solutions, periodic orbits, stability,
bifurcation, and
boundary problems are covered in an integrated fashion with numerous
worked examples and computer program demonstrations using
Mathematica.
Topics and Features:*Explains how to use the Mathematica package ODE.m
to support qualitative and quantitative problem solving *End-of-
chapter exercise sets incorporating the use of Mathematica programs
*Detailed description and explanation of the mathematical procedures
underlying the programs written in Mathematica *Appendix describing
the use of ten notebooks to guide the reader through all the
exercises.
This book is an essential text/reference for students, graduates and
practitioners in applied mathematics and engineering interested in
ODE's problems in both the qualitative and quantitative description of
solutions with the Mathematica program. It is also suitable as a self-

Cover of Continuum Mechanics Using "Mathematica"
This book examines mathematical tools, principles, and fundamental applications of continuum mechanics, providing a solid basis for a deeper study of more challenging problems in elasticity, fluid mechanics, plasticity, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes. The work is suitable for advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering.

Cover of Mechanics and Dynamical Systems with Mathematica (R)
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.

Cover of Mechanics and Dynamical Systems with Mathematica
Providing a unified treatment of the subject, this text addresses modelling, qualitative analysis and simulation of real physical systems using ordinary differential equations. The scientific computational aspects are presented using the computer program, Mathematica, both for plentiful exercises and examples. Special attention is given to classical mechanics in light of new computational methods and concept.

Cover of Scientific Computing with Mathematica

Cover of Generalized Collocation Methods

Analysis of nonlinear models and problems is crucial in the application of mathematics to real-world problems. This book approaches this important topic by focusing on collocation methods for solving nonlinear evolution equations and applying them to a variety of mathematical problems. These include wave motion models, hydrodynamic models of vehicular traffic flow, convection-diffusion models, reaction-diffusion models, and population dynamics models. The book may be used as a textbook for graduate courses on collocation methods, nonlinear modeling, and nonlinear differential equations. Examples and exercises are included in every chapter.