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Mechanics and Dynamical Systems with Mathematica®

  • Nicola Bellomo
  • Luigi Preziosi
  • Antonio Romano

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Mathematical Methods for Differential Equations

    1. Front Matter
      Pages xv-xv
    2. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 1-17
    3. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 19-55
    4. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 57-90
  3. Mathematical Methods of Classical Mechanics

    1. Front Matter
      Pages 91-91
    2. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 93-138
    3. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 139-182
    4. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 183-230
  4. Bifurcations, Chaotic Dynamics, Stochastic Models, and Discretization of Continuous Models

    1. Front Matter
      Pages 231-231
    2. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 233-265
    3. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 267-312
    4. Nicola Bellomo, Luigi Preziosi, Antonio Romano
      Pages 313-339
  5. Back Matter
    Pages 341-417

About this book

Introduction

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.

Keywords

Lagrangian mechanics algorithm calculus chaos dynamical systems dynamische Systeme evolution mathematical modeling mathematics mechanics model modeling numerical methods programming simulation

Authors and affiliations

  • Nicola Bellomo
    • 1
  • Luigi Preziosi
    • 1
  • Antonio Romano
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.Department of MathematicsUniversity di NapoliNapoliItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1338-3
  • Copyright Information Birkhäuser Boston 2000
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7101-7
  • Online ISBN 978-1-4612-1338-3
  • Series Print ISSN 2164-3679
  • Buy this book on publisher's site