Bellomo N., Preziosi L., Romano A. Mechanics and Dynamical Systems with Mathematica

Springer Science+Business Media New York, USA 2002. — 423 p. — ISBN: 1461271010.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.Mathematical Methods for Differential Equations
Models and Differential Equations
Models and Mathematical Problems
Stability and Perturbation Methods
Mathematical Methods of Classical Mechanics
Newtonian Dynamics
Rigid Body Dynamics
Energy Methods and Lagrangian Mechanics
Bifurcations, Chaotic Dynamics, Stochastic Models, and Discretization of Continuous Models
Deterministic and Stochastic Models in Applied Sciences
Chaotic Dynamics, Stability, and Bifurcations
Discrete Models of Continuous Systems
Appendixes
Numerical Methods for Ordinary Differential Equations
Kinematics, Applied Forces, Momentum and Mechanical Energy
Scientific Programs