Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.
Rezensionen / Stimmen
"The style of presentation is simply excellent. The authors carefully separate definitions, examples, theory, and remarks. This organization makes this text highly readable, suitable for use as both a text and a reference."
- F. Jafari, Appl. Mech. Rev., 49(5), May 1996
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Professional
Illustrationen
Maße
Höhe: 234 mm
Breite: 156 mm
Gewicht
ISBN-13
978-0-8493-8331-1 (9780849383311)
Schweitzer Klassifikation
Preface
Mathematical Modelling
Introduction
Definition of Mathematical Modelling
Classification of Mathematical Modelling
Modelling Methods
Validation of Mathematical Models
Mathematical Modelling as a Science
Discrete Models
Plan of Chapter 2
About Mathematical Modelling
Mathematical Formulation of Problems
On Existence, Uniqueness and Continuity
Linear Systems
Stability and Linearization
From Bifurcation to Chaos
Numerical Methods for Initial Value Problems
Scientific Programs
Continuous Models
Introduction
Mathematical Modelling
Equilibrium Equation for the Vibration of an Elastic String
Mathematical Models of Continuum Mechanics
Mathematical Models of Electromagnetism
Direct Simulation Models in Biology
Classification and Characteristics
Mathematical Formulation of Problems
Finite Difference Methods
The Collocation Method
Decomposition of Domains
Applications and Scientific Programs
Inverse and Stochastic Problems
Inverse Problems and Stochastic Models
Classification of Inverse Problems
Solution by Decomposition of Domains
Solution by Minimization Techniques
Mathematical Modelling and Stochasticity
Classification of Discrete Stochastic Models
Classification of Continuous Stochastic Models
Modelling and Solution of Problems
Stochastic Aspects and Inverse Problems
Kinetic Models
Application
Discussion and Developments
Scientific Programs
Appendix 1. Functional Spaces and Fixed Point Theorems
Appendix 2. Interpolation and Approximation
Appendix 3. Random Variables
References
Subjects Index
