Modelling Mathematical Methods and Scientific Computation  book cover
1st Edition

Modelling Mathematical Methods and Scientific Computation

ISBN 9780849383311
Published December 22, 1994 by CRC Press
512 Pages

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Book Description

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.

Table of Contents

Mathematical Modelling
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
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
Discussion and Developments
Scientific Programs
Appendix 1. Functional Spaces and Fixed Point Theorems
Appendix 2. Interpolation and Approximation
Appendix 3. Random Variables
Subjects Index

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"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