Modelling mathematical methods and scientific computation

Nicola Bellomo, Luigi Preziosi

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.

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[目次]

  • 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

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この本の情報

書名 Modelling mathematical methods and scientific computation
著作者等 Bellomo, Nicola
Preziosi, Luigi
シリーズ名 Mathematical modelling series
出版元 CRC Press
刊行年月 1995
ページ数 xiv, 497 p.
大きさ 24 cm
付随資料 1 floppy disk (3 1/2 in.)
ISBN 0849383315
NCID BA24647713
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言語 英語
出版国 アメリカ合衆国
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