Mathematical Modeling and Simulation: Introduction for Scientists and Engineers / Edition 1

Mathematical Modeling and Simulation: Introduction for Scientists and Engineers / Edition 1

by Kai Velten
     
 

ISBN-10: 3527407588

ISBN-13: 9783527407583

Pub. Date: 02/24/2009

Publisher: Wiley

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those

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Overview

This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail.

Based on the author's modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation?

The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).

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Product Details

ISBN-13:
9783527407583
Publisher:
Wiley
Publication date:
02/24/2009
Edition description:
New Edition
Pages:
362
Product dimensions:
6.60(w) x 9.40(h) x 0.70(d)

Table of Contents

Preface

1. Principles of Mathematical Modeling
1.1 A complex world needs models
1.2 Systems, models, simulations
1.3 Mathematics is the natural modeling language
1.4 Definition of mathematical models
1.5 Examples and some more definitions
1.6 Even more definitions
1.7 Classification of mathematical models
1.8 Everything looks like a nail?

2. Phenomenological models
2.1 Elementary statistics
2.2 Linear regression
2.3 Multiple linear regression
2.4 Nonlinear regression
2.5 Neural networks
2.6 Design of experiments
2.7 Other phenomenological modeling approaches

3. Mechanistic models I: ODE's
3.1 Distinguished role of differential equations
3.2 Introductory examples
3.3 General idea of ODE's
3.4 Setting up ODE models
3.5 Some theory you should know
3.6 Solution of ODE's: Overview
3.7. Closed form solution
3.8 Numerical solutions
3.9 Fitting ODE's to data
3.10 More examples

4. Mechanistic models II: PDE's
4.1. Introduction
4.2. The heat equation
4.3. Some theory you should know
4.4 Closed form solution
4.5 Numerical solution of PDE's
4.6 The finite difference method
4.7 The finite element method
4.8 Finite element software
4.9 A sample session using Salome Meca
4.10 A look beyond the heat equation
4.11 Other mechanistic modeling approaches

A CAELinux and the book software
B R (programming language and software environment)
C Maxima

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