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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


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Product Details

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

About the Author

Kai Velten is a professor of mathematics at the University of Applied Sciences, Wiesbaden, Germany, and a modeling and simulation consultant. Having studied mathematics, physics and economics at the Universities of Göttingen and Bonn, he worked at Braunschweig Technical University (Institute of Geoecology, 1990-93) and at Erlangen University (Institute of Applied Mathematics, 1994-95). From 1996-2000, he held a post as project manager and group leader at the Fraunhofer-ITWM in Kaiserslautern (consultant projects for the industry). His research emphasizes differential equation models and is documented in 34 scientific publications and one patent.

Table of Contents


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

4. Mechanistic models II: PDÉs
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 PDÉs
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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