Mathematical Modeling and Simulation

Introduction for Scientists and Engineers

Velten, Kai / Schmidt, Dominik M. / Kahlen, Katrin

2. Edition August 2024
496 Pages, Softcover
7 Pictures
9 tables
Practical Approach Book

ISBN: 978-3-527-41414-7

Wiley-VCH, Berlin

Short Description

Practice-oriented introduction to mathematical modeling and simulation using only open-source tools for scientists and engineers from all professions in the physical and life sciences and for advanced undergraduate and graduate students - now in its second edition!

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Further versions

Reviews of the first edition (2009):

»Perfectly fits introductory modeling courses [...] and is an enjoyable reading in the first place. Highly recommended [...]«
Zentralblatt MATH, European Mathematical Society, 2009

»This book differs from almost all other available modeling books in that [the authors address] both mechanistic and statistical models as well as 'hybrid' models. [...] The modeling range is enormous.«
SIAM Society of Industrial and Applied Mathematics, USA, 2011

This completely revised and substantially extended second edition answers the most important questions in the field of modeling: 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? What kind of mathematical problems appear and how can these be efficiently solved using professional free of charge open source software?
The book addresses undergraduates and practitioners alike. Although only basic knowledge of calculus and linear algebra is required, the most important mathematical structures are discussed in sufficient detail, ranging from statistical models to partial differential equations and accompanied by examples from biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical, and process engineering.
About 200 pages of additional material include a unique chapter on virtualization, Crash Courses on the data analysis and programming languages R and Python and on the computer algebra language Maxima, many new methods and examples scattered throughout the book and an update of all software-related procedures and a comprehensive book software providing templates for typical modeling tasks in thousands of code lines. The book software includes GmLinux, an operating system specifically designed for this book providing preconfigured and ready-to-use installations of OpenFOAM, Salome, FreeCAD/CfdOF workbench, ParaView, R, Maxima/wxMaxima, Python, Rstudio, Quarto/Markdown and other free of charge open source software used in the book.

Preface

1 PRINCIPLES OF MATHEMATICAL MODELING
1.1 A Complex World Needs Models
1.2 Systems, Models, Simulations
1.3 Mathematics as a 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 Smoothing Splines
2.6 Neural Networks
2.7 Big Data Analysis
2.8 Signal Processing
2.9 Design of Experiments
2.10 Other Phenomenological Modeling Approaches

3 MECHANISTIC MODELS I: ODES
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 Solutions
3.8 Numerical Solutions
3.9 Fitting ODE?s to Data
3.10 More Examples

4 MECHANISTIC MODELS II: PDES
4.1 Introduction
4.2 The Heat Equation
4.3 Some Theory You Should Know
4.4 Closed Form Solutions
4.5 Numerical Solution of PDE?s
4.6 The Finite Difference Method
4.7 The Finite Element Method
4.8 The Finite Volume Method
4.9 Software packages to solve PDEs
4.10 A Sample Session on the Numerical Solution of Thermal Conduction
4.11 A Look Beyond the Heat Equation
4.12 Computational Fluid Dynamics (CFD)
4.13 Numerical solutions of exaple flow problems

5 VIRTUALIZATION
5.1 Introduction
5.2 Virtual Plants
5.3 Examples of Advanced Applications

6 CRASH COURSES AND BOOK SOFTWARE
6.1 Crashcourse R
6.2 Crashcourse Maxima
6.3 CrashCrashcourse Python (and all the rest)
6.4 Book software and GmLinux

References
Index

Kai Velten is a mathematician and modeling and simulation consultant focusing on data analysis and differential equations. He held scientific positions at Braunschweig and Erlangen Universities and the Fraunhofer-ITWM in Kaiserslautern between 1990-2000, works as professor of mathematics at Hochschule Geisenheim University since 2000 and was offered another professorship at Lüneburg University in 2012.

Dominik Schmidt holds M.Sc. (Beverage Technology) and PhD (Agriculture) degrees obtained from Hochschule Geisenheim University and University of Gießen. Working in the Department of Modeling and Systems Analysis of Hochschule Geisenheim University since 2013, he performed a broad range of research projects in the fields of data science, mathematical modeling and computational fluid dynamics.

Katrin Kahlen is a mathematician working at Hochschule Geisenheim University since 2011. She holds PhD (Mathematics) and habilitation (Agronomy) degrees obtained from University of Hannover and became Adjunct Professor at Hochschule Geisenheim University in 2021. She is particularly interested in modeling and simulation of plant-environment interactions, and the development and use of virtual plants.