Mathematical Modeling and Simulation

1. Preface
2. Principles of Mathematical Modeling
2.1. Modeling as a strategy to treat complex systems
2.2. Mathematics as a natural modeling language
2.3. Definition of mathematical models
2.4. Examples and further definitions
2.5. Classification of mathematical models
3. Phenomenological models
3.1. Basic descriptive statistics
3.2. Regression models
3.3. Neural network models
3.4. Basic inferential statistics
3.5. Other models
4. Mechanistic models
4.1. Understanding an unexpected effect
4.2. Ordinary Differential Equation Models
4.3. Partial Differential Equation Models
4.4. Other models
5. Practical issues
5.1 Experimental design
5.2 Parameter identification
5.3 Validation
5.4 Databases
5.5 Software and Project Management
5.6 Everything looks like a nail?
6. Introduction to the Book Software
6.1 CAE-Linux
6.2 R
6.3 Maxima
6.4 Salome and Code Aster
7. Appendix
8. References

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 he 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.

Very solid introductory text at the undergraduate level aimed at wide audience. Perfectly fits introductory modeling courses at colleges and universities that prefer to use open-source software rather than commercial one, and is an enjoyable reading in the first place. Highly recommended both as a main text and a supplementary one. (...) This delightful book has two unbeatable features that should absolutely win the audience (...) First of all, it illuminates many important conceptual ideas of mathematical modelling (...) Second, (...) this book enthusiastically promotes open-source software that works on most computers and operating systems and is freely available on the web. (...) Professor Velten suggests an elegant approach to mathematical modeling, carefully going through all important steps from identification of a problem, definition of the associated system under study and analysis of the system's properties to design of a mathematical model for the system, its numerical simulation and validation.(Yuri V. Rogovchenko, Zentralblatt MATH, European Mathematical Society)

"Very solid introductory text at the undergraduate level aimed at wide audience. Perfectly fits introductory modeling courses at colleges and universities that prefer to use open-source software rather than commercial one, and is an enjoyable reading in the first place. Highly recommended both as a main text and a supplementary one. (...) This delightful book has two unbeatable features that should absolutely win the audience (...) First of all, it illuminates many important conceptual ideas of mathematical modelling (...) Second, (...) this book enthusiastically promotes open-source software that works on most computers and operating systems and is freely available on the web. (...) Professor Velten suggests an elegant approach to mathematical modeling, carefully going through all important steps from identification of a problem, definition of the associated system under study and analysis of the system's properties to design of a mathematical model for the system, its numerical simulation and validation."
(Yuri V. Rogovchenko, Zentralblatt MATH, European Mathematical Society)
 
"The book is certainly a reference for those, beginners or professional, who search for a complete and easy to follow step-by-step guide in the amazing world of modeling and simulation (...) it is shown that mathematical models and simulation, if adequately used, help to reduce experimental costs by a better exploration of the information content of experimental data (...) it is explained how to analyze a real problem arising from science or engineering and how to best describe it through a mathematical model. A number of examples help the reader to follow step by step the basics of modelling."
(Marcello Vasta, Meccanica: International Journal of Theoretical and Applied Mechanics, Vol. 44(3), 2009)
 
"The broad subject area covered in this book reflects the background of the author, an experienced mathematical consultant and academic (...) This book differs from almost all