Mathematical Modeling and Simulation

Learn to use modeling and simulation methods to attack real-world problems, from physics to engineering, from life sciences to process engineering

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, 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.

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 M. Schmidt holds MSc (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.