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Mathematical Modeling and Simulation.pdf
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students at the undergraduate level. The only mathematical prerequisites are some calculus and linear algebra – all other concepts and ideas will be developed in the course of the book. The reader will find answers to basic questions such as:
What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? How does one set up a mathematical model? What is simulation, parameter estimation, validation? The book aims to
be a practical guide, enabling the reader to setup simple mathematical models on his own and to interpret his own and other people’s results critically. To achievethis, many examples from various fields such as biology, ecology, economics,
medicine, agricultural, chemical, electrical, mechanical and process engineering are discussed in detail.
The book relies exclusively upon open-source software, which is available to everybody free of charge. The reader is introduced into CAELinux, Calc, Code-Saturne, Maxima, R, and Salome-Meca, and 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, see Appendix A).
The book is organized as follows. Chapter 1 explains the principles of mathematical modeling and simulation. It provides definitions and illustrative examples of the important concepts as well as an overview of the main types of mathematical models.
After a treatment of phenomenological (data-based) models in Chapter 2, the rest of the book introduces the most important classes of mechanistic (process-oriented) models (ordinary and partial differential equation models in Chapters 3 and 4, respectively).
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