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Mathematical Modeling Handbook
The whole picture of Mathematical Modeling is systematically and thoroughly explained in this text for undergraduate and graduate students of mathematics, engineering, economics, finance, biology, chemistry, and physics. This textbook gives an overview of the spectrum of modeling techniques, deterministic and stochastic methods, and first-principle and empirical solutions.
Complete range: The text continuously covers the complete range of basic modeling techniques: it provides a consistent transition from simple algebraic analysis methods to simulation methods used for research. Such an overview of the spectrum of modeling techniques is very helpful for the understanding of how a research problem considered can be appropriately addressed.
Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do hardly have access to stochastic methods, which are described in advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it shows how deterministic methods are generalized by stochastic methods.
Complete solutions: A variety of empirical approximations is often available for the modeling of processes. The question of which assumption is valid under certain conditions is clearly relevant. The book provides a bridge between empirical modeling and first-principle methods: it explains how the principles of modeling can be used to explain the validity of empirical assumptions. The basic features of micro-scale and macro-scale modeling are discussed – which is an important problem of current research.
Givi, P. 2012 ” … this text very useful … as it is accessible to almost all of the students, regardless of background.”… “The book has several other pleasing features: conciseness of writing, clarity of figures, presentation of relevant examples, and inclusion of a large number of exercises at the end of each chapter. …
Rogovchenko, S. P. 2012 ” … is aimed at students in mathematics, physics, engineering, biology, chemistry, economics, finance. … well-written, generously illustrated, and contains many carefully explained examples that are often based on real data. Each chapter starts with a brief ‘Motivation’ section and concludes with a ‘Summary’ that emphasizes the most important ideas and techniques.
Borchers, B. 2012 “… focuses on the construction of mathematical models, the derivation of analytical solutions to tractable models, and the qualitative analysis of the behavior of solutions to the less tractable models. … “Amazon Reader
Mathematical Modeling Handbook PDF
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