Mathematical Modeling Handbook PDF

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Mathematical Modeling Handbook PDF

Mathematical Modeling Handbook

Book Description:

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.

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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.

Book Review:

This is an excellent textbook. Kudos to the author for the effort and time that he had put into his book. I could not say more than what other reviewers said: Roekaerts, D. 2013 “Reading this book “Mathematical Modeling” by Stefan Heinz, reminded me about the best teachers I have had. They not only explained how to solve equations, but also provided the story why a certain model is possible or useful … the book is of particular interest for teachers and researchers …[and] wider audience in science and engineering. … it treats both deterministic and stochastic models … presents a complete range of modeling techniques, from simple algebraic analysis to statistical equations systems requiring numerical simulation. And finally, it is really great that the presentation is complete. Not only are the assumptions and steps in the derivations, but also the reasoning leading to the use of a specific type of mode made fully clear. … In conclusion I strongly recommend the book to anyone wanting to acquire good understanding what mathematical modeling is about.”
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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About the Author:

Heinz studied political science and history at the Free University of Berlin. In 2005 he graduated with a diploma in political science. In 2009, Heinz received his doctorate with a study on historical trade union and KPD research at Siegfried Mielke. Since 2007 he has been a lecturer at the Otto Suhr Institute of the Free University Berlin. Heinz initially worked as an assistant to Mielke. Since 2010 he has been a research assistant at the Department of Political and Social Sciences of the Free University of Berlin in the department of National and International Trade Union Policy at the Otto Suhr Institute.”

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