Ebook: Mathematical modeling

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.

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This textbook makes the difference whether one can see the whole picture of something or not. In its two parts, the book gives a complete overview of the spectrum of modeling techniques, basic modeling methods, and modeling solutions. Part I is focused on the explanation of basic modeling concepts based on analytical methods. Part II is focused on the introduction of simulation methods used for the solution of research problems."Mathematical Modeling" provides: A complete range: The textbook covers continuously 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 veryhelpful for the understanding, and it enables applications to research problems.Complete methods: Real-world processes always involve uncertainty, and the consideration of randomness is often relevant. Many students know deterministic methods, but they do not have access to stochastic methods because they cannot follow advanced textbooks on probability theory. The book develops consistently both deterministic and stochastic methods. In particular, it will be shown how deterministic methods are generalized by stochastic methods.Complete solutions: A bridge between empirical modeling and ‘first-principle’ methods.The book explains how the principles of modeling can be used to generalize empirical assumptions. Special emphasis is placed on a thorough discussion of basic features of micro-scale and macro-scale modeling – which is a very important problem of current research.