Mathematical Modeling

This textbook makes the difference whether one can see the whole picture of something or not. In its two parts, this 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 [...]
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This textbook makes the difference whether one can see the whole picture of something or not. In its two parts, this 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 very helpful 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. This 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. This 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.