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.
General
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