Mathematical Modeling (eBook)

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 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. 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.

Dr. Stefan Heinz is a Professor of Mathematics at the University of Wyoming. He holds a Ph.D. in Physics from the Heinrich-Hertz Institute, Berlin. His research interests are in mathematical modeling, multiscale processes, stochastic analysis, Monte Carlo simulations, computational fluid dynamics, turbulence, combustion, and multiphase flows. He has authored more than seventy refereed publications and the textbook Statistical Mechanics of Turbulent Flows (Springer, 2003). For more than ten years he has taught a variety of courses: calculus, probability, ordinary, partial, and stochastic differential equations, applied mathematics, and deterministic and stochastic mathematical modeling. His exceptional teaching was awarded in 2007 by the College of Arts and Sciences Extraordinary Merit in Teaching Award. In 2008 he was honored as Adjunct Professor of Mechanical Engineering. He has held visiting professor appointments at ETH Zurich, Delft Technical University, and the National Center for Atmospheric Research (NCAR) at Boulder.