Mathematical Modeling

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 Centerfor Atmospheric Research (NCAR) at Boulder.

• Deterministic Analysis of Observations.-Stochastic Analysis of Observations.-Deterministic States.-Stochastic States.-Deterministic Changes.-Stochastic Changes.-Deterministic Evolution.-Stochastic Evolution.-Deterministic Multivariate Evolution.-Stochastic Multivariate Evolution."

From the reviews: "It is of special interest for a fluid dynamics audience since most types of models one would like to apply in fluid dynamic systems are introduced. ... Mathematical modeling is of great use as background reading material for any course on advanced fluid dynamics. ... A total of 570 exercise questions are organized in 220 problems ... . I strongly recommend the book to anyone wanting to acquire good understanding what mathematical modeling is about." (Dirk J. E. M. Roekaerts, Theoretical and Computational Fluid Dynamics, Vol. 27, 2013) "The book covers two primary types of modeling: deterministic and stochastic. ... The text can be used for a course at the undergraduate or graduate level. ... This course would be particularly beneficial to students outside of science and engineering. ... I like this book and recommend it as a text in mathematical modeling. I also recommend it for those studying turbulent fluid mechanics, stochastic vibration & structures, noise, meteorology, random data management, and stock market analysis." (Peyman Givi, AIAA Journal, Vol. 50 (12), December, 2012) "This book is aimed at advanced undergraduate and graduate students in mathematics who have a background in single and multivariable calculus, linear algebra, and ordinary differential equations. ... 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. ... The entire book could be covered in a two-semester sequence of courses at the graduate level. Summing Up: Recommended. Upper-division undergraduates and graduate students." (B. Borchers, Choice, Vol. 49 (5), January, 2012) "The book under review 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. ... This textbook nicely complements existing literature on mathematical modeling and can be used both as a main source or as a supplementary text ... in applied mathematics and mathematical modeling." (Svitlana P. Rogovchenko, Zentralblatt MATH, Vol. 1239, 2012) "It is a collection of examples of models ... with a large emphasis on engineering, the author's major field as well as the theme of its Springer series. ... this book may serve as a reference for those seeking examples of modeling in different specializations, or as a resource for exercises; several of the latter are at the end of each chapter." (J. David Logan, SIAM Review, Vol. 54 (3), 2012)