id: 05937037
dt: b
an: 2012d.00545
au: Heinz, Stefan
ti: Mathematical modeling.
so: Berlin: Springer (ISBN 978-3-642-20310-7/hbk; 978-3-642-20311-4/ebook).
xvi, 460~p. (2011).
py: 2011
pu: Berlin: Springer
la: EN
cc: M15
ut: mathematical modeling; deterministic models; stochastic models;
observations; optimization
ci:
li: doi:10.1007/978-3-642-20311-4
ab: The book under review is aimed at students in mathematics, physics,
engineering, biology, chemistry, economics, finance. It is based on the
material used by the author for teaching an undergraduate course
“Introduction to Mathematical Modeling” and a graduate course
“Deterministic and Stochastic Mathematical Modeling” over the past
ten years. The essential prerequisites for the reader include basic
algebra, single variable calculus, and acquaintance with a computer
algebra system. Professor Heinz mentions that “examples for
calculations that students should be able to perform after the
explanation of the corresponding concepts are the plot of model
functions in comparison to random data, the calculation of a
probability density function, and the numerical solution of ordinary
differential equations.” The characteristic feature of this book is
the parallel development of deterministic and stochastic modeling
approaches. The author points out that “the consideration of
stochastic methods enables a comprehensive understanding, for example,
of the basis of optimal deterministic models and how closed
deterministic equations can be obtained.” This approach to
mathematical modeling influences significantly the way the material is
grouped and presented. In fact, all chapters in the book are
practically paired up: Chapters 1 and 2 “Deterministic Analysis
Observations” and “Stochastic Analysis Observations,” Chapters 3
and 4 “Deterministic States” and “Stochastic States,” Chapters
5 and 6 “Deterministic Changes” and “Stochastic Changes,”
Chapters 7 and 8 “Deterministic Evolution” and “Stochastic
Evolution,” Chapters 9 and 10 “Deterministic Multivariate
Evolution” and “Stochastic Multivariate Evolution.” In the
Preface, Professor Heinz provides several useful ideas regarding
organization of different courses based on the material included in the
book. In particular, it is suggested to use the first four chapters for
teaching an undergraduate course “Introduction to Mathematical
Modeling,” Chapters 5, 7, and 9 for teaching an undergraduate or
graduate course “Deterministic Mathematical Modeling,” and Chapters
6, 8, and 10 for teaching a graduate course “Stochastic Mathematical
Modeling.” The book is 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. There are 570 exercise questions in the text organized
in 220 problems; detailed solutions to all questions are given in the
Instructor’s Solutions Manual provided to instructors by the
publisher upon request. In the final part of the book, the reader can
find a substantial list of references, author and subject indices, as
well as a brief information about the author. This textbook nicely
complements existing literature on mathematical modeling and can be
used both as a main source or as a supplementary text for a variety of
courses in applied mathematics and mathematical modeling.
rv: Svitlana P. Rogovchenko (Umeå)