[Selected] Principles of Mathematical Modeling, 2ed, 2004, Elsevier.pdf

Principles of Mathematical Modeling
by Clive L. Dym



· ISBN: 0122265513
· Pub. Date: June 2004
· Publisher: Elsevier Science & Technology Books
Preface
My Goals For This Book
Science and engineering students depend heavily on concepts of math-
ematical modeling. In an age where almost everything is done on a
computer, it is my conviction that students of engineering and science are
better served if they understand and “own” the underlying mathematics
that puters are doing on their behalf. Mathematics is a necessary
language for doing engineering and science. This will remain true no mat-
ter how putation es. I repeatedly tell students that it is
risky to puter calculations without having done some parallel
closed-form modeling to benchmark puter results. Without such
benchmarking and validation, how do we know that puter isn’t talking
nonsense? Finally, I find it satisfying and fun to do mathematical manipula-
tions that explain how or why something happens, and to use mathematics
to obtain corresponding numerical data or predictions.
Thus, as it was for the first edition, my primary goal for this second edition
remains to engage the reader in developing a foundation for mathematical
modeling. Further, knowing that mathematical models are built in a range
of disciplines—including physics, biology, ecology, economics, sociology,
military strategy, as well as all of the many branches of engineering—and
knowing that mathematical modeling prised of a very diverse set of
skills and tools, I focused on techniques of particular interest to engineers,
scientists, and others who model continuous systems.
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xiv Preface
Features of This Edition
Aided by a variety of reviewers’ comments and suggestions, this second
edition features:
• A more formal statement of a principled approach to mathematical
modeling (in Chapter 1). Ten principles are articulated and invoked
as applications are developed, and each of them is iden