Principles of Mathematical Modeling
- Clive Dym, Harvey Mudd College, Claremont, California, U.S.A.
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. Prospective students should have already completed courses in elementary algebra, trigonometry, and first-year calculus and have some familiarity with differential equations and basic physics.View full description
Students in Mathematical Modeling courses taught in either mathematics or engineering departments; also professional engineers and mathematicians.
- Published: June 2004
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-226551-8
"It is one of the best introductory texts in mathematical modeling which the reviewer warmly recommends to anyone who wishes to learn the foundations of mathematical modeling with enjoyment." -Yuri V. Rogovchenko, in ZENTRALBLATT FUR MATHEMATIK, 2005 "Principles of Mathematical Modeling is a delightfully readable, well-written account of the way engineers look at the world. It covers a surprizingly wide range of topics...The many examples treated in the text are drawn from the practical world that engineers inhabit, with some surprises thrown in for good measure..." - Robert Borelli, Harvey Mudd College "The book itself is marvelously interdisciplinary, treating biological and human designed systems in addition to physical systems. These examples show that engineers can do more than simply analyze simple physical systems with known, exact solutions." - Bill Wood, University of Maryland at Baltimore
Table of ContentsPrefaceAcknowledgmentsPart A: Foundations1. What is Mathematical Modeling?2. Dimensional Analysis3. Scale4.Approximating and Validating ModelsPart B: Applications5. Exponential Growth and Decay6. Traffic Flow Models7. Modeling Free Vibration8. Applying Vibration Models 9. Optimization: What is the Best...?Index