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Principles of Mathematical Modeling

Principles of Mathematical Modeling 3rd edition describes, in clear and simple language, the essential corpus of modelling principles, and then builds on them with a set of fou… Read more

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Description

Principles of Mathematical Modeling 3rd edition describes, in clear and simple language, the essential corpus of modelling principles, and then builds on them with 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.　

The work will be particularly of interest to scientific and professional students of various stripes who depend heavily on concepts of mathematical modeling. In an age where many modelling applications turn increasingly to the cloud, author Clive Dym believes that students need to understand and ‘own’ the underlying mathematics that computers are doing on their behalf. This work aims to continue to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers.　

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.

Key features

  • Treatment of a hugely diverse array of multidisciplinary topics - from engineering to economics to biological science

  • The work focuses on modeling methods of particular interest to engineers, scientists, and others who model continuous systems with pertinent application examples.

  • Offers more than 400 problems and case studies, providing ample opportunities for practice

  • Uses straightforward language and explanations that make modeling easy to understand and apply

  • Uses a systematic approach to mathematical modeling, outlining ten specific principles with articles progressing in complexity.

Readership

Students in Mathematical Modeling courses taught in either mathematics or engineering departments; also professional engineers and mathematicians.

Table of contents

Preface

Acknowledgments

Part A: Foundations

1. What is Mathematical Modeling?

2. Dimensional Analysis

3. Scale

4.Approximating and Validating Models

Part B: Applications

5. Exponential Growth and Decay

6. Traffic Flow Models

7. Modeling Free Vibration

8. Applying Vibration Models

9. Optimization: What is the Best...?

Index

Product details

About the author

CD

Clive Dym

Clive L. Dym is Fletcher Jones Professor of Engineering Design and Director of the Center for Design Education at Harvey Mudd College. His primary interests are in engineering design and structural mechanics. After receiving the PhD from Stanford University, Dr. Dym held appointments at the University at Buffalo; the Institute for Defense Analyses; Carnegie Mellon University; Bolt, Beranek and Newman; and the University of Massachusetts at Amherst. He was also head of his department at UMass (1977-85) and chair of his department at Harvey Mudd (1999-2002). Dr. Dym has held visiting appointments at the TECHNION-Israel Institute of Technology, the Institute for Sound and Vibration Research at Southampton, Stanford, Xerox PARC, Carnegie Mellon, Northwestern and USC. He has authored or coauthored some 85 refereed journal articles, was Founding Editor of the journal Artificial Intelligence for Engineering Design, Analysis, and Manufacturing, and has served on the editorial boards of several other journals, including the ASME’s Journal of Mechanical Design.

Dr. Dym is a Fellow of the Acoustical Society of America, the American Society of Mechanical Engineers, the American Society of Civil Engineers and the American Society for Engineering Education, and is a Member of the American Academy of Mechanics. Dr. Dym’s awards include the Walter L. Huber Research Prize (ASCE, 1980), the Western Electric Fund Award (ASEE, 1983), the Boeing Outstanding Educator Award (first runner-up, 2001), the Fred Merryfield Design Award (ASEE, 2002), the Joel and Ruth Spira Outstanding Design Educator Award (ASME, 2004), the Archie Higdon Distinguished Educator Award (Mechanics Division, ASEE, 2006), the Gordon Prize for Innovation in Engineering and Technology Education (co-winner, National Academy of Engineering, 2012), the Benjamin Garver Lamme Award (ASEE, 2015), and the 1st Design Theory and Methodology Award (ASME, 2015).

Affiliations and expertise
Harvey Mudd College, Claremont, California, U.S.A.