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.
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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...?
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).