Principles of Mathematical Modeling

ISBN-13: 9780122265518 / Angielski / Twarda / 2004 / 303 str.

Clive L. Dym

Opis

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.

• Serves as an introductory text on the development and application of mathematical models
• Focuses on techniques of particular interest to engineers, scientists, and others who model continuous systems
• Offers more than 360 problems, providing ample opportunities for practice
• Covers a wide range of interdisciplinary topics--from engineering to economics to the sciences
• Uses straightforward language and explanations that make modeling easy to understand and apply

New to this Edition:

• A more systematic approach to mathematical modeling, outlining ten specific principles
• Expanded and reorganized chapters that flow in an increasing level of complexity
• Several new problems and updated applications
• Expanded figure captions that provide more information
• Improved accessibility and flexibility for teaching

Recenzje

"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

Spis treści

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...?

O autorze

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).