E-Book Overview
Mathematical modeling the ability to apply mathematical concepts and techniques to real-life systems has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to elaborated case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.
E-Book Content
mm13_molenaarfm-a.qxp
2/5/2007
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Continuum Modeling in the Physical Sciences
mm13_molenaarfm-a.qxp
2/5/2007
1:56 PM
Page 2
Mathematical Modeling and Computation About the Series The SIAM series on Mathematical Modeling and Computation draws attention to the wide range of important problems in the physical and life sciences and engineering that are addressed by mathematical modeling and computation; promotes the interdisciplinary culture required to meet these large-scale challenges; and encourages the education of the next generation of applied and computational mathematicians, physical and life scientists, and engineers. The books cover analytical and computational techniques, describe significant mathematical developments, and introduce modern scientific and engineering applications. The series will publish lecture notes and texts for advanced undergraduate- or graduate-level courses in physical applied mathematics, biomathematics, and mathematical modeling, and volumes of interest to a wide segment of the community of applied mathematicians, computational scientists, and engineers. Appropriate subject areas for future books in the series include fluids, dynamical systems and chaos, mathematical biology, neuroscience, mathematical physiology, epidemiology, morphogenesis, biomedical engineering, reaction-diffusion in chemistry, nonlinear science, interfacial problems, solidification, combustion, transport theory, solid mechanics, nonlinear vibrations, electromagnetic theory, nonlinear optics, wave propagation, coherent structures, scattering theory, earth science, solid-state physics, and plasma physics. E. van Groesen and Jaap Molenaar, Continuum Modeling in the Physical Sciences Gerda de Vries, Thomas Hillen, Mark Lewis, Johannes Müller, and Birgitt Schönfisch, A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods Ivan Markovsky, Jan C. Willems, Sabine Van Huffel, and Bart De Moor, Exact and Approximate Modeling of Linear Systems: A Behavioral Approach R. M. M. Mattheij, S. W. Rienstra, and J. H. M. ten Thije Boonkkamp, Partial Differential Equations: Modeling, Analysis, Computation Johnny T. Ottesen, Mette S. Olufsen, and Jesper K. Larsen, Applied Mathematical Models in Human Physiology Ingemar Kaj, Stochastic Modeling in Broadband Communications Systems Peter Salamon, Paolo Sibani, and Richard Frost, Facts, Conjectures, and Improvements for Simulated Annealing Lyn C. Thomas, David B. Edelman, and Jonathan N. Crook, Credit Scoring and Its Applications Frank Natterer and Frank Wübbeling, Mathematical Methods in Image Reconstruction Per Christian Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear I