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Stock Market Modeling and Forecasting translates experience in system adaptation gained in an engineering context to the modeling of financial markets with a view to improving the capture and understanding of market dynamics. The modeling process is considered as identifying a dynamic system in which a real stock market is treated as an unknown plant and the identification model proposed is tuned by feedback of the matching error. Like a physical system, a financial market exhibits fast and slow dynamics corresponding to external (such as company value and profitability) and internal forces (such as investor sentiment and commodity prices) respectively. The framework presented here, consisting of an internal model and an adaptive filter, is successful at considering both fast and slow market dynamics. A double selection method is efficacious in identifying input factors influential in market movements, revealing them to be both frequency- and market-dependent.
Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It shows how the differential geometric approach is used when the coefficients of partial differential equations (PDEs) are variable in space (waves/plates), when the PDEs themselves are defined on curved surfaces (shells), and when the systems have quasilinear principal parts.
To make the book self-contained, the author starts with the necessary background on Riemannian geometry. He then describes differential geometric energy methods that are generalizations of the classical energy methods of the 1980s. He illustrates how a basic computational technique can enable multiplier schemes for controls and provide mathematical models for shells in the form of free coordinates. The author also examines the quasilinearity of models for nonlinear materials, the dependence of controllability/stabilization on variable coefficients and equilibria, and the use of curvature theory to check assumptions.
With numerous examples and exercises throughout, this book presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics.
A modern approach to mathematical modeling, featuring unique applications from the field of mechanics
An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics.
The author streamlines a comprehensive understanding of the topic in three clearly organized sections:
Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study.
Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.
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