Mathematical and Computational Modeling: With Applications by Roderick Melnik

By Roderick Melnik

Illustrates the appliance of mathematical and computational modeling in quite a few disciplines

With an emphasis at the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With functions within the common and Social Sciences, Engineering, and the Arts beneficial properties chapters written via famous, overseas specialists in those fields and presents readers with a bunch of cutting-edge achievements within the improvement of mathematical modeling and computational scan technique. The booklet is a invaluable consultant to the equipment, principles, and instruments of utilized and computational arithmetic as they follow to different disciplines akin to the average and social sciences, engineering, and technology.  Mathematical and Computational Modeling: With purposes within the usual and Social Sciences, Engineering, and the Arts additionally features:

  • Rigorous mathematical methods and purposes because the motive force at the back of mathematical innovation and discovery
  • Numerous examples from quite a lot of disciplines to stress the multidisciplinary program and universality of utilized arithmetic and mathematical modeling
  • Original effects on either basic theoretical and utilized advancements in different parts of human knowledge
  • Discussions that advertise interdisciplinary interactions among mathematicians, scientists, and engineers

Mathematical and Computational Modeling: With purposes within the usual and Social Sciences, Engineering, and the humanities is an amazing source for execs in a variety of parts of mathematical and statistical sciences, modeling and simulation, physics, machine technological know-how, engineering, biology and chemistry, business, and computational engineering. The booklet additionally serves as a very good textbook for graduate classes in mathematical modeling, utilized arithmetic, numerical tools, operations examine, and optimization. 

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Additional info for Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts

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6. Chelkak, D. , Universality in the 2D Ising model and conformal invariance of fermionic observables, Inventiones Mathematicae, 189 (3), 515–580 (2012). 7. Dolan, B. , Modular invariance, universality and crossover in the quantum Hall effect, Nuclear Physics B, 554 (3), 487–513 (1999). 8. , and Runborg, O. ), Multiscale modeling and simulation in science, Berlin; Springer, 2009. 9. Foster, D. , Multiscale modeling of solar cells with interface phenomena, Journal of Coupled Systems and Multiscale Dynamics, 1, 179–204 (2013).

These equations appear also in particle physics, as the Abelean-Higgs model, which is the simplest, and arguably most important, ingredient of the standard model [93]. Geometrically, they are the simplest equations describing the interaction of the electromagnetic field and a complex field, and can be thought of as the ‘Dirichlet’ problem for a connection of U(1)−principal bundle and a section of associated vector bundle. One of the most interesting mathematical and physical phenomena connected with Ginzburg–Landau equations is the presence of vortices in their solutions.

Based on geometric and analytic ideas, the authors present a general mathematical framework for learning. These ideas are centered around building a network or a graph whose nodes are observations. In this framework, the authors propose to maintain connections between observations by constantly reconfiguring them and calibrating in order to achieve learning characteristics for specific tasks. The developed methods are then related to ideas from Harmonic Analysis. The intrinsic connection between harmonic analysis and other disciplines is well known.

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