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Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering

2020-11-02 Mathematics
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Release : 2020-11-02
Genre : Mathematics
Kind : eBook
Book Rating : 878/5 ( reviews)

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Book Synopsis Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering by : Fabio Silva Botelho

Download or read book Functional Analysis, Calculus of Variations and Numerical Methods for Models in Physics and Engineering written by Fabio Silva Botelho. This book was released on 2020-11-02. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.

Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory

2021-07-12 Mathematics
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Release : 2021-07-12
Genre : Mathematics
Kind : eBook
Book Rating : 028/5 ( reviews)

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Book Synopsis Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory by : Fabio Silva Botelho

Download or read book Advanced Calculus and its Applications in Variational Quantum Mechanics and Relativity Theory written by Fabio Silva Botelho. This book was released on 2021-07-12. Available in PDF, EPUB and Kindle. Book excerpt: Presents a rigorous study on manifolds in Rn. Develops in details important standard topics on advanced calculus, such as the differential forms in surfaces in Rn. Presents a proposal to connect classical and quantum mechanics. Presents variational formulations for relativistic mechanics through semi-Riemannian geometry and differential geometry. Develops a rigorous study on causal structures in space-time manifolds.

The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

2024-02-06 Science
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Release : 2024-02-06
Genre : Science
Kind : eBook
Book Rating : 427/5 ( reviews)

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Book Synopsis The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering by : Fabio Silva Botelho

Download or read book The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering written by Fabio Silva Botelho. This book was released on 2024-02-06. Available in PDF, EPUB and Kindle. Book excerpt: The book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models. The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.

Mathematical Analysis and Numerical Methods for Science and Technology

2015-03-20 Mathematics
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Release : 2015-03-20
Genre : Mathematics
Kind : eBook
Book Rating : 66X/5 ( reviews)

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Book Synopsis Mathematical Analysis and Numerical Methods for Science and Technology by : Robert Dautray

Download or read book Mathematical Analysis and Numerical Methods for Science and Technology written by Robert Dautray. This book was released on 2015-03-20. Available in PDF, EPUB and Kindle. Book excerpt: These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.

Functional Analysis, Calculus of Variations and Optimal Control

2013-02-06 Mathematics
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Release : 2013-02-06
Genre : Mathematics
Kind : eBook
Book Rating : 207/5 ( reviews)

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Book Synopsis Functional Analysis, Calculus of Variations and Optimal Control by : Francis Clarke

Download or read book Functional Analysis, Calculus of Variations and Optimal Control written by Francis Clarke. This book was released on 2013-02-06. Available in PDF, EPUB and Kindle. Book excerpt: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

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