Surveys In Applied Mathematics

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Surveys In Applied Mathematics

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Author : Nicholas Constantine Metropolis
language : en
Publisher:
Release Date : 1976

Surveys In Applied Mathematics written by Nicholas Constantine Metropolis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.

Surveys In Applied Mathematics

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Author : Joseph B. Keller
language : en
Publisher: Springer
Release Date : 2013-12-21

Surveys In Applied Mathematics written by Joseph B. Keller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Mathematics categories.

Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity.

Surveys In Applied Mathematics

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Author : Stanislaw Ulam
language : en
Publisher:
Release Date : 1976

Surveys In Applied Mathematics written by Stanislaw Ulam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.

Surveys In Applied Mathematics

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Author : Mark I. Freidlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Surveys In Applied Mathematics written by Mark I. Freidlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Volume 2 offers three in-depth articles covering significant areas in applied mathematics research. Chapters feature numerous illustrations, extensive background material and technical details, and abundant examples. The authors analyze nonlinear front propagation for a large class of semilinear partial differential equations using probabilistic methods; examine wave localization phenomena in one-dimensional random media; and offer an extensive introduction to certain model equations for nonlinear wave phenomena.

Surveys In Applied Mathematics

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Author :
language : en
Publisher:
Release Date : 1958

Surveys In Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with categories.

Applied Delay Differential Equations

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Author : Thomas Erneux
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-06

Applied Delay Differential Equations written by Thomas Erneux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-06 with Mathematics categories.

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

Higher Order Derivatives

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Author : Satya Mukhopadhyay
language : en
Publisher: CRC Press
Release Date : 2012-01-25

Higher Order Derivatives written by Satya Mukhopadhyay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-25 with Mathematics categories.

The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places, nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives, their uses, and the relations among them. It covers higher order generalized derivatives, including the Peano, d.l.V.P., and Abel derivatives; along with the symmetric and unsymmetric Riemann, Cesàro, Borel, LP-, and Laplace derivatives. Although much work has been done on the Peano and de la Vallée Poussin derivatives, there is a large amount of work to be done on the other higher order derivatives as their properties remain often virtually unexplored. This book introduces newcomers interested in the field of higher order derivatives to the present state of knowledge. Basic advanced real analysis is the only required background, and, although the special Denjoy integral has been used, knowledge of the Lebesgue integral should suffice.

Surveys In Applied Mathematics

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Author : Joseph B. Keller
language : en
Publisher: Springer
Release Date : 2014-01-04

Surveys In Applied Mathematics written by Joseph B. Keller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-04 with Mathematics categories.

Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity.

Survey Of Applicable Mathematics

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Author : K. Rektorys
language : en
Publisher: Springer
Release Date : 2013-12-19

Survey Of Applicable Mathematics written by K. Rektorys and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Mathematics categories.

This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969. The thirty-seven chapters cover all the important mathematical fields of use in applications: algebra, geometry, differential and integral calculus, infinite series, orthogonal systems of functions, Fourier series, special functions, ordinary differential equations, partial differential equations, integral equations, functions of one and several complex variables, conformal mapping, integral transforms, functional analysis, numerical methods in algebra and in algebra and in differential boundary value problems, probability, statistics, stochastic processes, calculus of variations, and linear programming. All proofs have been omitted. However, theorems are carefully formulated, and where considered useful, are commented with explanatory remarks. Many practical examples are given by way of illustration. Each of the two volumes contains an extensive bibliography and a comprehensive index. Together these two volumes represent a survey library of mathematics which is applicable in many fields of science, engineering, economics, etc. For researchers, students and teachers of mathematics and its applications.

Mathematical Aspects Of Numerical Solution Of Hyperbolic Systems

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Author : A.G. Kulikovskii
language : en
Publisher: CRC Press
Release Date : 2000-12-21

Mathematical Aspects Of Numerical Solution Of Hyperbolic Systems written by A.G. Kulikovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-12-21 with Mathematics categories.

This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.