Mathematical and Computational Aspects PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Mathematical and Computational Aspects PDF full book. Access full book title Mathematical and Computational Aspects by Carlos A. Brebbia. Download full books in PDF and EPUB format.
Author: Carlos A. Brebbia Publisher: Springer Science & Business Media ISBN: 3662219085 Category : Technology & Engineering Languages : en Pages : 601
Book Description
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.
Author: Carlos A. Brebbia Publisher: Springer Science & Business Media ISBN: 3662219085 Category : Technology & Engineering Languages : en Pages : 601
Book Description
This book contains the edited versions of most of the papers presented at the 9th International Conference on Boundary Elements held at the University of Stuttgart, Germany from August 31st to September 4th, 1987, which was organized in co-operation with the Computational Mechanics Institute and GAMM (Society for Applied Mathematics and Mechanics). This Conference, as the previous ones, aimed to review the latest developments in technique and theory and point out new advanced future trends. The emphasis of the meeting was on the engineering advances versus mathematical formulations, in an effort to consolidate the basis of many new applications. Recently engineers have proposed different techniques to solve non-linear and time dependent problems and many of these formulations needed a better mathematical understanding. Furthermore, new approximate formulations have been proposed for boundary elements which appeared to work in engineering practice, but did not have a proper theoretical background. The Conference also discussed the engineering applications of the method and concentrated on a link between BEM practitioners, industrial users and researchers working on the latest development of the method. The editors would like to express their appreciation and thanks to Ms. Liz Newman and Mr. H. Schmitz for their unstinting work in the preparation of the Conference.
Author: Bas Edixhoven Publisher: Princeton University Press ISBN: 1400839009 Category : Mathematics Languages : en Pages : 438
Book Description
Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special cases. The case of elliptic curves (Schoof's algorithm) was at the birth of elliptic curve cryptography around 1985. This book gives an algorithm for computing coefficients of modular forms of level one in polynomial time. For example, Ramanujan's tau of a prime number p can be computed in time bounded by a fixed power of the logarithm of p. Such fast computation of Fourier coefficients is itself based on the main result of the book: the computation, in polynomial time, of Galois representations over finite fields attached to modular forms by the Langlands program. Because these Galois representations typically have a nonsolvable image, this result is a major step forward from explicit class field theory, and it could be described as the start of the explicit Langlands program. The computation of the Galois representations uses their realization, following Shimura and Deligne, in the torsion subgroup of Jacobian varieties of modular curves. The main challenge is then to perform the necessary computations in time polynomial in the dimension of these highly nonlinear algebraic varieties. Exact computations involving systems of polynomial equations in many variables take exponential time. This is avoided by numerical approximations with a precision that suffices to derive exact results from them. Bounds for the required precision--in other words, bounds for the height of the rational numbers that describe the Galois representation to be computed--are obtained from Arakelov theory. Two types of approximations are treated: one using complex uniformization and another one using geometry over finite fields. The book begins with a concise and concrete introduction that makes its accessible to readers without an extensive background in arithmetic geometry. And the book includes a chapter that describes actual computations.
Author: Sabine Van Huffel Publisher: SIAM ISBN: 0898712750 Category : Mathematics Languages : en Pages : 302
Book Description
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Author: Sabine Van Huffel Publisher: SIAM ISBN: 9781611971002 Category : Mathematics Languages : en Pages : 313
Book Description
This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.
Author: Chi Tat Chong Publisher: Walter de Gruyter GmbH & Co KG ISBN: 311038129X Category : Mathematics Languages : en Pages : 320
Book Description
This monograph presents recursion theory from a generalized point of view centered on the computational aspects of definability. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using techniques and ideas from recursion theory, hyperarithmetic theory, and descriptive set theory. The emphasis is on the interplay between recursion theory and set theory, anchored on the notion of definability. The monograph covers a number of fundamental results in hyperarithmetic theory as well as some recent results on the structure theory of Turing and hyperdegrees. It also features a chapter on the applications of these investigations to higher randomness.
Author: Donald Brown Publisher: Springer Science & Business Media ISBN: 3540765913 Category : Business & Economics Languages : en Pages : 204
Book Description
This monograph presents a general equilibrium methodology for microeconomic policy analysis. It is intended to serve as an alternative to the now classical, axiomatic general equilibrium theory as exposited in Debreu`s Theory of Value (1959) or Arrow and Hahn`s General Competitive Analysis (1971). The monograph consists of several essays written over the last decade. It also contains an appendix by Charles Steinhorn on the elements of O-minimal structures.
Author: David F. Griffiths Publisher: Springer ISBN: 3319225693 Category : Mathematics Languages : en Pages : 368
Book Description
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods. Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems. The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test understanding. They are starred according to level of difficulty. Solutions to odd-numbered exercises are available to all readers while even-numbered solutions are available to authorised instructors. Written in an informal yet rigorous style, Essential Partial Differential Equations is designed for mathematics undergraduates in their final or penultimate year of university study, but will be equally useful for students following other scientific and engineering disciplines in which PDEs are of practical importance. The only prerequisite is a familiarity with the basic concepts of calculus and linear algebra.
Author: Carlos A. Brebbia
Author: Carlos A. Brebbia
Author: Bas Edixhoven
Author: C. A. Brebbia
Author: Sabine Van Huffel
Author: Sabine Van Huffel
Author: Chi Tat Chong
Author: Donald Brown
Author: J. Antoch
Author: Jaromir Antoch
Author: David F. Griffiths