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Author: Ferenc Szidarovszky Publisher: Springer ISBN: 1489927506 Category : Mathematics Languages : en Pages : 338
Book Description
It is an incontestable fact that numerical analysis techniques are used rou tinely (although not always effectively) in virtually every quantitative field of scientific endeavor. In this book, which is directed toward upper-division and graduate level students in engineering and mathematics, we have selected for discussion subjects that are traditionally found in numerical analysis texts. But our choice of methodology rejects the traditional where analysis and experience clearly warrant such a departure, and one of our primary aspirations in this work is to equip the reader with the wherewithal to apply numerical analysis thinking to nontraditional subjects. For there is a plethora of computer-oriented sciences such as optimization, statistics, and system analysis and identification that are sorely in need of methods comparable to those related here for classical numerical analysis problems. Toward uncovering for the reader the structure of numerical methods we have, for example, devoted a chapter to a metric space theory for iter ative application of operators. In this chapter, we have collected those definitions and concepts of real and functional analysis that are requisite to a modern intermediate-level exposition of the principles of numerical anal ysis. Further, we derive the abstract theory (most notably, the contraction mapping theorem) for iteration processes.
Author: Ferenc Szidarovszky Publisher: Springer ISBN: 1489927506 Category : Mathematics Languages : en Pages : 338
Book Description
It is an incontestable fact that numerical analysis techniques are used rou tinely (although not always effectively) in virtually every quantitative field of scientific endeavor. In this book, which is directed toward upper-division and graduate level students in engineering and mathematics, we have selected for discussion subjects that are traditionally found in numerical analysis texts. But our choice of methodology rejects the traditional where analysis and experience clearly warrant such a departure, and one of our primary aspirations in this work is to equip the reader with the wherewithal to apply numerical analysis thinking to nontraditional subjects. For there is a plethora of computer-oriented sciences such as optimization, statistics, and system analysis and identification that are sorely in need of methods comparable to those related here for classical numerical analysis problems. Toward uncovering for the reader the structure of numerical methods we have, for example, devoted a chapter to a metric space theory for iter ative application of operators. In this chapter, we have collected those definitions and concepts of real and functional analysis that are requisite to a modern intermediate-level exposition of the principles of numerical anal ysis. Further, we derive the abstract theory (most notably, the contraction mapping theorem) for iteration processes.
Author: Ferenc Szidarovszky Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 352
Book Description
Approximation and interpolation of functions; Numerical differentiation and integration; General theory for iteration methods; Solution of nonlinear equations; The solution of simultaneous linear equations; The solution of matrix eigenvalue problems; The numerical solution of ordinary differential equations; The numerical solution of partial differential equations.
Author: F. J. Murray Publisher: Springer Science & Business Media ISBN: 1468433121 Category : Science Languages : en Pages : 235
Book Description
The primary objective of the course presented here is orientation for those interested in applying mathematics, but the course should also be of value or in using math to those interested in mathematical research and teaching ematics in some other professional context. The course should be suitable for college seniors and graduate students, as well as for college juniors who have had mathematics beyond the basic calculus sequence. Maturity is more significant than any formal prerequisite. The presentation involves a number of topics that are significant for applied mathematics but that normally do not appear in the curriculum or are depicted from an entirely different point of view. These topics include engineering simulations, the experience patterns of the exact sciences, the conceptual nature of pure mathematics and its relation to applied mathe matics, the historical development of mathematics, the associated conceptual aspects of the exact sciences, and the metaphysical implications of mathe matical scientific theories. We will associate topics in mathematics with areas of application. This presentation corresponds to a certain logical structure. But there is an enormous wealth of intellectual development available, and this permits considerable flexibility for the instructor in curricula and emphasis. The prime objective is to encourage the student to contact and utilize this rich heritage. Thus, the student's activity is critical, and it is also critical that this activity be precisely formulated and communicated.
Author: K. Wolf Publisher: Springer Science & Business Media ISBN: 1475708726 Category : Science Languages : en Pages : 495
Book Description
Integral transforms are among the main mathematical methods for the solution of equations describing physical systems, because, quite generally, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one can often bring about a mathematical uncoupling of the equations in such a way that the solution becomes that of noninteracting constituents. The "tilt" in the reference frame is a finite or integral transform, according to whether the system has a finite or infinite number of elements. The types of coupling which yield to the integral transform method include diffusive and elastic interactions in "classical" systems as well as the more common quantum-mechanical potentials. The purpose of this volume is to present an orderly exposition of the theory and some of the applications of the finite and integral transforms associated with the names of Fourier, Bessel, Laplace, Hankel, Gauss, Bargmann, and several others in the same vein. The volume is divided into four parts dealing, respectively, with finite, series, integral, and canonical transforms. They are intended to serve as independent units. The reader is assumed to have greater mathematical sophistication in the later parts, though.
Author: Justin Solomon Publisher: CRC Press ISBN: 1482251892 Category : Computers Languages : en Pages : 400
Book Description
Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig
Author: David Ronald Kincaid Publisher: American Mathematical Soc. ISBN: 0821847880 Category : Mathematics Languages : en Pages : 810
Book Description
This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.
Author: Ferenc Szidarovszky
Author: Ferenc Szidarovszky
Author: Chao-cheng Wang
Author: Ferenc Szidarovszky
Author: F. J. Murray
Author: K. Wolf
Author: F. Szidarovszky
Author: Justin Solomon
Author: David Ronald Kincaid
Author: 
Author: