Download or read book On the General Principles of Analysis The Analysis of Numerical Equations written by John Radford YOUNG and published by . This book was released on 1850 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the General Principles of Analysis written by John Radford Young and published by . This book was released on 1850 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Theoretical Introduction to Numerical Analysis written by Victor S. Ryaben'kii and published by CRC Press. This book was released on 2006-11-02 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An accessible yet rigorous mathematical introduction, this book provides a pedagogical account of the fundamentals of numerical analysis. The authors thoroughly explain basic concepts, such as discretization, error, efficiency, complexity, numerical stability, consistency, and convergence. The text also addresses more complex topics like intrinsic error limits and the effect of smoothness on the accuracy of approximation in the context of Chebyshev interpolation, Gaussian quadratures, and spectral methods for differential equations. Another advanced subject discussed, the method of difference potentials, employs discrete analogues of Calderon’s potentials and boundary projection operators. The authors often delineate various techniques through exercises that require further theoretical study or computer implementation. By lucidly presenting the central mathematical concepts of numerical methods, A Theoretical Introduction to Numerical Analysis provides a foundational link to more specialized computational work in fluid dynamics, acoustics, and electromagnetism.
Download or read book Principles of Numerical Analysis written by Alston S. Householder and published by Courier Corporation. This book was released on 2006-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer science rests upon the building blocks of numerical analysis. This concise treatment by an expert covers the essentials of the solution of finite systems of linear and nonlinear equations as well as the approximate representation of functions. A final section provides 54 problems, subdivided according to chapter. 1953 edition.
Download or read book Principles and Procedures of Numerical Analysis written by Ferenc Szidarovszky and published by Springer. This book was released on 2013-11-11 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book On the General Principles Analysis Vol 1 written by J. R. Young and published by Forgotten Books. This book was released on 2018-02-03 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the General Principles Analysis, Vol. 1: Being a Series of Original Investigations in Different Departments of Pure Mathematics It seems to me to be a libel upon mathematical science to pronounce any of its departments to be inherently too difficult and recondite for the comprehension of a mind thus trained and prepared. Analysis is too frequently and too unjustly branded with this stigma, when the reproach more properly belongs to those who are the exponents of its doctrines. If superior clear ness and perspicuity can reasonably be looked for in any subject, surely that subject is mathematics: and yet no department of scientific research can be adduced which is enveloped in so much unnatural and repulsive Obscurity as the science of abstract analysis. Still, however, I must acknowledge, that this fault is not always without its advantages what is of easy attainment is Often undervalued; and, in the minds of some, the only way to enhance the estimate is to increase the difficulty of access. It was, no doubt, a conviction of this truth, that influenced Mr. Horner to invest his important discovery of the general solution of numerical equations, in the dress in which it appears in the 'transactions of the Royal Society.' With admirable tact and sagacity, he shrouded a very simple matter in a garb of transcen dental mystery; but, as soon as his primary Object was secured, the object, namely, of the early publication of his results, under the auspices of a learned body, he proceeded to strip the subject of its unnatural disguise, and to exhibit it in all its native simplicity. From these introductory remarks, it will be perceived, that my object will be to convey the contents Of this volume to the reader with as little expenditure of thought and labour, on his part, as he can reasonably expect to incur in the perusal. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Numerical Analysis written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover everything, the goal is to guide readers towards the basic ideas and general principles by way of the main and important numerical methods. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis -- indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. The text is presented in a concise and easily understandable fashion so as to be successfully mastered in a one-year course.
Download or read book Principles and Procedures of Numerical Analysis written by Ferenc Szidarovszky and published by . This book was released on 2014-01-15 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book FIRST PRINCIPLES OF NUMERICAL ANALYSIS AN UNDERGRADUATE TEXT written by BURTON WENDROFF and published by . This book was released on 1969 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Quarterly Journal of Pure and Applied Mathematics written by and published by . This book was released on 1862 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Principles of Numerical Analysis written by Alston Scott Householder and published by . This book was released on 1963 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the General Principles Analysis Vol 1 written by J. R. Young and published by Forgotten Books. This book was released on 2015-06-25 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from On the General Principles Analysis, Vol. 1: Being a Series of Original Investigations in Different Departments of Pure Mathematics The work, of which this is the First Part, was intended to be issued in monthly portions, and to embrace the following topics: 1. Conjugate Functions, and their application to the Analysis of Equations. 2. Researches respecting the Theory of Numbers. 3. A Disquisition on Diverging Series. 4. On Zeros, real and imaginary, Conjugate Points, and Imaginary Logarithms. 5. On certain Theorems of Leibnitz, Abel, Murphy, &c. 6. On the Law of Continuity in Analysis. 7. Miscellaneous Investigations in the Calculus of Operations, the Theory of Probability, the Law of Population, &c. 8. Prefatory matter, in a Dedication to the Earl of Clarendon, containing statements and explanations of interest to the friends of Science. The author feels it necessary here to state, that the further prosecution of this design must, for the present, be suspended. The subscribers to the work, although including some of the most distinguished names in the kingdom, are nevertheless too few in number, as yet, to justify him in incurring the expense of the publication. The proceeds of this First Part of the work are not likely to cover one half of the outlay: as soon as this obstacle is removed, the publication will be regularly proceeded with. The Statements, &c., intended for Part VIII will shortly be printed in a distinct form. The pamphlet will be published separately at One Shilling: the subscribers to the work originally proposed will not be considered as pledged to the purchase of it, nor will it be forwarded to them unless expressly ordered. One remark more must be made, though it would be gladly avoided. It was the early-formed resolution of the author that duplicate copies should not be forwarded to any individual subscriber; this resolution was founded upon reasons cogent to his own mind, but which he may, perhaps, here be excused from formally stating. Some of the most eminent persons whose names occur in the following list, have each ordered several copies of the publisher. But the author respectfully requests permission to adhere to his original determination, though at the risk of incurring the charge of inconsistency. His hope and aim was, and is, that his book might, in some degree, be acceptable to science; and he must be suffered to indulge the delusion - if delusion it be - that the countenance extended to it is justified by the expectation of at least partial success in his endeavours, irrespective of all considerations personal to the author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Download or read book Numerical Analysis in Modern Scientific Computing written by Andreas Hohmann and published by Springer Science & Business Media. This book was released on 2003-01-14 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations. The presentation draws on geometrical intuition wherever appropriate and is supported by a large number of illustrations, exercises, and examples.
Download or read book Introduction to Numerical Continuation Methods written by Eugene L. Allgower and published by SIAM. This book was released on 2003-01-01 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. The book also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.
Download or read book Numerical Solution of Partial Differential Equations written by K. W. Morton and published by Cambridge University Press. This book was released on 1994-10-20 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This book provides a concise introduction to standard numerical techniques, ones chosen on the basis of their general utility for practical problems. The authors emphasise finite difference methods for simple examples of parabolic, hyperbolic and elliptic equations; finite element, finite volume and spectral methods are discussed briefly to see how they relate to the main theme. Stability is treated clearly and rigorously using maximum principles, energy methods, and discrete Fourier analysis. Methods are described in detail for simple problems, accompanied by typical graphical results. A key feature is the thorough analysis of the properties of these methods. Plenty of examples and exercises of varying difficulty are supplied. The book is based on the extensive teaching experience of the authors, who are also well-known for their work on practical and theoretical aspects of numerical analysis. It will be an excellent choice for students and teachers in mathematics, engineering and computer science departments seeking a concise introduction to the subject.
Download or read book Numerical Analysis written by Walter Gautschi and published by Birkhäuser. This book was released on 2011-12-08 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
