Theoretical Numerical Analysis

Author: Kendall Atkinson
Publisher: Springer Science & Business Media
ISBN: 1441904581
Format: PDF, ePub, Docs
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This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier edition: "...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." R. Glowinski, SIAM Review, 2003

Numerical Analysis

Author: Rainer Kress
Publisher: Springer Science & Business Media
ISBN: 1461205999
Format: PDF, Docs
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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.

Partial Differential Equations Modeling Analysis and Numerical Approximation

Author: Hervé Le Dret
Publisher: Birkhäuser
ISBN: 3319270672
Format: PDF, ePub, Docs
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This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.

Numerical Methods and Analysis of Multiscale Problems

Author: Alexandre L. Madureira
Publisher: Springer
ISBN: 3319508660
Format: PDF
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This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics – or researchers seeking a no-nonsense approach –, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods. The problems considered are given by singular perturbed reaction advection diffusion equations in one and two-dimensional domains, partial differential equations in domains with rough boundaries, and equations with oscillatory coefficients. This work shows how asymptotic analysis can be used to develop and analyze models and numerical methods that are robust and work well for a wide range of parameters.

Introductory Functional Analysis

Author: B.D. Reddy
Publisher: Springer Science & Business Media
ISBN: 9780387983073
Format: PDF, Mobi
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The book is aimed particularly at students and researchers who do not have the traditional prerequisites (for example, real analysis) for a first course in functional analysis, and are interested in the applications of this subject to areas such as partial differential equations and the finite element method. The selection, presentation and organization of material are guided by the principle that abstract concepts should be conveyed in a carefully structured and well-placed manner, in order to make these readily accessible to the target readership.

Analysis for Applied Mathematics

Author: Ward Cheney
Publisher: Springer Science & Business Media
ISBN: 9780387952796
Format: PDF, ePub
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This book evolved from a course at our university for beginning graduate stu dents in mathematics-particularly students who intended to specialize in ap plied mathematics. The content of the course made it attractive to other math ematics students and to graduate students from other disciplines such as en gineering, physics, and computer science. Since the course was designed for two semesters duration, many topics could be included and dealt with in de tail. Chapters 1 through 6 reflect roughly the actual nature of the course, as it was taught over a number of years. The content of the course was dictated by a syllabus governing our preliminary Ph. D. examinations in the subject of ap plied mathematics. That syllabus, in turn, expressed a consensus of the faculty members involved in the applied mathematics program within our department. The text in its present manifestation is my interpretation of that syllabus: my colleagues are blameless for whatever flaws are present and for any inadvertent deviations from the syllabus. The book contains two additional chapters having important material not included in the course: Chapter 8, on measure and integration, is for the ben efit of readers who want a concise presentation of that subject, and Chapter 7 contains some topics closely allied, but peripheral, to the principal thrust of the course. This arrangement of the material deserves some explanation.

Nonlinear Inclusions and Hemivariational Inequalities

Author: Stanisław Migórski
Publisher: Springer Science & Business Media
ISBN: 146144232X
Format: PDF
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This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Verbal Behavior

Author: B. F. Skinner
Publisher: B. F. Skinner Foundation
ISBN: 0989983900
Format: PDF, Docs
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In 1934, at the age of 30, B. F. Skinner found himself at a dinner sitting next to Professor Alfred North Whitehead. Never one to lose an opportunity to promote behaviorism, Skinner expounded its main tenets to the distinguished philosopher. Whitehead acknowledged that science might account for most of human behavior but he would not include verbal behavior. He ended the discussion with a challenge: "Let me see you," he said, "account for my behavior as I sit here saying, 'No black scorpion is falling upon this table.'" The next morning Skinner began this book. It took him over twenty years to complete. This book extends the laboratory-based principles of selection by consequences to account for what people say, write, gesture, and think. Skinner argues that verbal behavior requires a separate analysis because it does not operate on the environment directly, but rather through the behavior of other people in a verbal community. He illustrates his thesis with examples from literature, the arts, and sciences, as well as from his own verbal behavior and that of his colleagues and children. Perhaps it is because this theoretical work provides a way to approach that most human of human behavior that Skinner ofter called Verbal Behavior his most important work.