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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations

Measure, Topology, and Fractal Geometry (Paperback, Softcover reprint of hardcover 2nd ed. 2008): Gerald Edgar Measure, Topology, and Fractal Geometry (Paperback, Softcover reprint of hardcover 2nd ed. 2008)
Gerald Edgar
R1,559 Discovery Miles 15 590 Ships in 10 - 15 working days

Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

Interpolation Processes - Basic Theory and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2008): Giuseppe... Interpolation Processes - Basic Theory and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2008)
Giuseppe Mastroianni, Gradimir Milovanovic
R2,997 Discovery Miles 29 970 Ships in 10 - 15 working days

Interpolation of functions is one of the basic part of Approximation Theory. There are many books on approximation theory, including interpolation methods that - peared in the last fty years, but a few of them are devoted only to interpolation processes. An example is the book of J. Szabados and P. Vertesi: Interpolation of Functions, published in 1990 by World Scienti c. Also, two books deal with a special interpolation problem, the so-called Birkhoff interpolation, written by G.G. Lorentz, K. Jetter, S.D. Riemenschneider (1983) and Y.G. Shi (2003). The classical books on interpolation address numerous negative results, i.e., - sultsondivergentinterpolationprocesses, usuallyconstructedoversomeequidistant system of nodes. The present book deals mainly with new results on convergent - terpolation processes in uniform norm, for algebraic and trigonometric polynomials, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. Basic tools in this eld (orthogonal polynomials, moduli of smoothness, K-functionals, etc.), as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. The rstchapterprovidesanaccountofbasicfactsonapproximationbyalgebraic and trigonometric polynomials introducing the most important concepts on appro- mation of functions. Especially, in Sect. 1.4 we give basic results on interpolation by algebraic polynomials, including representations and computation of interpolation polynomials, Lagrange operators, interpolation errors and uniform convergence in some important classes of functions, as well as an account on the Lebesgue function and some estimates for the Lebesgue constant.

Measurement Uncertainty - An Approach via the Mathematical Theory of Evidence (Paperback, Softcover reprint of hardcover 1st... Measurement Uncertainty - An Approach via the Mathematical Theory of Evidence (Paperback, Softcover reprint of hardcover 1st ed. 2007)
Simona Salicone
R1,559 Discovery Miles 15 590 Ships in 10 - 15 working days

The expression of uncertainty in measurement poses a challenge since it involves physical, mathematical, and philosophical issues. This problem is intensified by the limitations of the probabilistic approach used by the current standard (the GUM Instrumentation Standard). This text presents an alternative approach. It makes full use of the mathematical theory of evidence to express the uncertainty in measurements. Coverage provides an overview of the current standard, then pinpoints and constructively resolves its limitations. Numerous examples throughout help explain the book 's unique approach.

Stationary Oscillations of Elastic Plates - A Boundary Integral Equation Analysis (Hardcover, 2011 ed.): Gavin R. Thomson,... Stationary Oscillations of Elastic Plates - A Boundary Integral Equation Analysis (Hardcover, 2011 ed.)
Gavin R. Thomson, Christian Constanda
R1,702 Discovery Miles 17 020 Ships in 10 - 15 working days

Many problems in mathematical physics rely heavily on the use of elliptical partial differential equations, and boundary integral methods play a significant role in solving these equations."Stationary Oscillations of Elastic Plates"" "studies the latter in the context ofstationaryvibrations of thin elastic plates. The techniquespresented herereduce the complexity of classical elasticity to a system of two independent variables, modeling problemsof flexural-vibrational elastic body deformation with the aid of eigenfrequencies and simplifying them to manageable, uniquely solvable integral equations.

The book isintended foran audiencewith a knowledge of advanced calculus and some familiarity with functional analysis. It is a valuable resource for professionals in pure and applied mathematics, and for theoretical physicists and mechanical engineerswhose work involveselastic plates. Graduate students in these fieldscan also benefit from the monograph as a supplementary text for courses relating to theories of elasticity or flexural vibrations."

Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics (Paperback, Softcover... Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics (Paperback, Softcover reprint of hardcover 1st ed. 2008)
T. Aoki, H. Majima, Y. Takei, N Tose
R2,970 Discovery Miles 29 700 Ships in 10 - 15 working days

This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the conference "Algebraic Analysis of Differential Equations - from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. This volume is dedicated to Professor Takahiro Kawai, who is one of the creators of microlocal analysis and who introduced the technique of microlocal analysis into exponential asymptotics.

Exercises in Functional Analysis (Paperback, Softcover reprint of hardcover 1st ed. 2003): C. Costara, D. Popa Exercises in Functional Analysis (Paperback, Softcover reprint of hardcover 1st ed. 2003)
C. Costara, D. Popa
R4,511 Discovery Miles 45 110 Ships in 10 - 15 working days

This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.

The Fast Solution of Boundary Integral Equations (Paperback, Softcover reprint of hardcover 1st ed. 2007): Sergej Rjasanow,... The Fast Solution of Boundary Integral Equations (Paperback, Softcover reprint of hardcover 1st ed. 2007)
Sergej Rjasanow, Olaf Steinbach
R2,947 Discovery Miles 29 470 Ships in 10 - 15 working days

Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences. These methods turn out to be powerful tools for numerical studies of various physical phenomena which can be described mathematically by partial differential equations.

The most prominent example is the potential equation (Laplace equation), which is used to model physical phenomena in electromagnetism, gravitation theory, and in perfect fluids. A further application leading to the Laplace equation is the model of steady state heat flow. One of the most popular applications of the BEM is the system of linear elastostatics, which can be considered in both bounded and unbounded domains. A simple model for a fluid flow, the Stokes system, can also be solved by the use of the BEM. The most important examples for the Helmholtz equation are the acoustic scattering and the sound radiation.

The Fast Solution of Boundary Integral Equations provides a detailed description of fast boundary element methods which are based on rigorous mathematical analysis. In particular, a symmetric formulation of boundary integral equations is used, Galerkin discretisation is discussed, and the necessary related stability and error estimates are derived. For the practical use of boundary integral methods, efficient algorithms together with their implementation are needed. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given which underline both theoretical results and the practical relevance of boundary element methods in typical computations.

Representation of Lie Groups and Special Functions - Volume 2: Class I Representations, Special Functions, and Integral... Representation of Lie Groups and Special Functions - Volume 2: Class I Representations, Special Functions, and Integral Transforms (Paperback, Softcover reprint of hardcover 1st ed. 1992)
N. Ja. Vilenkin, A.U. Klimyk
R4,538 Discovery Miles 45 380 Ships in 10 - 15 working days

One service mathematics has rendered the "Et moi, ..., si j'avait su comment en revenir, human race. It has put common sense back je n 'y serais point all

Substitution Dynamical Systems - Spectral Analysis (Paperback, 2nd ed. 2010): Martine Queffelec Substitution Dynamical Systems - Spectral Analysis (Paperback, 2nd ed. 2010)
Martine Queffelec
R2,459 Discovery Miles 24 590 Ships in 10 - 15 working days

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters.

This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.

Integration II - Chapters 7-9 (Paperback, Softcover reprint of the original 1st ed. 2004): N. Bourbaki Integration II - Chapters 7-9 (Paperback, Softcover reprint of the original 1st ed. 2004)
N. Bourbaki; Translated by Sterling K. Berberian
R4,449 Discovery Miles 44 490 Ships in 10 - 15 working days

Integration is the sixth and last of the books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Theories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

The first volume of the English translation comprises Chapters 1-6; the present volume completes the translation with the remaining Chapters 7-9.

Chapters 1-5 received very substantial revisions in a second edition, including changes to some fundamental definitions. Chapters 6-8 are based on the first editions of Chapters 1-5. The English edition has given the author the opportunity to correct misprints, update references, clarify the concordance of Chapter 6 with the second editions of Chapters 1-5, and revise the definition of a key concept in Chapter 6 (measurable equivalence relations)."

Gaussian Random Functions (Paperback, Softcover reprint of hardcover 1st ed. 1995): M.A. Lifshits Gaussian Random Functions (Paperback, Softcover reprint of hardcover 1st ed. 1995)
M.A. Lifshits
R7,989 Discovery Miles 79 890 Ships in 10 - 15 working days

It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht< classical normal distribution, go to work as such exemplary objects in the theory of Gaussian random functions. When one switches to the infinite dimension, some "one-dimensional" properties are extended almost literally, while some others should be profoundly justified, or even must be reconsidered. What is more, the infinite-dimensional situation reveals important links and structures, which either have looked trivial or have not played an independent role in the classical case. The complex of concepts and problems emerging here has become a subject of the theory of Gaussian random functions and their distributions, one of the most advanced fields of the probability science. Although the basic elements in this field were formed in the sixties-seventies, it has been still until recently when a substantial part of the corresponding material has either existed in the form of odd articles in various journals, or has served only as a background for considering some special issues in monographs.

Geometric Properties of Banach Spaces and Nonlinear Iterations (Paperback, 2009 ed.): Charles Chidume Geometric Properties of Banach Spaces and Nonlinear Iterations (Paperback, 2009 ed.)
Charles Chidume
R1,577 Discovery Miles 15 770 Ships in 10 - 15 working days

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, "... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces". Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Operator-Valued Measures and Integrals for Cone-Valued Functions (Paperback, 2009 ed.): Walter Roth Operator-Valued Measures and Integrals for Cone-Valued Functions (Paperback, 2009 ed.)
Walter Roth
R1,583 Discovery Miles 15 830 Ships in 10 - 15 working days

Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures whereas suprema and infima are replaced with topological limits in the vector-valued case.

A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases.

Spectral Theory in Inner Product Spaces and Applications - 6th Workshop on Operator Theory in Krein Spaces and Operator... Spectral Theory in Inner Product Spaces and Applications - 6th Workshop on Operator Theory in Krein Spaces and Operator Polynomials, Berlin, December 2006 (Hardcover, 2009 ed.)
Jussi Behrndt, Karl-Heinz Foerster, Heinz Langer, Carsten Trunk
R3,056 Discovery Miles 30 560 Ships in 10 - 15 working days

This volume contains papers written by participants of the 6th Workshop on - erator Theory in Krein Spaces and Operator Polynomials, which was held at the Technische Universit. at Berlin, Germany, December 14 to 17, 2006. This workshop was attended by 67 participants from 14 countries. The lectures covered topics from spectral and perturbation theory of linear operators in inner product spaces and from operator polynomials. They included the theory of generalized Nevanlinna and Schur functions, di?erential operators, singular perturbations, de Branges spaces, scattering problems, block numerical ranges, nonnegative matrices and relations. All these topics are re?ected in the present volume. Besides, it contains an after dinner speech from an earlier wo- shop, which we think may be of interest for the reader, as well as a speech on the occasion of the retirement of Peter Jonas. It is a pleasure to acknowledge the substantial ?nancial support received from the - Deutsche Forschungsgemeinschaft (DFG), - Berlin Mathematical School (BMS), - DFG-Forschungszentrum MATHEON "Mathematik fur .. Schlussel- .. technologien", - Institute of Mathematics of the Technische Universit. at Berlin. WewouldalsoliketothankPetraGrimbergerforhergreathelpintheorganisation. Without her assistance the workshop might not have taken place.

Mathematical Theory of Feynman Path Integrals - An Introduction (Paperback, 2nd, corr. and enlarged ed. 2008): Sergio... Mathematical Theory of Feynman Path Integrals - An Introduction (Paperback, 2nd, corr. and enlarged ed. 2008)
Sergio Albeverio, Rafael Hoegh-Krohn, Sonia Mazzucchi
R1,343 Discovery Miles 13 430 Ships in 10 - 15 working days

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. An entire new chapter on the current forefront of research has been added. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained. At the end of each chapter the reader will also find notes with further bibliographical information.

A Concise Course on Stochastic Partial Differential Equations (Paperback, 2007 ed.): Claudia Prevot, Michael Roeckner A Concise Course on Stochastic Partial Differential Equations (Paperback, 2007 ed.)
Claudia Prevot, Michael Roeckner
R1,318 Discovery Miles 13 180 Ships in 10 - 15 working days

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach," the "mild solution approach" and the "variational approach." The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach." A large part of necessary background material is included in appendices.

Differential Equations and Dynamical Systems (Hardcover, 3rd ed. 2001. Corr. 3rd printing 2008): Lawrence Perko Differential Equations and Dynamical Systems (Hardcover, 3rd ed. 2001. Corr. 3rd printing 2008)
Lawrence Perko
R2,913 Discovery Miles 29 130 Ships in 10 - 15 working days

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

Topics on Concentration Phenomena and Problems with Multiple Scales (Paperback, 2006 ed.): Andrea Braides, Valeria Chiado Piat Topics on Concentration Phenomena and Problems with Multiple Scales (Paperback, 2006 ed.)
Andrea Braides, Valeria Chiado Piat
R1,676 Discovery Miles 16 760 Ships in 10 - 15 working days

The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena is a challenging topic of very active research. This volume collects lecture notes on the asymptotic analysis of such problems when multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes, and on concentration effects in Ginzburg-Landau energies and in subcritical growth problems.

Vector Integration and Stochastic Integration in Banach Spaces (Hardcover): N. Dinculeanu Vector Integration and Stochastic Integration in Banach Spaces (Hardcover)
N. Dinculeanu
R5,396 Discovery Miles 53 960 Ships in 12 - 17 working days

A breakthrough approach to the theory and applications of stochastic integration The theory of stochastic integration has become an intensely studied topic in recent years, owing to its extraordinarily successful application to financial mathematics, stochastic differential equations, and more. This book features a new measure theoretic approach to stochastic integration, opening up the field for researchers in measure and integration theory, functional analysis, probability theory, and stochastic processes. World-famous expert on vector and stochastic integration in Banach spaces Nicolae Dinculeanu compiles and consolidates information from disparate journal articles-including his own results-presenting a comprehensive, up-to-date treatment of the theory in two major parts. He first develops a general integration theory, discussing vector integration with respect to measures with finite semivariation, then applies the theory to stochastic integration in Banach spaces. Vector Integration and Stochastic Integration in Banach Spaces goes far beyond the typical treatment of the scalar case given in other books on the subject. Along with such applications of the vector integration as the Reisz representation theorem and the Stieltjes integral for functions of one or two variables with finite semivariation, it explores the emergence of new classes of summable processes that make applications possible, including square integrable martingales in Hilbert spaces and processes with integrable variation or integrable semivariation in Banach spaces. Numerous references to existing results supplement this exciting, breakthrough work.

Selected Topics in Convex Geometry (Paperback, 2006 ed.): Maria Moszynska Selected Topics in Convex Geometry (Paperback, 2006 ed.)
Maria Moszynska
R1,623 Discovery Miles 16 230 Ships in 10 - 15 working days

The field of convex geometry has become a fertile subject of mathematical activity in the past few decades. This exposition, examining in detail those topics in convex geometry that are concerned with Euclidean space, is enriched by numerous examples, illustrations, and exercises, with a good bibliography and index.

The theory of intrinsic volumes for convex bodies, along with the Hadwiger characterization theorems, whose proofs are based on beautiful geometric ideas such as the rounding theorems and the Steiner formula, are treated in Part 1. In Part 2 the reader is given a survey on curvature and surface area measures and extensions of the class of convex bodies. Part 3 is devoted to the important class of star bodies and selectors for convex and star bodies, including a presentation of two famous problems of geometric tomography: the Shephard problem and the Busemanna "Petty problem.

Selected Topics in Convex Geometry requires of the reader only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory. The book can be used in the classroom setting for graduates courses or seminars in convex geometry, geometric and convex combinatorics, and convex analysis and optimization. Researchers in pure and applied areas will also benefit from the book.

Integral Methods in Science and Engineering - Theoretical and Practical Aspects (Hardcover, 2006 ed.): M. Zuhair Nashed, D.... Integral Methods in Science and Engineering - Theoretical and Practical Aspects (Hardcover, 2006 ed.)
M. Zuhair Nashed, D. Rollins
R1,597 Discovery Miles 15 970 Ships in 10 - 15 working days

The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration.

The book, consisting of twenty seven selected chapters presented by well-known specialists in the field, is an outgrowth of the Eighth International Conference on Integral Methods in Science and Engineering, held August 2a "4, 2004, in Orlando, FL. Contributors cover a wide variety of topics, from the theoretical development of boundary integral methods to the application of integration-based analytic and numerical techniques that include integral equations, finite and boundary elements, conservation laws, hybrid approaches, and other procedures.

The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.

Convolution-like Structures, Differential Operators and Diffusion Processes (Paperback, 1st ed. 2022): Ruben Sousa, Manuel... Convolution-like Structures, Differential Operators and Diffusion Processes (Paperback, 1st ed. 2022)
Ruben Sousa, Manuel Guerra, Semyon B Yakubovich
R1,640 Discovery Miles 16 400 Ships in 12 - 17 working days

T his book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.

Basic Real Analysis (Hardcover, 2005 ed.): Anthony W. Knapp Basic Real Analysis (Hardcover, 2005 ed.)
Anthony W. Knapp
R3,106 Discovery Miles 31 060 Ships in 10 - 15 working days

Basic Real Analysis and Advanced Real Analysis systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.Basic Real Analysis requires of the reader only familiarity with some linear algebra and real variable theory, the very beginning of group theory, and an acquaintance with proofs. It is suitable as a text in an advanced undergraduate course in real variable theory and in most basic graduate courses in Lebesgue integration and related topics. Because it focuses on what every young mathematician needs to know about real analysis, the book is ideal both as a course text and for self-study, especially for graduate students preparing for qualifying examinations. Its scope and unique approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. addition to the personal library of every mathematician.

Approximation Theory Using Positive Linear Operators (Paperback, 2004 ed.): Radu Paltanea Approximation Theory Using Positive Linear Operators (Paperback, 2004 ed.)
Radu Paltanea; Adapted by george A. Anastassiou
R1,544 Discovery Miles 15 440 Ships in 10 - 15 working days

This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, particularly as it affects computer-aided geometric design. In this book, the crucial role of the second order moduli of continuity in the study of such operators is emphasized. New and efficient methods, applicable to general operators and to diverse concrete moduli, are presented. The advantages of these methods consist in obtaining improved and even optimal estimates, as well as in broadening the applicability of the results.

*Additional Topics and Features:

* Examination of the multivariate approximation case

* Special focus on the Bernstein operators, including applications, and on two new classes of Bernstein-type operators

* Many general estimates, leaving room for future applications (e.g. the B-spline case)

* Extensions to approximation operators acting on spaces of vector functions

* Historical perspective in the form of previous significant results

This monograph will be of interest to those working in the field of approximation or functional analysis. Requiring only familiarity with the basics of approximation theory, the book may serve as a good supplementary text for courses in approximation theory, or as a reference text on the subject.

An Introduction to Integration and Measure Theory V16 (Hardcover, New): O. A. Nielsen An Introduction to Integration and Measure Theory V16 (Hardcover, New)
O. A. Nielsen
R5,256 Discovery Miles 52 560 Ships in 12 - 17 working days

This book describes integration and measure theory for readers interested in analysis, engineering, and economics. It gives a systematic account of Riemann-Stieltjes integration and deduces the Lebesgue-Stieltjes measure from the Lebesgue-Stieltjes integral.

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