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Algorithms for the numerical computation of definite integrals have been proposed for more than 300 years, but practical considerations have led to problems of ever-increasing complexity, so that , even with current computing speeds, numerical integration may be a difficult task. High dimension and complicated structure of the region of integration and singularities of the integrand are the main sources of difficulties. This volume contains 27 papers presented at the fourth conference on numerical integration held at the Mathematical Research Institute, Oberwolfach, in November 1992. The contributions give a survey of the latest results in quadrature and cubature. Since the subject matter lies somewhere between practical mathematics and analysis, a wide spectrum of topics is discussed. One main theme is the construction of rules, especially for integrands with singularities. Further focal points are error estimation in various classes of functions, structure of general rules of interpolatory type, lattice rules, and the many facets of the Gaussian rule. Many open problems were discussed in Oberwolfach, showing a liveliness and actuality of the theory.Nine of these problems could be given precise formulations; they are collected at the end of this volume. ... Read more

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With Classified Reference Tables Of Integrals And Methods Of Integration. ... Read more

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With Classified Reference Tables Of Integrals And Methods Of Integration. ... Read more

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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. ... Read more

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This book considers problems arising the theory of differential equations. This book is not only intended for mathematicians specializing in the theory of differential equations or in probability theory but also for specialists in asymptotic methods and functional analysis. ... Read more

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This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps.

The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines.

------  Reviews

The first eight chapters of Spring’s monograph contain a detailed exposition of convex integration theory for open and ample relations with detailed proofs that were often omitted in Gromov’s book. (…) Spring’s book makes no attempt to include all topics from convex integration theory or to uncover all of the gems in Gromov’s fundamental account, but it will nonetheless (or precisely for that reason) take its place as a standard reference for the theory next to Gromov’s towering monograph and should prove indispensable for anyone wishing to learn about the theory in a more systematic way.

- Mathematical Reviews

This volume provides a comprehensive study of convex integration theory. (…) We recommended the book warmly to all interested in differential topology, symplectic topology and optimal control theory.

- Matematica

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This book gives a general definition of the (abstract)integral, using the Daniell method. A most welcome consequence of thisapproach is the fact that integration theory on Hausdorff topologicalspaces appears simply to be a special case of abstract integrationtheory. The most important tool for the development of the abstracttheory is the theory of vector lattices which is presented here ingreat detail. Its consequent application not only yields new insightinto integration theory, but also simplifies many proofs. For example,the space of real-valued measures on a d-ring turns out to be anorder complete vector lattice, which permits a coherent development ofthe theory and the elegant derivation of many classical and newresults. The exercises occupy an important part of the volume. In addition totheir usual role, some of them treat separate topics related to vectorlattices and integration theory. Audience: This work will be of interest to graduate-levelstudents and researchers with a background in real analysis, whosework involves (abstract) measure and integration, vector lattices,real functions of a real variable, probability theory and integraltransforms. ... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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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 Théories 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).