**Mathematical Surveys and Monographs**

Volume: 178;
2011;
363 pp;
Hardcover

MSC: Primary 41;
Secondary 65

Print ISBN: 978-0-8218-5361-0

Product Code: SURV/178

List Price: $99.00

Individual Member Price: $79.20

**Electronic ISBN: 978-1-4704-1405-4
Product Code: SURV/178.E**

List Price: $99.00

Individual Member Price: $79.20

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#### Supplemental Materials

# Quadrature Theory: The Theory of Numerical Integration on a Compact Interval

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*Helmut Brass; Knut Petras*

Every book on numerical analysis covers
methods for the approximate calculation of definite integrals. The
authors of this book provide a complementary treatment of the topic by
presenting a coherent theory of quadrature methods that encompasses
many deep and elegant results as well as a large number of interesting
(solved and open) problems.

The inclusion of the word “theory” in the title
highlights the authors' emphasis on analytical questions, such as the
existence and structure of quadrature methods and selection criteria
based on strict error bounds for quadrature rules. Systematic analyses
of this kind rely on certain properties of the integrand, called
“co-observations,” which form the central organizing
principle for the authors' theory, and distinguish their book from
other texts on numerical integration. A wide variety of
co-observations are examined, as a detailed understanding of these is
useful for solving problems in practical contexts.

While quadrature theory is often viewed as a branch of numerical
analysis, its influence extends much further. It has been the starting
point of many far-reaching generalizations in various directions, as
well as a testing ground for new ideas and concepts. The material in
this book should be accessible to anyone who has taken the standard
undergraduate courses in linear algebra, advanced calculus, and real
analysis.

#### Readership

Graduate students and research mathematicians interested in quadrature theory, numerical integration, and approximation theory.

#### Table of Contents

# Table of Contents

## Quadrature Theory: The Theory of Numerical Integration on a Compact Interval

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Preface vii8 free
- Introduction 110 free
- The abstract framework 716 free
- Norm and kernel of the remainder functional 2938
- Co-observations 4756
- Quadrature rules of interpolatory type 99108
- Gaussian quadrature 149158
- Quadrature rules with equidistant nodes 211220
- Periodic integrands 261270
- Variance and Chebyshev-type rules 291300
- Problems 307316
- Orthogonal polynomials 315324
- Bernoulli polynomials 325334
- Validation of co-observations 329338
- Bibliography 335344
- Symbols 357366
- Index 361370 free
- Back Cover Back Cover1376