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Product Code:  SURV/178 
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Hardcover ISBN:  9780821853610 
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Hardcover ISBN:  9780821853610 
Product Code:  SURV/178 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470414054 
Product Code:  SURV/178.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821853610 
eBook ISBN:  9781470414054 
Product Code:  SURV/178.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 178; 2011; 363 ppMSC: Primary 41; Secondary 65
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 “coobservations,” which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of coobservations 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 farreaching 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.
ReadershipGraduate students and research mathematicians interested in quadrature theory, numerical integration, and approximation theory.

Table of Contents

Chapters

1. Introduction

2. The abstract framework

3. Norm and kernel of the remainder functional

4. Coobservations

5. Quadrature rules of interpolatory type

6. Gaussian quadrature

7. Quadrature rules with equidistant nodes

8. Periodic integrands

9. Variance and Chebyshevtype rules

10. Problems

Appendix A. Orthogonal polynomials

Appendix B. Bernoulli polynomials

Appendix C. Validation of coobservations


Additional Material

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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 “coobservations,” which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of coobservations 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 farreaching 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.
Graduate students and research mathematicians interested in quadrature theory, numerical integration, and approximation theory.

Chapters

1. Introduction

2. The abstract framework

3. Norm and kernel of the remainder functional

4. Coobservations

5. Quadrature rules of interpolatory type

6. Gaussian quadrature

7. Quadrature rules with equidistant nodes

8. Periodic integrands

9. Variance and Chebyshevtype rules

10. Problems

Appendix A. Orthogonal polynomials

Appendix B. Bernoulli polynomials

Appendix C. Validation of coobservations