# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Methods of numerical integration. 2nd ed. (English) Zbl 0537.65020
Computer Science and Applied Mathematics. Orlando etc.: Academic Press, Inc. (Harcourt Brace Jovanovich, Publishers). XIV, 612 p. \$ 52.00; £36.50 (1984).
This is the second edition of the well-known book on numerical integration [for the first edition from 1975 see Zbl 0304.65016]. The basic difference between the first and the second edition is that some new material is given on approximate integration in ${R}^{n}$, $n\ge 2$, and on automatic integration, and the bibliography is updated. The plan and the objectives of the book remain the same. The authors mention that the new results on optimal quadratures (especially on cubatures), and the work of the Soviet school are not well represented in the book. There are several books on this subject [see V. I. Krylov, Approximate calculation of integrals (1959; Zbl 0086.329), I. M. Sobol’, Cubatures and Haar’s functions (1969; Zbl 0195.169), V. I. Krylov and L. T. Shul’gina, Reference book on numerical integration (1966; Zbl 0152.151), S. L. Sobolev, Introduction into the theory of cubatures, ibid. (1974; Zbl 0294.65013), A. H. Stroud, Approximate calculation of multiple integrals, Prentice-Hall, Englewood Cliffs (1971; Zbl 0379.65013) and I. Mysovskikh, Interpolational cubature formulas (1981; reviewed above)]. The books by I. Sobol’ and I. Mysovskikh are not mentioned in the bibliography, and many results in these two books and in the book by Sobolev are not represented. The book will be useful for many people in applied mathematics and numerical analysis.
Reviewer: A.G.Ramm

##### MSC:
 65D32 Quadrature and cubature formulas (numerical methods) 65-02 Research monographs (numerical analysis) 65D30 Numerical integration 41A55 Approximate quadratures 41A63 Multidimensional approximation problems