Numerical methods for mathematics, science and engineering. 2nd ed. (English) Zbl 0753.65002

Mathews, John H.

London etc.: Prentice-Hall International. X, 646 p. (1992).

The book (paperback edition) is the second edition of the work published under the title “Numerical methods for computer science, engineering, and mathematics” (1987). The intention of the author is to give an introduction to numerical methods for undergraduate students in computer science, engineering, and mathematics. On more than 600 pages, the book provides an ample material in different fields of numerical analysis such as the solution of nonlinear equations and linear systems of equations, interpolation and polynomial approximation, curve fitting, numerical differentiation, numerical integration, numerical optimization, solution of ordinary and partial differential equations, and calculation of eigenvalues as well as eigenvectors.
It is assumed that the reader is familiar with calculus and basic aspects of structured programming languages. The book contains a well-balanced minimum of the theory of numerical analysis and takes care to provide a good understanding of the essential ideas of numerical methods. Otherwise, special emphasis is placed on the presentation of algorithms for various numerical processes. Some algorithms are described by pseudo- code and are easy to translate into BASIC, C, FORTRAN, or Pascal. Computer calculations given in the form of tables and graphs, and many examples as well as figures improve the readability of the text. Numerous exercises and the computer-oriented presentation of numerical methods are special features of this book.

Reviewer: B.Heinrich (Chemnitz)

MSC:

65-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65Dxx	Numerical approximation and computational geometry (primarily algorithms)
65Fxx	Numerical linear algebra
65Hxx	Nonlinear algebraic or transcendental equations
65Lxx	Numerical methods for ordinary differential equations
65Mxx	Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65Nxx	Numerical methods for partial differential equations, boundary value problems
65Kxx	Numerical methods for mathematical programming, optimization and variational techniques

Keywords:

elementary textbook; nonlinear equations; linear systems; interpolation; polynomial approximation; curve fitting; numerical differentiation; numerical integration; numerical optimization; ordinary and partial differential equations; eigenvalues; eigenvectors; algorithms; tables; graphs; exercises; computer-oriented presentation