×

Fundamentals of computer numerical analysis. Incl. 1 disk. (English) Zbl 0838.65001

Boca Raton, FL: CRC Press. xi, 587 p. (1994).
This is an introductory textbook on numerical analysis for undergraduate students in mathematics, computer science or related areas in science and engineering. The emphasis is on direct application rather than study of numerical methods.
The topics discussed include (roughly in this order): Taylor series, elementary functions of a complex variable, partial derivatives, floating point arithmetic, iteration methods (including Newton’s), linear difference equations, interpolation and approximation (including splines, Chebyshev polynomials and approximation by rational functions), numerical integration and differentiation, linear equations, eigenvalues (the power method and deflation), ordinary differential equations (including the Runge-Kutta-Fehlberg method, multistep methods and stability), numerical solution of partial differential equations (general ideas on elliptic, parabolic and hyperbolic equations, finite difference and finite element methods).
The mathematics of the book usually do not go very far. For example backward stability of a solution method for linear equations is not discussed. A system \(Ax = b\) is called stable if small changes of the system do not cause a sizeable change in the solution to the system.
On the other hand, as an introduction for people interested in applications the book is fine. It contains very detailed introductions, explanations, examples and exercises. It can certainly be recommended as a textbook for a first course on numerical analysis. On the other hand, it cannot replace (and does not try to replace) the more sophisticated works in the field which are appropriate for an advanced course or study.
Reviewer: W.Govaerts (Gent)

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
65Gxx Error analysis and interval analysis
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
PDFBibTeX XMLCite