id: 06208342
dt: b
an: 2014c.00912
au: Nassif, Nabil R.; Fayyad, Dolly Khuwayri
ti: Introduction to numerical analysis and scientific computing.
so: Boca Raton, FL: CRC Press (ISBN 978-1-4665-8948-3/hbk;
978-1-4665-8950-6/ebook). xix, 311~p. (2014).
py: 2014
pu: Boca Raton, FL: CRC Press
la: EN
cc: N15
ut: nonlinear equations; bisection method; Newton’s method; secant method;
Gaussian elimination method; interpolation; fitting; numerical
differentiation and integration; convergence; stability
ci:
li:
ab: The book under review is an introduction to basic topics of numerical
analysis which can be covered in a one-semester course for students of
mathematics, natural sciences or engineering. The topics covered
include finding roots of nonlinear equations using the bisection
method, Newton’s method and the secant method; the Gaussian
elimination method for solving linear systems; function interpolation
and fitting; numerical differentiation and integration; and numerical
methods for ordinary differential equations. The methods are introduced
and their convergence and stability are discussed in some details. It
also includes a chapter on computer number systems and floating point
arithmetic. Computer codes written in MATLAB are also included. This
book is suitable for undergraduate students and people who begin to
learn about numerical analysis. Exercises and computer projects
provided at the end of each chapter can help students to practise
computational and programming skills. Table of contents: Chapter 1:
Computer number systems and floating point arithmetic; Chapter 2:
Finding roots of real single-valued functions; Chapter 3: Solving
systems of linear equations by Gaussian elimination; Chapter 4:
Polynomial interpolation and splines fitting; Chapter 5: Numerical
differentiation and integration; Chapter 6: Advanced numerical
integration; Chapter 7: Numerical solutions of ordinary differential
equations (ODEs); Answers to odd-numbered exercises; Bibliography;
Index. Reviewer’s remark: The statement at the beginning of Chapter 7
“Differential equations involve the dependence of some variable
$y(t)$ with respect to an independent time variable $t$” is
misleading. Derivatives of $y(t)$ must be involved in the differential
equations. Moreover, the independent variable $t$ can be of other
natures, it does not only have to represent the time.
rv: Trung Thanh Nguyen (Charlotte)