Download this **PDF **book: A First Course in Numerical Analysis: Second Edition (Dover Books on Mathematics) Second Edition by Anthony Ralston, Philip Rabinowitz

We both are very pleased that Dover is reissuing the second edition of A First Course in Numerical Analysis. Although it has been 24 years since the publication in 1977 of the second edition (which itself was published 12 years after the first edition), we think that this book still contains plenty of material to interest students of numerical analysis.

It is true that revolutions in computing that have ensued since 1977 have been accompanied by large advances in the science and art of numerical analysis, but the fundamentals of the subject remain much as they were in 1977.

Thus, the student who reads this book and, in particular, tack-les the problems at the end of each chapter will be well placed to study any of the advances that have occurred since 1977. A separate manual with hints and answers to most of the problems was published to accompany the second edition.

That manual, essentially unchanged, has been bound into this book. It contains hints or the out-lines of answers to almost all of the problems. When a problem—or part of a problem—does not appear in the Hints and Answers section, this is because a hint or answer was deemed unnecessary or because the space a useful hint or answer would have occupied would have been greater than was feasible.

Apart from the inclusion of the Hints and Answers section, this edition is unchanged from the 1977 second edition, except that a few typographical and other minor errors have been corrected. Enjoy!

This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents relatively few theorems and proofs.

Oriented toward computer solutions of problems, it stresses errors in methods and computational efficiency, and it compares different solutions to the same problem.

Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms, interpolation, numerical differentiation and numerical quadrature, the numerical solution of ordinary differential equations, functional approximation by least squares and by minimum-maximum error techniques, the solution of nonlinear equations and of simultaneous linear equations, and the calculation of eigenvalues and eigenvectors of matrices.

This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems some strictly mathematical, others requiring a computer appear at the end of each chapter.

## Contents:

Chapter 1: Introduction and preliminaries

Chapter 2: Approximation and algorithms

Chapter 3: Interpolation

Chapter 4: Numerical differentiation, numerical quadrature, and summation

Chapter 5: The numerical solution of ordinary differential equations

Chapter 6: Functional approximation: least-squares techniques

Chapter 7: Functional approximation: minimum maximum error techniques

Chapter 8: The solution of nonlinear equations

Chapter 9: The solution of simultaneous linear equations

Chapter 10: The calculation of eigenvalues and eigenvectors of matrices

## About the book:

Publisher : Dover Publications; Second edition (February 6, 2001)

Language : English

Pages : 624

File : **PDF**, 12MB

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