Synopses & Reviews
This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The established style of the original is retained with the subject matter being organized into fundamental topics and presented as a series of 'steps.' At the end of each step, checkpoints are included to allow the reader to gauge their understanding of the concepts introduced. In addition, pseudocode is included to allow students to develop computer programs using standard numerical algorithms.
The revisions reflect the huge advances that have occurred in inexpensive computational aids in recent years. New material has been included on systems of linear equations, curve fitting and differential equations. There are additional exercises, and the total number of steps has increased to 35. The result is an invaluable introduction to the basic ideas and methods underlying numerical analysis for all those new to the subject, whether they study at school, college or university.
Description
Includes bibliographical references (p. [216]) and index.
Table of Contents
Preface to the second edition
Preface to the first edition
Prologue
Errors
1. Sources of error
2. Approximation to numbers
3. Error propagation and generation
4. Floating point arithmetic
5. Approximation to functions
Nonlinear Equations
6. Nonlinear algebraic and transcendental equations
7. The bisection method
8. Method of false position
9. The method of simple iteration
10. The Newton-Raphson iterative method
Systems of Linear Equations
11. Solution by elimination
12. Errors and ill-conditioning
13. The Gauss-Seidel iterative method
14. Matrix inversion*
15. Use of LU decomposition*
16. Testing for ill-conditioning*
The Eigenvalue Problem
17. The power method
18. Tables
19. Forward, backward, and central difference notations
20. Polynomials
Interpolation
21. Linear and quadratic interpolation
22. Newton interpolation formulae
23. Lagrange interpolation formula
24. Divided differences*
25. Inverse interpolation*
Curve Fitting
26. Least squares
27. Least squares and linear equations*
28. Splines*
Numerical Differentiation
29. Finite differences
Numerical Integration
30. The trapezoidal rule
31. Simpson's rule
32. Gaussian integration formulae
Ordinary Differential Equations
33. Single-step methods
34. Multistep methods
35. Higher order differential equations*
Applied Exercises
Appendix: Pseudo-code
Answers to the Exercises
Bibliography
Index