Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored.
Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations.
This book will be of interest to mathematicians and students of mathematics.
Notations and Abbreviations
Chapter 1. The Algorithms of Gauss, Borchardt and Carlson
Chpater 2. Orders of Magnitude and Rates of Convergence
Chapter 3. Recurrence Relations for Powers
Chapter 4. The Solution of Equations
Chapter 5. Uniform Convergence and Approximation
Chapter 6. The Acceleration Processes of Aitken and Euler
Chapter 7. Asymptotic Series
Chapter 8. Interpolation
Chapter 9. Quadrature
Chapter 10. Difference Equations, Differentiation and Differential Equations
Appendix: Bessel Functions
Solutions to Selected Problems
Table of Contents, Vol. 2 Numerical Algebra
- No. of pages:
- © Academic Press 1979
- 28th March 1981
- Academic Press
- eBook ISBN: