Numerical Analysis
Published on 10. May 2014
254 pages
978-1-4832-6891-0 (ISBN)
Description
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.
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Content
Notations and AbbreviationsPrefaceChapter 1. The Algorithms of Gauss, Borchardt and CarlsonChpater 2. Orders of Magnitude and Rates of ConvergenceChapter 3. Recurrence Relations for PowersChapter 4. The Solution of EquationsChapter 5. Uniform Convergence and ApproximationChapter 6. The Acceleration Processes of Aitken and EulerChapter 7. Asymptotic SeriesChapter 8. InterpolationChapter 9. QuadratureChapter 10. Difference Equations, Differentiation and Differential EquationsAppendix: Bessel FunctionsSolutions to Selected ProblemsBibliographical RemarksTable of Contents, Vol. 2 Numerical AlgebraIndex
