INTRODUCTION TO NUMERICAL ANALYSIS: SECOND EDITION

The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known highly respected volume provides an introduction to the fundamental processes of numerical analysis including substantial grounding in the basic operations of computation approximation interpolation numerical differentiation and integration and the numerical solution of equations as well as in applications to such processes as the smoothing of data the numerical summation of series and the numerical solution of ordinary differential equations.Chapter headings include:l. Introduction2. Interpolation with Divided Differences3. Lagrangian Methods4. Finite-Difference Interpolation5. Operations with Finite Differences6. Numerical Solution of Differential Equations7. Least-Squares Polynomial ApproximationIn this revised and updated second edition Professor Hildebrand (Emeritus Mathematics MIT) made a special effort to include more recent significant developments in the field increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method and numerous other important topics.In addition reference lists have been expanded and updated and more than 150 new problems have been added. Widely considered the classic book in the field Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students or the general reader in search of a strong clear introduction to the theory and analysis of numbers.