About the book

The basic aim of this book is to give as far as possible a systematic and modern presentation of the most important methods and techniques of computational mathematics on the basis of the general course of higher mathematics taught in higher technical schools. The. book has been arranged so. that the basic portion constitutes a manual for the first cycle of studies in approximate computations for higher technical colleges.The text contains supplementary matetial Which goes beyond the scope of the ordinary college course, but the reader can select those sections which interest him and omit any extra material without loss of continuity.The chapters and sections which may be dropped out in a first reading are marked with an asterisk.This text makes wide use of matrix calcu]us.The concepts of a vector, matrix, inverse matrix,eigenvalue and eigenvector of a matrix, etc.are workaday tools.The use of matrices offers a number of advantages in presenting the subject matter since they greatly facilitate an understanding of the development of many computations. In this sense a particular gain is achieved in the proofs of the convergence theorems of various numerical processes. Also, modern high-speed computers are nicely adapted to the performance of the basic matrix operations.

A few words about the contents of the book. In the main it is devoted to the following problems:operations involving approximate numbers,computation of functions by means of series and iterative processes,approximate and numerical solution of algebraic and transcendental equations,computational methods of linear algebra,interpolation of functions,numerical differentiation and integration of functions,and the Monte Carlo method.

Contents

Preface

Introduction. General Rules of Computational Work

Chapter 1 Approximate Numbers

Chapter 2 Some Facts from the Theory of Continued Fractions

Chapter 3 Computing the Values of Functions

Chapter 4 Approximate Solutions of Algebraic and Transcendental Equations

Chapter 5 Special Techniques for Approximate Solution of Algebraic Equations

Chapter 6 Accelerating the Convergence of Series

Chapter 7 Matrix Algebra

Chapter 8 Solving Systems of Linear Equations

Chapter 9 The Convergence Of Iteration Processes For Systems Of Linear Equations

Chapter 10 Essentials of the Theory of Linear Vector Spaces

Chapter 11 Additional Facts about the Convergence of Iteration Processes For Systems of Linear Equations

Chapter 12 Finding the Eigenvalues and Eigenvectors of a Matrix

Chapter 13 Approximate Solution of Systems of Nonlinear Equations

Chapter 14 The Interpolation Of Functions

Chapter 15 Approximate Differentiation

Chapter 16 Approximate Integration of Functions

Chapter 17 The Monte Carlo Method               

Complete List of References

Index