Computational Mathematics | B. P. Demidovich, I. A. Maron

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 ma- tetial 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.
For a full comprehension of the contents of this. book, the reader should have a background of linear algebra and the theory of linear vector spaces. With the aim of making the text as self-contained as possible, the authors have included all the necessary starting material in these subjects. The appropriate chapter~ are completely independent of the basic text and can be omitted by readers who have already studied these sections.
The present text offers selected methods in computational mathematics and does not include material that involves empirical formulas, quadratic approximation of functions, approximate solutions of differential equations, etc. Likewise, the book does not include material on programming and the technical aspects of solving mathematical problems on computers. The interested reader must consult the special literature on these subjects.