Computational Mathematics

The mathematical education of the investigating engineer can no longer be confined to the traditional departments of the so-called "classical analysis" which was established in its basic outlines at the beginning of last century.
Research engineers have to know many areas of modern mathematics and, primarily, require a firm grasp of the methods and techniques of computational mathematics insofar as the solution of almost every engineering problem must be carried to a numerical result.
Present-day computing devices have greatly extended the realm of computational work, making it possible, in many instances, to reject approximate interpretations of applied problems and pass on utilization of deeper specialized divisions of mathematics (nonlinear differential equations, functional analysis, probabilistic methods, etc.). Proper utilization of modern computers is impossible without the skilled use of methods of approximate and numerical analysis. All this explains the universal enhanced interest in the methods of computational mathematics.
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.
Brief Contents:
Approximate Numbers • Some Facts from the Theory of Continued Fractions
* Computing the Values of Functions • Approximate Solutions of Algebraic and Transcendental Equations • Special Techniques for Approximate Solution of Algebraic Equations • Accelerating the Convergence of Series • Matrix Algebra • Solving Systems of Linear Equations • The Convergence of Iteration Processes for Systems of Linear Equations • Essentials of the Theory of Linear Vector Spaces • Additional Facts About the Convergence of Iteration Processes for Systems of Linear Equations • Finding the Eigenvalues and Eigenvectors of a Matrix • Approximate Solution of Systems of Nonlinear Equations • The Interpolation of Functions • Approximate Differentiation
* Approximate Integration of Functions • The Monte Carlo Method.