Computing Algorithms for Solutions of Problems in Applied Mathematics and Their Standard Program Realization: Deterministic Mathematics, Part 1

Algorithms of the approached decision of various classes of mathematical problems always constitute the important part of many branches of the exact sciences. The evolution of computer means, and in particular, the modern level of development of personal computers has led to the necessity to overestimate significances in both existing algorithms and approaches to the solution of many applied problems.

Widespread use of personal computers offers the possibility to eliminate these imperfections which prevent modern levels of achievement in research. To this end in the considered work computing algorithms for the solution of the most widespread and important problems of applied mathematics and their program realization in the form of standard modules for their direct inclusion in applied programs of users are offered, written in different programming languages. All material is distributed in ten chapters of the present book depending on their belonging to corresponding domains of mathematics. Different algorithms for the solution of the same problems result in items joining in sections devoted to the solving of corresponding problems.

Algorithms are realized in the programming language Object Pascal and presented in the form of procedures, functions and classes in several modules. The computer programs written for IBM-compatible personal computers can include any such modules entirely or use any of its components.

The offered work is the outcome of many years work on the part of the authors in solving the different problems and tasks from the domains of instrument making, metrology, system analysis, ecology, data analysis from ecology, agriculture, medicine and the creation of corresponding universal computer packages and systems. Therefore, every one of these programs has been tested repeatedly and variously for the solution of corresponding practical problems and in the systems introduced and working on real objects. The working capacity and reliability of results of their work do not raise doubts.

Table of Contents

Chapter 1 Numerical Methods of Linear Algebra
Chapter 2 Numerical Analysis of Power Series and Polynomials
Chapter 3 Solution of Nonlinear Equations and Determination of Extremums
Chapter 4 Interpolation and Approximation of Functions
Chapter 5 Numerical Differentiation and Integration
Chapter 6 Calculation of Values of Some Functions
Chapter 7 Numerical Methods for Solving Differential Equations
Chapter 8 Numerical Methods Used in Geometry