Numerical Analysis in Pascal ABC
Studies in Applied Mathematics
Leonid Zhavoronkov
The book is an adopted translation of the monograph Numeric analysis and modelling in Pascal ABC, in russian, 366 pages.
ISBN 978-5-906886-71-2, L.M. Zhavoronkov, 2017.
The monograph is translated and edited by the author in 2019.
Categories
Applied mathematics. Numerical analysis
Key words:
Transcendental equation, numerical differentiation, integration, interpolation, extrapolation, digital filter, cryptography.
Annotation
The aim of the book is maintenance of task setting, mathematical description and computer solving of the investigated problem. There are 79 code examples in the book that explain how to solve theoretical and practical problems in mathematics, mechanics, economics, experimental data treatment, numeric row prediction, automatic control, dynamic modelling and information security. These items are associated by numerical analysis methods and using of programming language Pascal ABC as the main research instrument.
The monograph is destined to broad sections of readers who apply information technologies in mathematics and mathematical methods in different practical activities. They are students of professional middle and high technical schools, educational and economic universities as well as specialists that are not professional programmers but are to use numerical methods and computer modelling in practice. Software package is applied.
Book review
The monograph is intended to persons who wants to master programming languages for their professional activities. Firstly, the book may be useful for students of colleges and high schools technical, pedagogical, economical. It may be interesting also for working specialists that are not professional programmers.
The monograph continues edition of series in Russian devoted to decision of scientific and practical problems by means of numerical methods. These means became necessary part of mathematical provision of modern computers with huge productivity and memory resources. But these opportunities can be realized only under condition that investigator is able to use corresponding methods of modelling complex processes and systems in different spheres of activity.
Obvious dignity of the monograph is multi-discipline, wide scope of actual science problems. It is an excellent manual for many disciplines such as Informatic, Programming technology, Information technology, Mathematical modelling, Econometric, Automatic control, Information security.
The book has 11 chapters. They are heterogeneous as to complexity of problems and decision methods. Some of them demand serious previous mathematical training of readers. It is explainable quite enough universal programming language may be illustrated using diverse tasks only. But it is the reason to appear different mathematical methods of approach from elementary algebra to higher algebra and number theory. For instance, digit filters and decision of modern differential equations are based on z-transform theory. However, this subject is still out of education programs in many high schools in Russia.
These theoretical materials may be interested to aspirants who study profoundly control methods in economic, engineering, information security. In spite of these restrictions, the complex theoretical materials are expedient in the book and do no prevent from studying by less trained readers. They can omit the theoretical computations and use concluding formulae. The last are enough sufficient to develop own programming codes.
The author suggests multiple examples of codes in Pascal ABC, but in the same time calls the reader to seek new decision variants and optimize his codes.
The book examples and illustrations are worked out in details. They are adjusted in many years of teaching information technologies in professional middle and high schools. All examples are based on own methodical books, scientific publications and inventions of the author.
In conclusion one may affirm that the book Numerical analysis and modelling in Pascal ABC will be interesting both to beginners and more experienced in programming and mathematical analysis.
Reviewer:
V.M. Troyanovsky, candidate of economic sciences,
Federal Research Center Information and Management,
Russian Academy of Sciences.
Moscow, 17.05.2017
CONTENT
8.4. Three basketball throws
EX
INTRODUCTION
Interest for methods of approximate solution of applied problems had arisen long before Christ, but only in 17 th century significant incentives had occurred owing to development of european science, growth of industry, astronomy, navigation. Share of numerical methods in mathematical analysis was arising continuous during the next centuries. No serious scientific research is possible now without above-mentioned methods.
Achievements in numerical analysis are owing to works of notable mathematicians such as I. Newton, P. Fermat, G. Leibniz, L. Euler, G. Lagrange, A. Legendre, S. Poisson, A. Cauchy, K. Gauss, F. Bessel, P. Chebyshev. Nowadays progress in discrete mathematics keeps step with invention of the first electromechanical and then electronical computers in the middle of 20 th century. It should be rendered in that cause oustanding mathematicians C. Shannon, N. Wiener, A. Lyapunov, L. Pontryagin, A. Kholmogorov, A. Vitushkin.
High-capacity computers are available now at the working place of every specilist due to fantastic success in microelectronic technology. That is why educational standards involve using a computer in any professional activity. However new educatoinal problem occured in that field of knowledge. The matter is how to teach student to automated approximate solution of applied problems and in the same time to keep in mind methods of fundamenal mathematics based on the principles of infinitesimal quantity. The situation is complicated by the next circumstances:
- limited duration of learning in educational institutions;
- a lot of programming languages;
- a lot of mathematical applications for personal computer.
The education standard for information technologies in secondary school (at least in Russian Federation) provides being able to use basics even if one of high-level programming languages - Visual Basic, Visual Basic for Applications, Pascal, Visual C++.
History of the language Pascal is very notable. It was developed by Niklaus Wirth in 1970 for educational need. The aim has been achieved completely. Pascal turned out the best language for beginners as well for professional programmers for a period of 30 years. Several successive basic versions were issued then - Turbo, Extended, Object. Nowaday these are not more at the market of software products, but a great number of enthusiastics are making attempts to promote succesfull educational language. Compilators Free Pascal, Pascal Lazarus and Pascal ABC have been developed as a result.
Pascal ABC is destined to beginners but the compilator is also in fact the excellent instrument for solving the very complicated professional problems. One ought only to study vast potential possibilities of Pascal ABC and to set worthy practical problems.
Some manuals concerning basics of Pascal ABC for secondary school in Russia can be found in World Wide Web [1], but there is acute dificiency of practical textbooks for professional trainig. Three categories of potential Pascal users can be seen distinctly:
