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Numerical methods of approximation

ОК 19

Обов’язкова дисципліна для ОП

First

2021/2022

3 Semester

3

Learning outcomes involve the study of basic numerical methods and their characteristics: methods of approximation, differentiation and integration of functions, solving equations and systems of equations, solving ordinary differential equations and partial differential equations. Acquisition of practical skills of their application. Mastering the basic methods and rules of analysis of experimental results, working with the most common specialized mathematical packages, the basics of structuring large volumes of data.

Full-time form

The student must have basic knowledge of higher mathematics and practical skills in programming.

Approximation and interpolation of functions. Principles of approximation of deriva-tives. Principles of construction of formulas of numerical integration. Runge's princi-ple of approximate determination of the error of the numerical method. Methods for solving linear and nonlinear equations: bisection methods, chords, tangents, iteration method. Iterative methods for solving systems of equations. Basic methods for solving the Cauchy problem and the boundary value problem for ordinary differential equations. Differential schemes for equations of parabolic, elliptical and hyperbolic types with partial derivatives. Basic methods of data processing in physics. Estimation of measurement error. Least squares method. An overview of modern means of automating numerical and sym-bolic calculations and data processing - computer algebra systems, software packages for statistical data processing and data visualization. Fundamentals of Data Science. Structuring data using cluster analysis.

1. Гаврилюк І.П., Макаров В.Л. Методи обчислювань: Підруч. для студ. вузів, які навч. за спец. "Прикладна математика". – К. : Вища школа, 1995. — Ч. 1 . - 368 с. 2. Довгий Б.П., Ловейкін А.В., Вакал Є.С., Вакал Ю.Є. Сплайн-функції та їх застосування. – К.: Видавничо-поліграфічний центр "Київський університет", 2017. – 122 с 3. Лященко М.Я., Головань М.С. Чисельні методи. — К.: Либідь, 2016. – 356с. 4. Фельдман Л.П., Петренко А.І., Дмитрієва О.А. Чисельні методи в інформатиці. – К.: Видавнича група BHV, 2006. – 480 c. 5. Цегелик Г.Г. Чисельні методи. – Л: Видавничий центр ЛНУ ім. Івана Франка, 2004. – 408с.

Lectures, computational work, self-dependent work of students

The grade for studying the course consists of grades for computational work (up to 80 points) and final modular tests (up to 20 points).

Ukrainian