Numerical Methods

Major: Computer Science (Design and programming of intelligent systems and devices)
Code of subject: 6.122.12.O.021
Credits: 5.00
Department: Computer-Aided Design
Lecturer: Pavlo Denysyuk
Semester: 3 семестр
Mode of study: денна
Мета вивчення дисципліни: The purpose of studying the discipline "Numerical methods" is for students to acquire the knowledge, skills and abilities necessary for complex analysis, forecasting, design and decision-making in complex systems
Завдання: The study of an academic discipline involves the formation of the following necessary competencies in students: integral competence: • the ability to solve complex specialized tasks and practical problems in the field of computer science or in the learning process, which involves the application of theories and methods of information technologies and is characterized by the complexity and uncertainty of conditions; general competencies: • Ability to abstract thinking, analysis, and synthesis; • Ability to apply knowledge in practical situations; Professional competences of the specialty : • The ability to carry out a formalized description of operations research tasks in organizational-technical and socio-economic systems of various purposes, to determine their optimal solutions, to build optimal management models taking into account changes in the economic situation, to optimize management processes in systems of various purposes and hierarchy levels.
Learning outcomes: As a result of the completion of the module the student should: • apply knowledge of numerical methods to mathematical modeling; • choose algorithms and develop programs for solving problems in a specific subject area.
Required prior and related subjects: • Algorithmic and programming; Mathematical analysis. • Mathematical modeling in CAD
Summary of the subject: Elementary theory of calculations errors. Methods of interpolation and extrapolation. Methods of approximation. Approximate calculation of the indicated integrals. Approximate differentiation of functions. Methods for the solution of systems of linear algebraic equations. Directions of increasing the efficiency of algorithms for solving systems of linear algebraic equations. Iterative algorithms for the solution of systems of linear algebraic equations. Approximate methods for the solution of transcendental equations. Methods of integration of ordinary differential equations.
Опис: The educational course "Numerical methods" covers the main methods of numerical analysis, such as numerical solutions of nonlinear equations, systems of linear equations, eigenvalue problems; finding solutions with a given accuracy; integration; approximation, etc.
Assessment methods and criteria: 1. Studying the theoretical material of the discipline. 2. Performing laboratory works and their protection. 3. Performing calculation and graphic work (control work) and its protection. 4. Credit control, which consists of a written component and an oral component.
Критерії оцінювання результатів навчання: • Current control (30%); written reports on laboratory work, oral examination, control work • Final control (70%): written, oral examination
Recommended books: Вступ до числових методів: Навч. посіб. для вищ. закл. освіти / П. І. Каленюк, В. А. Бакалець, І. І. Бакалець, Н. В. Горбачова, П. Л. Сохан; Держ. ун-т «Львів. політехніка». — Л., 2000. — 145 c. — (Математика для інженерів) Чисельні методи: Підруч. для студ. вищ. навч. закл. / Г. Г. Цегелик; Львів. нац. ун-т ім. І.Франка. — Л., 2004. — 407 c. G.R. Lindfield, J.E.T. Penny, Numerical Methods: using MATLAB (Third Edition), Academic Press, 2012, ISBN 9780123869425, 534 p. Андруник В.А., Висоцька В.А., Пасічник В.В., Чирун Л.Б., Чирун Л.В. Чисельні методи в комп‘ютерних науках: навчальний посібник – Львів:Видавництво «Новий світ – 2000», 2020. – 470 с.