Numerical Methods

Major: Applied Physics and Nanomaterials
Code of subject: 6.105.00.O.053
Credits: 5.00
Department: Mathematics
Lecturer: Chaban A. V.
Semester: 4 семестр
Mode of study: денна
Learning outcomes: 1. Knowledge of the basic languages ??of programming numerical methods for solving problems of research and technological nature. 2. Knowledge of methods, software, computer design, modeling and calculation of physical properties and technological processes in the production, processing and modification of materials. 3. Work on modern computer technology and use specialized software to design, model and calculate the basic physical properties of the studied objects and technological modes.
Required prior and related subjects: Higher mathematics, physics, mechanics, basics of computer science and programming part 1 and part 2, basics of engineering and computer graphics, electricity and magnetism.
Summary of the subject: The academic discipline consists of the following sections: "Numerical solutions of algebraic and transcendental equations and their systems", "Numerical differentiation and integration", "Numerical integration of nonlinear differential equations with partial derivatives and their systems", "Numerical integration of nonlinear differential equations with partial derivatives». In the section "Numerical solutions of algebraic and transcendental equations and their systems" the following main topics are considered: "Elements of theories of approximations and errors", "Methods of solving nonlinear algebraic equations", "Methods of solving systems of linear and nonlinear algebraic equations" , "Optimization of functions" "Approximation of functions". The section "Numerical differentiation and integration" consists of the following main topics: "Numerical differentiation of functions", "Numerical integration of functions". In the section "Numerical integration of ordinary nonlinear differential equations and their systems" the following main topics are considered: "General principles of integration of ordinary differential equations", "Non-rigid and rigid differential equations and their systems". In the section "Numerical integration of nonlinear differential equations with partial derivatives" the following main topics are considered: "Theory of numerical solution of boundary and mixed problems", "Differential methods for solving stationary and nonstationary differential equations of mathematical physics", "Variational methods of numerical integration and mixed problems of applied physics ".
Assessment methods and criteria: Assessment of students' knowledge is carried out with the help of oral and written surveys in practical classes, as well as tests and independent work, terminological dictations, individual calculation and graphic works. Current control - 50 points; Examination Control - 50 points; Total for discipline - 100 points.
Recommended books: 1. Рудавський Ю.К, Понеділок Г.В.. та ін. Математичний аналіз. – .Львів. В-во НУ “ЛП”,2003. 2. Рудавський Ю.К. та ін. Теорія рядів. – Львів.: В-во НУ “ЛП”, 2001 3. Рудавський Ю.К. та ін. Збірник задач з математичного аналізу. Частини 1, 2. Львів.: В-во НУ “ЛП”, 2001 4. Бахвалов Н.С., Житков Н.П., Кобельков Г.М. Численные методы. –М.: Наука, 1987. 5. Гаврилюк І.П., Макаров В.Л. Методи обчислень. –К.: Вища школа, 1995, ч.1, ч.2. 6. Калиткин Н.Н. Численныеметоды. –М.: Наука, 1978. 7. Каленюк П.І., Бакалець В.А. та ін. Вступ до числових методів. –Львів, 2000.