Methods of computational mathematics

Course: Applied Mathematics

Structural unit: Faculty of Computer Science and Cybernetics

Title
Methods of computational mathematics
Code
ДВС.3.06.04.02
Module type
Вибіркова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2023/2024
Semester/trimester when the component is delivered
8 Semester
Number of ECTS credits allocated
3
Learning outcomes
LO 1.1 Know the main problems of computational mathematics and approaches to their solution, in particular from the optimal control section LO 1.2 Know the theoretical and practical approaches to the study of optimal control problems for systems with distributed parameters LO 2.1 Be able to find out the issues of solvability for optimal control problems LO 2.2 Be able to implement and research algorithms for computational mathematics problems LO 3.1 Argue one's own choice of approaches to solving a problem, communicate with colleagues on issues of design and program development LO 4.1 Organize your independent work to achieve results LO 4.2 Be responsible for the work performed, bear responsibility for their quality
Form of study
Full-time form
Prerequisites and co-requisites
1. Know: Mathematical analysis, functional analysis, theory of differential equations, theory of optimal control, algebra and numerical methods in the scope of relevant university courses. 2. Be able to: create programs in at least one programming language, read and analyze mathematical texts, implement mathematical algorithms. Read literature in English. 3. Have skills: working with a computer, searching for information on the Internet, using translation tools, creating presentations.
Course content
Classical sections of optimization problems. Convex optimization. Optimization problems for systems with distributed parameters. Management options. Theoretical research is the problem of the existence and uniqueness of the solution. General construction approaches and classes of numerical methods for solving optimization problems for systems with distributed parameters. Classical methods of the gradient type for optimization problems and their implementation. Theoretical and practical study of the properties and behavior of numerical methods of the gradient type. Problems with the convergence of methods, ways to solve them.
Recommended or required reading and other learning resources/tools
1. Liashko S.І., Semenov V.V., Kliushin D.A. Spetsіal-nі pitannia optimіzatsії. Kiїv, VPТs “Kiїvs-kii unіversitet”, 2015 2. Vasil-ev F.P. Metody resheniia ekstremal-nykh zadach. – M.: Nauka, 1981. 3. Lyashko S. I. Generalized optimal control of linear systems with distributed parameters. Boston / Dordrecht / London: Kluwer Academic Publishers, 2002. 466 p. 4. Sea Zh. Optimizatsiia. Teoriia i algoritmy. – M.: Mir, 1973. 5. Iosida K. Funktsional-nyi analiz. – M.: Mir, 1967. 6. Nesterov Iu.E. Vvedenie v vypukluiu optimimzatsiiu. – M.: MТsNMO, 2010.
Planned learning activities and teaching methods
Lectures, laboratory, independent work
Assessment methods and criteria
Student evaluation forms: - semester assessment: 1. Modular control work - 25 points/15 points 2. Laboratory work 1 – 25 points/15 points 2. Laboratory work 2 – 25 points/15 points 3. Laboratory work 3 – 25 points/15 points - final assessment - credit. Credit is issued based on the results of work in the semester. A student receives a credit if, according to the results of work in the semester, he scored 60 or more points, while successfully writing a modular control paper and at least two laboratory works.
Language of instruction
Ukrainian

Lecturers

This discipline is taught by the following teachers

Departments

The following departments are involved in teaching the above discipline