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Computational Methods
Major: Computer Sciences (Computational Intelligence of Smart Systems)
Code of subject: 6.122.11.O.021
Credits: 5.00
Department: Automated Control Systems
Lecturer: Ph.D., Associate Professor, Seneta Mariana Yaroslavivna
Semester: 3 семестр
Mode of study: денна
Завдання: The study of an academic discipline involves the formation of the following necessary competencies in students:
integral competence:
• 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 learn and master modern knowledge;
professional competences of the specialty:
- ability to use modern methods of mathematical modeling of objects, processes and phenomena, to develop models and algorithms for the numerical solution of mathematical modeling problems, to take into account the errors of the approximate numerical solution of professional problems
- 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: Knowledges
Use the methods of numerical differentiation and integration of functions, solution of ordinary differential and integral equations, features of numerical methods and possibilities of their adaptation to engineering problems, have skills in software implementation of numerical methods.
Communication
1) Implementation of social communications in the process of communication with specialists and non-specialists in the field of computer science, ensuring the exchange of logical arguments in order to achieve mutual understanding and agreement.
2) The ability to communicate, emotional stability, endurance, tact, defending one's point of view, clearly expressing one's opinion.
Autonomy and responsibility
1) Responsibility for the assigned case, independence in decision-making regarding solving problems in the field of computer science.
2) Organizing work to achieve results, performing mental and practical actions, techniques and operations, realizing responsibility for the results of one's activities, applying self-control and self-evaluation.
Responsibility for the accuracy and correctness of statements in state and foreign languages.
Required prior and related subjects: Prerequisites: mathematical analysis; algebra and geometry
Requirements: operations research; system analysis; probability theory and mathematical statistics
Summary of the subject: The educational discipline "Numerical methods" covers the main methods of numerical analysis, such as: numerical solution of nonlinear equations, systems of linear equations, eigenvalue problems; finding solutions with a given accuracy; integration; approximation etc. The study of these methods for stability and convergence is considered. The complex problem of optimization of numerical methods is formulated, in particular, obtaining such methods that meet the requirements of high accuracy, stability and economy. The importance of the combination of numerical methods and computer technologies in processing the results of calculations is substantiated, which makes it possible to obtain an operationally effective result - a numerical experiment - for assessing the reliability of the obtained results.
Опис: Mathematical modeling.
Taking into account the errors of approximate calculations.
Direct methods of solving systems of linear algebraic equations.
Iterative methods of solving linear algebraic systems. Matrix rotation.
Solving nonlinear equations and systems.
Interpolation.
Approximation.
Numerical integration.
Numerical methods for solving the Cauchy problem for ordinary differential equations.
Numerical methods of solving partial differential equations.
Assessment methods and criteria: 1. Studying the theoretical material of the discipline.
2. Performance of laboratory works and their protection.
3. Execution of calculation and graphic work and its protection.
4. Examination control, which consists of written and oral components.
Критерії оцінювання результатів навчання: Current control - 45 points.
Examination control - 55 points.
Порядок та критерії виставляння балів та оцінок: 100-88 points - certified with an “excellent” grade - High level: the student demonstrates an in-depth mastery of the conceptual and categorical apparatus of the discipline, systematic knowledge, skills and abilities of their practical application. The mastered knowledge, skills and abilities provide the ability to independently formulate goals and organize learning activities, search and find solutions in non-standard, atypical educational and professional situations. The applicant demonstrates the ability to make generalizations based on critical analysis of factual material, ideas, theories and concepts, to formulate conclusions based on them. His/her activity is based on interest and motivation for self-development, continuous professional development, independent research activities, implemented with the support and guidance of the teacher. 87-71 points - certified with a grade of “good” - Sufficient level: involves mastery of the conceptual and categorical apparatus of the discipline at an advanced level, conscious use of knowledge, skills and abilities to reveal the essence of the issue. Possession of a partially structured set of knowledge provides the ability to apply it in familiar educational and professional situations. Aware of the specifics of tasks and learning situations, the student demonstrates the ability to search for and choose their solution according to the given sample, to argue for the use of a particular method of solving the problem. Their activities are based on interest and motivation for self-development and continuous professional development. 70-50 points - certified with a grade of “satisfactory” - Satisfactory level: outlines the mastery of the conceptual and categorical apparatus of the discipline at the average level, partial awareness of educational and professional tasks, problems and situations, knowledge of ways to solve typical problems and tasks. The applicant demonstrates an average level of skills and abilities to apply knowledge in practice, and solving problems requires assistance, support from a model. The basis of learning activities is situational and heuristic, dominated by motives of duty, unconscious use of opportunities for self-development. 49-00 points - certified with a grade of “unsatisfactory” - Unsatisfactory level: indicates an elementary mastery of the conceptual and categorical apparatus of the discipline, a general understanding of the content of the educational material, partial use of knowledge, skills and abilities. The basis of learning activities is situational and pragmatic interest.
Recommended books: - MIT OpenCourseWare [Електронний ресурс] Режим доступу: https://ocw.mit.edu/courses/mathematics/18-330-introduction-to-numerical-analysis-spring-2012/lecture-notes/
- Numerical Methods for Engineers [Електронний ресурс] Режим доступу: https://www.coursera.org/learn/numerical-methods-engineers
Уніфікований додаток: Lviv Polytechnic National University ensures the realization of the right of persons with disabilities to obtain higher education. Inclusive educational services are provided by the Service of accessibility to learning opportunities "Without restrictions", the purpose of which is to provide permanent individual support for the educational process of students with disabilities and chronic diseases. An important tool for the implementation of the inclusive educational policy at the University is the Program for improving the qualifications of scientific and pedagogical workers and educational and support staff in the field of social inclusion and inclusive education. Contact at: St. Karpinsky, 2/4, 1st floor, room 112
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