Home/ Majors directory/Applied Physics and Nanomaterials/Mathematical Analysis, part 1
Mathematical Analysis, part 1
Major: Applied Physics and Nanomaterials
Code of subject: 6.105.00.O.006
Credits: 5.00
Department: Mathematics
Lecturer: Tymoshenko N.M.
Semester: 1 семестр
Mode of study: денна
Завдання: The study of an educational discipline involves the formation of competencies in students of education:
• general competencies:
1) the ability to learn;
2) ability to think analytically;
3) ability to apply knowledge in practical situations;
4) ability to make informed decisions;
• professional competences:
1) basic knowledge of scientific concepts, theories and methods necessary for understanding the principles
operation of environmentally safe technologies;
2) the ability to argue the choice of methods for solving specialized problems is critical
evaluate the obtained results and justify the decisions made;
3) the ability to apply professional knowledge and practical skills to solve typical problems of the specialty and justify the choice of methods for solving them, critically evaluate the obtained results and defend the decisions made.
Learning outcomes: As a result of the study of the discipline, the student must be able to demonstrate the following learning outcomes:
• calculate the limit of a function and a numerical sequence;
• investigate the continuity of functions;
• find derivative functions of one variable and to investigate the functions on the extremum;
• find indefinite integrals; calculate and use definite integrals;
• apply the integral calculus to physical and geometric tasks, in particular to find the area and volume of the figures, the length of the arcs, calculate the static moments, the center of gravity of the flat regions.
Required prior and related subjects: General Mathematics: Algebra and Geometry;
Mechanics;
Linear algebra and analytic geometry.
Summary of the subject: The academic discipline "Mathematical analysis, part 1" is a component of the educational and professional program training of specialists at the first level of higher education "bachelor" in the specialty "Applied physics and nanomaterials". This discipline is mandatory, the task of which is to master the mathematical language and fundamental concepts of certain sections of mathematics.
Опис: The academic discipline "Mathematical analysis, part 1" consists of the following sections "Limits. Continuity of functions. Differential calculus'', ''Integral calculus of one real variable". The first section deals with the following topics: (a) Theory of sets. Set of real numbers. (b) Numerical sequences. Limits of a sequence and limits of a function. (c) Continuity of the function. Discontinuities. (d) Computation of derivatives and full investigation of functions. The second section consists of the topics: (a) Indefinite integral (b) Riemann integral. Improper integral.
Assessment methods and criteria: Student knowledge testing is carried out by means of oral questioning in practical classes, control and independent work in the virtual of learning environment, the terminologicals of dictations, individual calculation and graphic works.
Критерії оцінювання результатів навчання: Current control - 30 points;
Examination Control - 70 points;
Total for discipline - 100 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: 1. Математичний аналіз функцій однієї дійсної змінної / Х. Т. Дрогомирецька, П.І. Каленюк, М.І. Клапчук, Г.В. Понеділок – Львів : Вид-во НУ«ЛП», 2016. – 589 с.
2. Дороговцев А.Я. Математичний аналіз, ч.1,2. 1993. 1994.
3. Шкіль В.П. Курс математичного аналізу. – Київ: Наукова думка, 1995.
4. Фихтенгольц Г.М. Курс дифференциального и интегрального исчисления, т.1,2,3, 1966.
5. Кудрявцев Л. Д. Курс математического анализа, т.1-3. 1988.
6. Демидович В.П. Сборник задач и упражнений по математическому анализу, 1990.
7. Збірник задач з математичного аналізу. За ред. Рудавського Ю. К. 2001.
8. Давидов Н.С. Курс математичного аналізу, т.1,2. 1990.
9. Ляшко І.І., Ємельянов В.Ф., Боярчук О.К. Математичний аналіз, ч.1,2. 1992. 1993.
10. Рудин У. Основы математического анализа. 1996.
11. Задачи и упражнения по математическому анализу для втузов /Под ред. Б. П. Демидовича . – М.: Наука, 1986.
12. Ильин В.А., Позняк Э.Г. Основы математического анализа, ч.1,2. 1973.
13. Берман Т.М. Сборник задач по курсу математического анализа. 1985.
Інформаційні ресурси:
Електронний навчально-методичний комплекс «Математичний аналіз, ч.1» Сертифікат № 00250.
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