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Mathematical analysis

ОК 5

Обов’язкова дисципліна для ОП

First

2023/2024

1 Semester

14

- Understand the application of methods and techniques of analysis, design and research, as well as the limitations of their use - Know and be able to apply modern information technology to solve problems in metrology and information-measuring technology - Be able to apply basic mathematical knowledge used in physics, optics and laser physics: analytical geometry, linear algebra, mathematical analysis, differential and integral equations, probability theory and mathematical statistics, methods of mathematical physics, theory of functions of complex variables, mathematical modeling.

Elementary mathematics (algebra, geometry)

Real numbers. Number sequences. Limit and continuity of functions of one variable. Differential and integral calculus of functions of one variable. Improper integrals. Distance and metric space. Norm and normed vector space. Scalar (inner) product and Euclidean space. Differential and integral calculus of functions of multiple variables. Curve and surface integrals. Elements of mathematical field theory. Family of functions. Number and function series. Power series. Integrals with parameters. Trigonometric Fourier series. Fourier integral and transform. Fourier series in Euclidean space.

1. Ляшко І. І., Ємельянов В. Ф., Боярчук О. К. Математичний аналіз, ч. 1 . – К.: Вища школа, 1992. – 495 c. 2. Ляшко І. І., Ємельянов В. Ф., Боярчук О. К. Математичний аналіз, ч. 2 . – К.: Вища школа, 1993. – 375 с. 3. Дороговцев А. Я. Математичний аналіз, ч. 1. – К.: Либідь, 1993. – 320 с. 4. Дороговцев А. Я. Математичний аналіз, ч. 2. – К.: Либідь, 1994. – 302 с. 5.Кривошея С. А., Майко Н. В., Моторна О. В., Прощенко Т. М. Математичний аналіз. Завдання для самостійної роботи студентів. Частина 1: Навчально-методичний посібник. – К: ВПЦ "Київський університет", 2013. – 324 с. (Гриф МОН України, лист 1/11-4092 від 24.03.2014).

1st semester: lectures – 42 hrs, practical lessons – 60 hrs, independent work – 107 hrs, consultations – 1 hr, total – 210 hrs. 2nd semester: lectures – 30 hrs, practiacal lessons – 60 hrs, independent work – 90 hrs, total – 180 hrs. 3rd semester: lectures – 14 hrs, practical lessons – 28 hrs, independent work – 47 hrs, consultations – 1 hr., total – 90 hrs.

Knowledge and skills evaluation: 100-point scale. Current control (60 points): individual assignments, writing tests, colloquiums. Final control at the end of each semester (40 points): writing tests.

Ukrainian