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Advanced Mathematics 1 semester

ОК 08

Обов’язкова дисципліна для ОП

First

2022/2023

1 Semester

9

The student must know:differential and integral calculus; basic information about the Fourier series and Fourier transform; basic methods of integration of ordinary differential equations; vector algebra and analytic geometry; basic concepts of linear algebra; basic information about the systems of linear algebraic equations.

Full-time form

To learn the “Higher Mathematics” subject the student must have a thorough knowledge of those chapters of mathematics, which are included in the compulsory program of the Ukrainian secondary schools.

The “Higher Mathematics” subject involves the basic chapters of mathematical analysis, linear algebra and analytic geometry. The course is adapted to the needs of educational trends that are certificated for the faculty of radiophysics electronics and computer systems in the National Taras Shevchenko University of Kyiv. The basic chapters of the mathematical analysis are presented with the emphasis on their interrelation with linear algebra (especially the sections “Fourier series”, “ Fourier transform”, “Line integrals and surface integrals”, “Basis of the field theory”). The linear algebra is presented with the emphasis on its applicability to the linear space formed by the continuous functions: the inner product of the functions and the differential operators in the space of functions are considered. Due to this, the linear algebra is interrelated with mathematical analysis. Especial attention is paid to the study of matrices and their determinants.

1. Радченко О. М. Математичний аналіз. Ч. 1. Функції однієї змінної. Київ : вид-во «ТВіМС», 2003. 2. Радченко О. М. Математичний аналіз. Ч. 2. Функції декількох змінних. Київ : «КНУ імені Тараса Шевченка», 2003. 3. Заболоцький В. М., Сторож О. Г., Тарасюк С. І. Математичний аналіз. Київ : «Знання», 2008. 4. Кривошея С. А., Перестюк М. О., Бурим В. М. Диференціальні та інтегральні рівняння. Київ : «Либідь», 2004. 5. Придатченко Ю. В. Львов В. А. Алгебра для фізиків: метод координат у лінійній алгебрі. Київ : ВПЦ «Київський університет», 2004. 6. Придатченко Ю. В., Львов В. А., Єфіменко С. В. Векторна алгебра та аналітична геометрія. Київ : ВПЦ «Київський університет», 2010. 7. Придатченко Ю. В., Вільчинський С. Й. Лінійна алгебра для фізиків. Київ : ВПЦ «Київський університет», 2010.

Lectures, problem solutions, unsupervised work.

- Semester assessment. After each of two semantic modules the written test is carried out, the result of each test is scored from 0 to 30 points. -Final assessment. After each of two semesters the written examination is carried out; the permit to examination is given if the subtotal result of two tests is no less then 30 points; еру examination test consists of 2 tasks, the performance of each task is scored from 0 to 20 points. The result of learning of the subject is considered positive if the total score for semantic modules and exam exceeds 60 points, the score for exam must be higher than 20 points.

Ukrainian