Infopaket

Higher mathematics

Обов’язкова дисципліна для ОП

First

2025/2026

4 Semester

4

PR02. Use modern information technologies, software and Internet resources for information support of professional activity. PR06. Apply models, methods and data of physics, chemistry, ecology, mathematics in the process of learning and ensuring professional activity. PR07. Have the techniques of self-education and self-improvement. Be able to design the trajectory of professional growth and personal development, applying the acquired knowledge. PR20. Argue the choice of methods, algorithms for planning and conducting field, laboratory, clinical and laboratory research, including mathematical methods and software for research, processing and presentation of results.

External form

1. Possession of elementary skills and knowledge of mathematical disciplines that are studied in general education institutions for solving specific practical problems. 2. Ability to independently work with scientific and methodological literature in the field of mathematics.

The academic discipline "Higher Mathematics" is a mandatory educational component. The program of the discipline considers the fundamental concepts of analytical geometry and linear algebra (Vector. Cartesian coordinate system. Scalar and vector products. Equations of a line and a plane. Lines and surfaces of the second order. Systems of algebraic equations. Matrices, determinant and their properties), mathematical analysis (Function of one variable. Limit of a function. Continuity of a function. Derivative of a function. Its geometric and physical meaning. Differential of a function. Rules of differentiation. L'Hopital's rule. Derivatives of higher orders. Taylor's formula. Study of functions at the extremum. Asymptotes of graphs of functions. Function of many variables. Partial derivatives. Extremum of functions of two variables (least squares method). Indefinite integral. Basic methods of integrating functions. Definite integral (Newton-Leibniz formula). Improper integral of the first kind. Fourier series) and the theory of ordinary differential equations (Linear and nonlinear first-order differential equations. Cauchy problem. Linear and nonlinear second-order differential equations with constant coefficients. Complex numbers (Euler's formula)), which are subsequently necessary for the use of general mathematical methods and approaches when studying disciplines in the "Biology" educational program.

1. Yu.I. Prylutsky, S.O. Kosterin. Fundamentals of Higher Mathematics for Biologists. – Kyiv: Publishing and Printing Center "Kyiv University", 2024. – 143 p. 2. Kushnirenko S.V. Methodical development of the course "Fundamentals of Higher Mathematics" for students of the National Scientific Center "Institute of Biology and Medicine" – Kyiv, 2019. – 257 p. http://www.mechmat.univ.kiev.ua/wpcontent/uploads/2019/10/metod_kushnireno.pdf 3. Zheleznyak G., Lytvyn I., Kononchuk O. Higher Mathematics. – Kyiv, Center for Educational Literature, 2019. – 368 p. 4. Yu.I. Prylutsky, O.V. Ilchenko, O.V. Tsymbalyuk, S.O. Kosterin. Statistical Methods in Biology. – Kyiv: Naukova Dumka, 2017. – 211 p.

Lectures, practical classes, independent work

Semester assessment 1. Modular test 1, remotely (RN 1.1–1.2; 2.1–2.2; 4.1.) – 25 points/12 points. 2. Modular test 2 (RN 1.3–1.6; 2.1 –2.2; 4.1.) – 25 points/12 points. 3. Oral answers and other forms of control at lectures (tests) (RN 1.1. – 4.1.) – 10 points/5 points. 4. Oral answers at practical classes (RN 1.1.– 4.1.) – 20 points/10 points. 5. Solving (calculated) individual tasks (RN 1.1.– 4.1.) – 20 points/10 points. Final assessment – ​​in the form of a credit

Ukrainian