Infopaket

Fundamentals of vector and tensor analysis

ОК 28.

Обов’язкова дисципліна для ОП

First

2023/2024

3 Semester

3

Learning outcomes are the knowledge of orthogonal transformations of rectangular Cartesian coordinate systems, of the definition of the vector and tensor and ways to set them, of the operation on vectors and tensors in rectangular Cartesian, oblique and curvilinear coordinate systems. Students must be fluent in the operations of covariant differentiation of vector and tensor fields, vector differential operations in rectangular Cartesian and curvilinear coordinate systems. Also, students must be able to apply the acquired theoretical knowledge in this discipline in their professional activities in solving practical problems of physics and astronomy or in the process of further study.

Full-time form

Know the basic laws of mechanics, electricity, basics of mathematical analysis and differential equations. In particular, to know the theorems of Ostrogradsky-Gauss and Stokes, to have free knowledge of the course of analytical geometry and linear algebra. Know the representation of the gradient, divergence, rotor and Laplace operator in a rectangular Cartesian coordinate system and be able to apply them. Be able to apply the knowledge gained from the courses in mathematical analysis, analytical geometry and linear algebra. Have basic skills in calculating derivatives, integrals, operations with vectors, be able to build graphs of functions and decompose functions into a Taylor series.

The normative discipline "Fundamentals of Vector and Tensor Analysis" is a mandatory component of the cycle of professional training of specialists of educational and qualification level "Bachelor of Physics" and basic for the study of all physical disciplines. The course is designed to deepen knowledge and improve mastery of modern methods of vector and tensor calculus, theoretical principles and the basics of using these methods in mathematical applications in solving physical problems, promoting the development of logical and analytical thinking of students.

3. Ledney MF, Razumova MA, Romanenko OV, Khotyaintsev VM, Collection of problems in vector and tensor analysis, K., University of Kiev, 2011. - 119 p. 10. Senkiv MT Vector and tensor analysis: text of lectures. - Lviv: Lviv Publishing Department. un-tu. 1991. 146 p.

Lectures - 14 hours, practical classes - 30 hours, independent work - 45 hours, consultations - 1 hour.

The control is carried out according to the module-rating system, which consists of 2 content modules. The knowledge assessment system includes current, modular and semester control of knowledge. The results of students' learning activities are evaluated on a 100-point scale. Forms of current control: assessment of homework, written independent assignments, tests and tests performed by students during practical classes. The student can receive a maximum of 20 points for homework, independent assignments, oral answers, tests, additions to practical classes (10 points in each content module). Modular control includes 2 modular control works. The student can receive a maximum of 20 points for modular tests (10 points for each modular test). The final semester control is conducted in the form of a test in the third semester (60 points). The test task includes 1 theoretical question and 7 practical tasks.

Ukrainian