Fundamentals of Vector and Tensor Analysis

Major: Applied Physics and Nanomaterials
Code of subject: 6.105.00.O.015
Credits: 4.00
Department: Applied Physics and Nanomaterials Science
Lecturer: Dr. Science Professor. Lukiyanets Bohdan
Semester: 3 семестр
Mode of study: денна
Learning outcomes: the student must learn the basic concepts and provisions of the tensor analysis and differential geometry; be able to use them in practice
Required prior and related subjects: Linear Algebra and Analytic Geometry Calculuss Electricity and Magnetism Solid State Physics
Summary of the subject: Linear space. Linear transformation of the vector space and tensors of the second order. Reduction of linear transformation matrix. to a simpler form General theory of the second-order surfaces. Application of tensor analysis to some problems of mechanics and physics (Momentum of inertia tensor. Some properties of crystals associated with tensors of the second order.Tensors of stress and strain). Basics of tensor analysis (Tensor field and its differentiation. Curvilinear coordinate system. Differentiation of tensor field in curvilinear coordinates).
Assessment methods and criteria: oral examination during the workshops, evaluation of home practical tasks, control work (30%); final control (70%, exam), written-oral form (70%)
Recommended books: 1.Akivis M.A, V.V.Goldberg. Tensor analysis. - M .: Nauka, 1969 (in Rus,) 2. О.Val, S.Korolyuk, S.Melnychuk. Basics of vector and tensor analysis. - Chernivtsi. Knyga XXI. - 228 p. (in Ukr) 3. Pozniak at al. Differential Geometry: Introduction. - MGU, 1990. - 312 p. .(in Rus,)