| Individual course details | ||||||||||
| Study programme | Metereology, Applied and Computational physics | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Undergraduate | |||||||||
| Name of the course | Basic mathematical physics | |||||||||
| Professor (lectures) | doc. dr Sasa Dmitrovic | |||||||||
| Professor/associate (examples/practical) | doc. dr Sasa Dmitrovic | |||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 5 | Status (required/elective) | required | |||||||
| Access requi | Мathematics 1 (or 1B), Мathematics 2 (or 2B) | |||||||||
| Aims of the course | Adopting the concepts of finite-dimensional vector spaces and mastering linear algebra and vector analysis necessary for undergraduate physics studies. | |||||||||
| Learning outcomes | Applicable knowledge about vector and unit (euclidean) spaces, linear mappings, and spectral theory of normal operators used in physics. Acquired basic knowledge from vector analysis and the properties of vector and scalar fields in physics. |
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| Contents of the course | ||||||||||
| Lectures | 1. Definition of the vector space; dimension and base. Examples of vector spaces important for physics. 2. Vector space isomorphism. 3. Scalar product. Unitary and euclidean space.Examples in physics. 4. Bessel's and Schwarz's inequality. 5. Gram-Schmitt's orthonormalization process. 6. Linear operators and their geometry. Examples of operators in physics. 7. Operators in inner product spaces. Adjoint operator, normal operators. 8. Hermitian operators. Projectors. Unitarian and orthogonal operators. 9. An eigenproblem problem (geometry, eigenvector and eigenvalue). Operator spectrum and eigenspaces. 10. Eigen-projectors and spectral form. 11. Spectral characterization of normal operators. Spectral theorem in Euclidean space. 12. Scalar, vector fields. Gradient, divergence, curl,directional derivative. Hamilton's operator. 13. Special types of vector fields. Curvilinear coordinates. Hamilton and Laplace's operator in the orthogonal curvilinear system. Cylindrical and spherical coordinates. |
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| Examples/ practical classes | Examples: elaboration of terms used in lectures, solving problems and examples of the essentials for physics | |||||||||
| Recommended books | ||||||||||
| 1 | T. Vukovic, S. Dmitrovic: Osnovi matematicke fizike, Univerzitet u Beogradu, Fizicki Fakulete (2017). | |||||||||
| 2 | И. Милошевић , «Векторски простори и елементи векторске анализе», Београд, Физички факултет (1997), рецензиран уџбеник. | |||||||||
| 3 | M. Vujičić, Linear Algebra (thoroughly explained), Springer, Berlin, 2007. | |||||||||
| 4 | ||||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples& | Student project | Additional | |||||||
| 4 | 4 | |||||||||
| Teaching and learning methods | Lectures, examples | |||||||||
| Assessment (maximal 100) | ||||||||||
| assesed coursework | examination | mark | ||||||||
| coursework | 5 | written examination | 40 | |||||||
| practicals | 5 | oral examination | 30 | |||||||
| papers | 20 | |||||||||
| presentations | ||||||||||