| Individual course details | ||||||||||
| Study programme | Theoretical and experimental physics, Meteorology | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Undergraduate Studies | |||||||||
| Name of the course | Mathematics 4B | |||||||||
| Professor (lectures) | prof. Vladimir Grujić, doc. dr Đorđe Krtinić | |||||||||
| Professor/associate (examples/practical) | Milan Lazarević, Petar Melentijević | |||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 9 | Status (required/elective) | required | |||||||
| Access requirements | Mathematics 1B | |||||||||
| Aims of the course | Introduction to basic concepts of variational calculus and complex analysis, special functions of significance in physics, Fourier and Laplace transformation. Elementary introduction to infinite-dimensional spaces. | |||||||||
| Learning outcomes | Ability to use Fourier and Laplace transformation, variation calculus and complex analysis at the level necessary for undergraduate physics and meteorology studies basic studies of physics and meteorology. | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Elements of variational calculus with examples from physics. 2. Improper integral, criteria and examples. 3. Complex analysis: Cauchy-Riemann conditions, holomorphic and conformal functions, overview of elementary functions, complex integral, Cauchy theorem, Cauchy integral formula, Taylor and Laurent series, the residue (application to the calculation of integrals). 4. Some special functions: gamma, beta, Bessel and orthogonal polynomials. 5. Fourier integral, Laplas transform, applications on differential equations. 6. Elementary introduction to infinite-dimensional spaces: example l_2. |
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| Examples/ practical classes | Computational exercises: elaboration of concepts intorduced in lectures, solving problems and examples, especially examples important for physics. | |||||||||
| 1 | M. Krasnov, A. Kiselev, G. Makarenko I E. Shikin ” Mathematical Analysis for Engineers”, volume I-II, Mir Publishers Moscow 1990, textbook with selected problems. | |||||||||
| 2 | Mary L. Boas, ''Mathematical Methods in Physical Sciences'', Wiley , 2006, textbook with selected problems. | |||||||||
| 3 | Conway J.B., “Functions of one complex variable”, Springer, 1978. | |||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 4 | 4 | |||||||||
| Teaching and learning methods | Lectures
(theoretical representation of thematic units and examples), computational exercises (solving problems, homework), colloquiums. |
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| Assessment (maximal 100) | ||||||||||
| assesed coursework | mark | examination | mark | |||||||
| coursework | 5 | written examination | 20 | |||||||
| practicals | 15 | oral examination | 40 | |||||||
| papers | 20 | |||||||||
| presentations | ||||||||||