| Individual course details | ||||
| Study programme | Undergraduate Studies in Physics | |||
| Chosen research area (module) | Theoretical and Experimental Physics, Meteorology | |||
| Nature and level of studies | Undergraduate Studies | |||
| Name of the course | Mathematics 4B | |||
| Professor (lectures) | Miroslav Pavlović, Đorđe Krtinić | |||
| Professor/associate (examples/practical) | ||||
| 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, Fourier and Laplace transformations. Elementary introduction to the infinite - dimensional Hilbert spaces. | |||
| Learning outcomes | Ability to use Fourier and Laplace transform, variational calculus and complex analysis at the level necessary for undergraduate studies of physics and meteorology. | |||
| Contents of the course | ||||
| Lectures | 1.
Variational calculus 2. Improper integrals and integrals with parameters. 3. Introduction to complex analysis (Cauchy-Riemann equations, analytic functions, complex integration, Cauchy Theorem, Cauchy's Integral Formula, Taylor and Laurent series, residue, application to evaluation of the real integral). 4. Some special functions: Gamma and Beta function, Bessel and orthogonal polynomials. 5. Fourier integral, Laplace transform, application to differential equations. 6. Elementary introduction to the infinite - dimensional Hilbert spaces. |
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| Examples/ practical classes | Computing practice, elaboration of concepts treated in lectures, solving problems and examples. | |||
| Recommended books | ||||
| 1 | M. Krasnov, A. Kiselev, G. Makarenko I E. Shikin ” Mathematical Analysis for Engineers”, volume I-II, Mir Publishers Moscow 1990. | |||
| 2 | Mary L. Boas, ''Mathematical Methods in Physical Sciences'', Wiley , 2006, texbook with problems. | |||
| 3 | Conway J.B., “Functions of one complex variable”, Springer, 1978. | |||
| 4 | ||||
| 5 | ||||
| Number of classes (weekly) | ||||
| Lectures | Examples&practicals | Student project | Additional | |
| 4 | 4 | |||
| Teaching and learning methods | Lectures, Discussions, Written assignments, Calculation exercises (solving problems, homework), Tests. | |||
| Assessment (maximal 100) | ||||
| assesed coursework | mark | examination | mark | |
| coursework | 5 | written examination | 20 | |
| practicals | 15 | oral examination | 40 | |
| papers | 20 | |||
| presentations | ||||