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 | ||||