| 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 3B | |||||||||
| 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 series, with special emphasis on Fourier series, which are very important in physics, as well as methods of solving differential equations with emphasis on equations of second order. | |||||||||
| Learning outcomes | Ability to use series and solve differential equations which occur in undergraduate physics and meteorology studies. | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Series: general Cauchy convergence criterion, criteria from comparative to
Gauss, integral, Leibniz, Abel and Dirichlet criterion, absolute convergence,
uniform convergence and criteria for uniform convergence (Cauchy,
Weierstrass, Abel and Dirihlet), properties of the sum of uniform convergent
series, Cauchy-Hadamard formula, decomposition of the function in power
series with examples, Fourier series,
Dirichlet theorem. 2. Differential equations: Picard theorem, linear equation of n-th order, method of variation of constants, boundary problems (Green's function), systems, linear partial equations of the first order. Solving of equations using series expansion. Partial differential equations of the second order which occur in physics: Schrödinger, Poisson, Laplace, wave equation. Solving of those equations using the method of separating variables. |
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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 | Ляшко И.И., Боярчук А.К., Гай Я.,Г., Головач Г.П. “Математический анализ в примерах и задачах 2”, problem book. | |||||||||
| 4 | Svetlana Janković, Julka Kne˛ević-Miljanović „Diferencijalne jednačine, zadaci sa elementima teorije“, Математички факултет 2007. | |||||||||
| 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 | ||||||||||