| Individual course details | ||||||||||
| Study programme | Computer and Applied Physics | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Undergraduate Studies | |||||||||
| Name of the course | Mathematics III A | |||||||||
| Professor (lectures) | prof. Vladimir Grujić, doc. dr Đorđe Krtinić | |||||||||
| Professor/associate (examples/practical) | Milan Lazarević, Petar Melentijević | |||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 10 | Status (required/elective) | required | |||||||
| Access requirements | Mathematics I A, Mathematics II A | |||||||||
| Aims of the course | Introduction to basic concepts of series, with special emphasis on Fourier series, which are very important in physics. Understanding and using of Fourier and Laplace transformation. Methods of solving different types of ordinary differential equations and systems that occur in physics or electronics, as well as partial differential equations of second order. | |||||||||
| Learning outcomes | Ability to use series and solve differential equations which occur in undergraduate physics and electronics studies. Basic level of operability in calculating Laplace and Fourier transforms of functions significant for physics. | |||||||||
| 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, systems, linear partial equations of the first order. Solving of equations using series expansion. Examples. 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. 3. Fourier integral, Laplas transform, applications to differential equations. |
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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 | Ј. Кнежевић-Миљановић, С. Јанковић, Ј. Манојловић, В. Јовановић: Парцијалне диференцијалне једначине, Универзитетска штампа, Београд 2000. | |||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 4 | 5 | |||||||||
| 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 | ||||||||||