| Individual course details | ||||||||||
| Study programme | General Physics, Applied and Computational Physics | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Undergraduate studies | |||||||||
| Name of the course | Mathematics 2 | |||||||||
| Professor (lectures) | Dr Branka Pavlović | |||||||||
| Professor/associate (examples/practical) | ||||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | Status (required/elective) | |||||||||
| Access requirements | None | |||||||||
| Aims of the course | Introduction to linear algebra, analytic geometry, and multivariate calculus. Ability to solve systems of linear equations and to do calculations with matrices. Mastering of differential and integral calculus which is neccessary in physics applications. | |||||||||
| Learning outcomes | Understanding basic notions in linear algebra, analytic and differential geometry. Basic level of operative knowledge of multivariate calculus, solving systems of linear equations and working with matrices. | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Linear algebra: notion of a matrix and a determinant; transposition, rank and
inverse of a matrix; systems of linear equations; Cramer and
Kronecker-Capelli theorems. (10 lectures) 2. Analytic geometry: straight line and flat surface and various forms of their equations; second order curves and their canonic forms. (10 lectures) 3. Functions with multiple variables: notion of a metric space (completness, compactness and connectedness); limit, continuity, partial derivatives, differentiability and basic theorems concerning these; gradient; Taylor's formula; extreme values; implicit and inverse function theorems. 4. Differential geometry: curve and its natural trihedron, first and second curvature; surfaces; gradient, divergence, curl. (8 lectures). 5. Integrals: in two variables, in three variables, on curves and sufaces (definitions, calculations, examples); formulae of Green, Stokes, and Gauss-Ostrogradsky. (16 lectures) |
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| Examples/ practical classes | Teaching assistant sessions: elaboration of the material presented at the lectures; problem solving and examples encountered in physics. | |||||||||
| Recommended books | ||||||||||
| 1 | D. Adnadjević, Z. Kadelburg, Matematička analiza 2, 6. ed., Matematički fakultet, Krug, Beograd 2011. | |||||||||
| 2 | V. Jevremović, Matematika 1 - predavanja, Univerzitet u Beogradu, Gradjevinski fakultet, Beograd, 2001. | |||||||||
| 3 | ||||||||||
| 4 | ||||||||||
| 5 | ||||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 4 | 4 | |||||||||
| Lectures
(presentation of theory and working out of the main examples), Teaching assistant sessions (problem solving), midterm examinations. |
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| Assessment (maximal 100) | ||||||||||
| assesed coursework | mark | examination | mark | |||||||
| coursework | written examination | 60 | ||||||||
| practicals | oral examination | 40 | ||||||||
| papers | ||||||||||
| presentations | ||||||||||