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.
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