Fluid mechanics is complex scientific discipline. The goal of the subject is to learn mathematical methods which is necessary in study of specific areas of fluid mechanics.

The results from this topic will be gained knowledge from specific areas in mathematics, which are import for studies in fluid mechanics.

Tensors. Tensor algebra and tensor calculus. Partial differential equations (PDE). Classification of PDEs. Elliptic, hyperbolic and parabolic PDEs. Methods for solving partial differential equations. Methods of characteristics. Numerical methods in fluid mechanics. Finite difference and finite volume method. Finite elements method. Spectral methods. Fourier analysis. Fourier series. Fourier transform. Discrete Fourier transform. Complex functions. Complex analysis. Potential flows. Analytical complex functions. Singularities. Random variables. Methods of mathematical statistics. Probability and probability density functions. Correlations and moments.

In this part of the course, specific problems will be solved. Useful mathematical methods will be explained in that process.

Passed obligatory exams from Mathematics Department.

Course handouts.

Total assigned hours: 65

New material: 30
Elaboration and examples (recapitulation): 20

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 10
Test: 0
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50

The Fourier Transform and its Applications, Brad Osgood, Stanford University; Perturbation methods in fluid mechanics, Milton Van Dyke, THE PARABOLIC PRESS, Sranford, California, 1975., ISBN: 0-915760--01-0; Fractional Differential Equations (An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Meth. of the Sol.), Igor Podlubny, Academic Press, San Diego-Boston-New York, 1999; Function of a Complex Variable, Theory and Technique, Carrier, G.F., M.Krook and C.E. Pearson, Mc Graw-Hill, 1966. New York