Ability of abstract thinking and acquiring basic knowledge in the field of mathematical analysis.(array theory, integral functions of several variables, complex analysis, Fourrier and Laplace transforms)Ability of abstract thinking and acquiring basic knowledge in the field of mathematical analysis.(array theory, integral functions of several variables, complex analysis, Fourrier and Laplace transforms)

Student is competent to design and solve mathematical models in the field of mathematical analysis (array theory, integral functions of several variables, complex analysis, Fourrier and Laplace transforms) in further education and professional courses.

Number series, definitions and basic characteristics. Function sequences and series, power series. Double and curvilinear integral. Complex analysis-basic terms related to complex function of a complex variable, integral, Cauchy’s theorem and formula, Laurent series, singularities, residue, analytic continuation, conformal mapping. Fourrier series and transform. Laplace and inverse Laplace transform with applications.

Lectures; Numerical computing practice. Consultations. Lectures are combined. In lectures, theoretical part of the course is followed by typical examples for better understanding. In practice, which accompanies lectures, typical problems are solved and knowledge from the lectures is deepened. Besides lectures and practice, consultations are held on a regular basis. Part of the course, presenting a logical whole, can be passed during the teaching process in the form of the following 4 modules (the first module: Series, the second module: integral function of several variables, the third module: complex analysis, the fourth module: Fourrier and Laplace transforms). The oral part of the examination is not obligatory.