Faculty: Mechanics and Mathematics
Assoc. Prof. Dr. Veselin Kantchev - firstname.lastname@example.org
Contact hours: 75h, 30h lectures, 45h seminars
Self-study hours: 0h,
Assessment: written examination
Year, semester, weekly workload: Year 1, semester 2, lectures 2.0h, seminars 3.0h
ECTS - 6
Main topics: Functional series and sequences – convergence and uniform convergence. Power series. Abel’s theorem. Expanding a function to a power series. Trigonometric series. Fourier series. Conditions of Dirichlet for the expansion of a function in a Fourier series. Functions of n variables – limits, continuity, partial derivatives and differentials. Direction derivative. Gradient. Taylor’s formula. Extremums and conditional extremums. Implicit functions. Vector function of a scalar argument. Curves in the plane and in the space. Curvature and torsion. Vector function of two scalar arguments. Surfaces. Double and 3-fold integrals – definition, properties, calculation, change of variables, geometrical and mechanical applications. Contour line integrals of first and second kind – formula of Green-Gauss, conditions for independence from the integration path, applications. Surface integrals of first and second kind – formulas of Stokes and Gauss-Ostrogradski. Elements of the field theory.